IA Scholar Query: Bipartite density of cubic graphs.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 21 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Four Amazing Positivities with Dimers/i-Matchings
https://scholar.archive.org/work/hjspcdft2vgozcrkrfdobxylim
We collect a number of striking recent results in a study of dimers on infinite regular bipartite lattices and also on regular bipartite graphs. We clearly separate rigorously proven results from conjectures. A primary goal is to show people: here is a field which is ripe for further interesting research. We separate four classes of endeavor, of which we here extract two items to whet one's appetite. Primo,If r < 11, for hyper-rectangular lattices of every dimension the first 20 virial coefficients are positive. (One has no understanding of this yet!) Secondo, all regular bipartite graphs with less than 14 vertices satisfy graph positivity, defined below. (Here there is some understanding.)Paul Federbushwork_hjspcdft2vgozcrkrfdobxylimWed, 21 Sep 2022 00:00:00 GMTLong-range data transmission in a fault-tolerant quantum bus architecture
https://scholar.archive.org/work/rwxljckglfbyhkwqlkrkkyckue
We propose a scheme for fault-tolerant long-range entanglement generation at the ends of a rectangular array of qubits of length R and a square cross section of size d× d with d=O(log R). Up to an efficiently computable Pauli correction, the scheme generates a maximally entangled state of two qubits using a depth-6 circuit consisting of nearest-neighbor Clifford gates and local measurements only. Compared with existing fault-tolerance schemes for quantum communication, the protocol is distinguished by its low latency: starting from a product state, the entangled state is prepared in a time O(t_local) determined only by the local gate and measurement operation time t_local. Furthermore, the requirements on local repeater stations are minimal: Each repeater uses only Θ(log^2 R) qubits with a lifetime of order O(t_local). We prove a converse bound Ω(log R) on the number of qubits per repeater among all low-latency schemes for fault-tolerant quantum communication over distance R. Furthermore, all operations within a repeater are local when the qubits are arranged in a square lattice. The noise-resilience of our scheme relies on the fault-tolerance properties of the underlying cluster state. We give a full error analysis, establishing a fault-tolerance threshold against general (circuit-level) local stochastic noise affecting preparation, entangling operations and measurements. This includes, in particular, errors correlated in time and space. Our conservative analytical estimates are surprisingly optimistic, suggesting that the scheme is suited for long-range entanglement generation both in and between near-term quantum computing devices.Shin Ho Choe, Robert Koenigwork_rwxljckglfbyhkwqlkrkkyckueTue, 20 Sep 2022 00:00:00 GMTCharacteristic Power Series of Graph Limits
https://scholar.archive.org/work/pkeicnoqnfcuhk5oihxqi23s7q
In this note, we show how to obtain a "characteristic power series" of graphons -- infinite limits of dense graphs -- as the limit of normalized reciprocal characteristic polynomials. This leads to a new characterization of graph quasi-randomness and another perspective on spectral theory for graphons, a complete description of the function in terms of the spectrum of the graphon as a self-adjoint kernel operator. Interestingly, while we apply a standard regularization to classical determinants, it is unclear how necessary this is.Joshua N. Cooperwork_pkeicnoqnfcuhk5oihxqi23s7qMon, 19 Sep 2022 00:00:00 GMTLocality and error correction in quantum dynamics with measurement
https://scholar.archive.org/work/el2kgcz2qvhjjkiihua3w4olxa
The speed of light c sets a strict upper bound on the speed of information transfer in both classical and quantum systems. In nonrelativistic systems, the Lieb-Robinson Theorem imposes an emergent speed limit v ≪ c, establishing locality under unitary quantum dynamics and constraining the time needed to perform useful quantum tasks. We extend the Lieb-Robinson Theorem to quantum dynamics with measurements. In contrast to the general expectation that measurements can arbitrarily violate spatial locality, we find at most an (M + 1)-fold enhancement to the speed of quantum information v, provided the outcomes of M local measurements are known; this holds even when classical communication is instantaneous. Our bound is asymptotically optimal, and saturated by existing measurement-based protocols. We tightly constrain the resource requirements for quantum computation, error correction, teleportation, and generating entangled resource states (Bell, GHZ, W, and spin-squeezed states) from short-range entangled states. Our results impose limits on the use of measurements and active feedback to speed up quantum information processing, resolve fundamental questions about the nature of measurements in quantum dynamics, and constrain the scalability of a wide range of proposed quantum technologies.Aaron J. Friedman, Chao Yin, Yifan Hong, Andrew Lucaswork_el2kgcz2qvhjjkiihua3w4olxaFri, 16 Sep 2022 00:00:00 GMTSketching Distances in Monotone Graph Classes
https://scholar.archive.org/work/uzbbwq4hprbzjjvli5lqvpnwtm
We study the problems of adjacency sketching, small-distance sketching, and approximate distance threshold (ADT) sketching for monotone classes of graphs. The algorithmic problem is to assign random sketches to the vertices of any graph G in the class, so that adjacency, exact distance thresholds, or approximate distance thresholds of two vertices u,v can be decided (with probability at least 2/3) from the sketches of u and v, by a decoder that does not know the graph. The goal is to determine when sketches of constant size exist. Our main results are that, for monotone classes of graphs: constant-size adjacency sketches exist if and only if the class has bounded arboricity; constant-size small-distance sketches exist if and only if the class has bounded expansion; constant-size ADT sketches imply that the class has bounded expansion; any class of constant expansion (i.e. any proper minor closed class) has a constant-size ADT sketch; and a class may have arbitrarily small expansion without admitting a constant-size ADT sketch.Louis Esperet, Nathaniel Harms, Andrey Kupavskii, Amit Chakrabarti, Chaitanya Swamywork_uzbbwq4hprbzjjvli5lqvpnwtmThu, 15 Sep 2022 00:00:00 GMTSmall Transformers Compute Universal Metric Embeddings
https://scholar.archive.org/work/x4pqf4thszadvn667xhnsqe75u
We study representations of data from an arbitrary metric space 𝒳 in the space of univariate Gaussian mixtures with a transport metric (Delon and Desolneux 2020). We derive embedding guarantees for feature maps implemented by small neural networks called probabilistic transformers. Our guarantees are of memorization type: we prove that a probabilistic transformer of depth about nlog(n) and width about n^2 can bi-Hölder embed any n-point dataset from 𝒳 with low metric distortion, thus avoiding the curse of dimensionality. We further derive probabilistic bi-Lipschitz guarantees which trade off the amount of distortion and the probability that a randomly chosen pair of points embeds with that distortion. If 𝒳's geometry is sufficiently regular, we obtain stronger, bi-Lipschitz guarantees for all points in the dataset. As applications we derive neural embedding guarantees for datasets from Riemannian manifolds, metric trees, and certain types of combinatorial graphs.Anastasis Kratsios, Valentin Debarnot, Ivan Dokmanićwork_x4pqf4thszadvn667xhnsqe75uWed, 14 Sep 2022 00:00:00 GMTCollective Monte Carlo updates through tensor network renormalization
https://scholar.archive.org/work/elt7rzu4fzb4dprkehzgjhe2zm
We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present benchmarks for a wide variety of instances of the two-dimensional Ising model, including ferromagnetic, antiferromagnetic, (fully) frustrated and Edwards-Anderson spin glass cases, and we show that, with modest computational effort, our Markov chain achieves sizeable acceptance rates, even in the vicinity of critical points. In each of the situations we have considered, the Markov chain compares well with other Monte Carlo schemes such as the Metropolis or Wolff algorithm: equilibration times appear to be reduced by a factor that varies between 40 and 2000, depending on the model and the observable being monitored. We also present an extension to three spatial dimensions, and demonstrate that it exhibits fast equilibration for finite ferro and antiferromagnetic instances. Additionally, and although it is originally designed for a square lattice of finite degrees of freedom with open boundary conditions, the proposed scheme can be used as such, or with slight modifications, to study triangular lattices, systems with continuous degrees of freedom, matrix models, a confined gas of hard spheres, or to deal with arbitrary boundary conditions.Miguel Frías-Pérez, Michael Mariën, David Pérez García, Mari Carmen Bañuls, Sofyan Iblisdirwork_elt7rzu4fzb4dprkehzgjhe2zmWed, 14 Sep 2022 00:00:00 GMTFolding Molecular Dynamics Simulations of the Transmembrane Peptides of Influenza A, B M2, and MERS-, SARS-CoV E Viral Proteins
https://scholar.archive.org/work/uwrvrxdzqvcmdivb5uwfkhoqg4
Viroporins are small viral proteins that oligomerize in the membrane of host cells and induce the formation of hydrophilic pores in these membranes, thus altering the physiological properties of the host cells. Due to their significance for viral pathogenicity, they have become targets for pharmaceutical intervention, especially through compounds that block their pore-forming activity. Here we add to the growing literature concerning the structure and function of viroporins by studying and comparing – through molecular dynamics simulations – the folding of the transmembrane domain peptides of viroporins derived from four viruses : influenza A, influenza B, and the coronaviruses MERS-Cov-2 and SARS-CoV-2. Through a total of more than 50 μs of simulation time in explicit solvent (TFE) and with full electrostatics, we characterize the folding behavior, helical stability and helical propensity of these transmembrane peptides in their monomeric state and we identify common motifs that may reflect their quaternary organization and/or biological function. We show that the two influenza-derived peptides are significantly different in peptide sequence and secondary structure from the two coronavirus-derived peptides, and that they are organized in two structurally distinct parts : a significantly more stable N-terminal half, and a fast converting C-terminal half that continuously folds and unfolds between α-helical structures and non-canonical structures which are mostly turns. In contrast, the two coronavirus-derived transmembrane peptides are much more stable and fast helix formers when compared with the influenza ones. We discuss possible interpretations of these findings and their putative connection to the structural characteristics of the respective viroporins.Antonios Kolocouris, Isaiah Arkin, Nicholas M. Glykoswork_uwrvrxdzqvcmdivb5uwfkhoqg4Mon, 12 Sep 2022 00:00:00 GMTNon-planarity of Markoff graphs mod p
https://scholar.archive.org/work/3omn2zpofbcnborc5iude73i5i
We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x^2+y^2+z^2=xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these graphs. Non-planarity for large primes would follow assuming a spectral gap, which was the original motivation. For primes congruent to 1 modulo 4, or congruent to 1, 2, or 4 modulo 7, explicit constructions give an alternate proof of non-planarity.Matthew de Courcy-Irelandwork_3omn2zpofbcnborc5iude73i5iMon, 12 Sep 2022 00:00:00 GMTAdvances in honeycomb layered oxides: Part I – Syntheses and Characterisations of Pnictogen- and Chalcogen-Based Honeycomb Layered Oxides
https://scholar.archive.org/work/rhomrsoyujgbpfsxummz6kbhqm
Advancements in nanotechnology continue to unearth material vistas that presage a new age of revolutionary functionalities replete with unparalleled physical properties and avant-garde chemical capabilities that promise sweeping paradigm shifts in energy, environment, telecommunications and potentially healthcare. At the upper echelons of this realm, the pnictogen and chalcogen class of honeycomb layered oxides have emerged with fascinating crystal chemistry and exotic electromagnetic and topological phenomena that muster multifaceted concepts spanning from materials science to condensed matter physics and potential applications in electrochemistry, quantum mechanics and electronics. In a bid to shed light on the mechanisms governing these biomimetic nanostructures, this review highlights the significant milestones and breakthroughs that have augmented their current knowledgebase of theory, properties and utilities. Herein, we elucidate the vast promising crystal chemistry space against the backdrop of known synthesis and characterisation techniques employed in the development and optimisation of this class of materials. Further, we highlight key theoretical models that have reinvigorated the exploration and characterisation of honeycomb layered oxides within this class and are poised to redefine the frontiers of material research and their applications. We conclude by envisaging future research directions where fascinating physicochemical, topological and electromagnetic properties could be lurking and where valiant efforts ought to be inclined, particularly in the prospective realisation of exotic material compositional space as well as their utility as testing grounds for emergent two-dimensional (2D) topological quantum gravity and conformal field theories.Godwill Mbiti Kanyolo, Titus Masese, Abbas Alshehabi, Zhen-Dong Huangwork_rhomrsoyujgbpfsxummz6kbhqmSun, 11 Sep 2022 00:00:00 GMTA Predictive Chance Constraint Rebalancing Approach to Mobility-on-Demand Services
https://scholar.archive.org/work/gje3j6xy4jfi5d4aqpapmxqd2a
This paper considers the problem of supply-demand imbalances in Autonomous Mobility-on-Demand systems (AMoD) where demand uncertainty compromises both the service provider's and the customer objectives. The key idea is to include estimated stochastic travel demand patterns into receding horizon AMoD optimization problems. More precisely, we first estimate passenger demand using Gaussian Process Regression (GPR). GPR provides demand uncertainty bounds for time pattern prediction. Second, we integrate demand predictions with uncertainty bounds into a receding horizon AMoD optimization. In order to guarantee constraint satisfaction in the above optimization under estimated stochastic demand prediction, we employ a probabilistic constraining method with user defined confidence interval. Receding horizon AMoD optimization with probabilistic constraints thereby calls for Chance Constrained Model Predictive Control (CCMPC). The benefit of the proposed method is twofold. First, travel demand uncertainty prediction from data can naturally be embedded into AMoD optimization. Second, CCMPC can further be relaxed into a Mixed-Integer-Linear-Program (MILP) that can efficiently be solved. We show, through high-fidelity transportation simulation, that by tuning the confidence bound on the chance constraint close to "optimal" oracle performance can be achieved. The median wait time is reduced by 4% compared to using only the mean prediction of the GP.Sten Elling Tingstad Jacobsen, Balázs Kulcsár, Anders Lindmanwork_gje3j6xy4jfi5d4aqpapmxqd2aWed, 07 Sep 2022 00:00:00 GMTUnderstanding the Behavior of Belief Propagation
https://scholar.archive.org/work/hcvsy4klsnaatckaysmgy5yk6m
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference; because of the high-dimensional nature, however, one must often use approximate methods for this purpose. Belief propagation performs approximate inference, is efficient, and looks back on a long success-story. Yet, in most cases, belief propagation lacks any performance and convergence guarantees. Many realistic problems are presented by graphical models with loops, however, in which case belief propagation is neither guaranteed to provide accurate estimates nor that it converges at all. This thesis investigates how the model parameters influence the performance of belief propagation. We are particularly interested in their influence on (i) the number of fixed points, (ii) the convergence properties, and (iii) the approximation quality.Christian Knollwork_hcvsy4klsnaatckaysmgy5yk6mMon, 05 Sep 2022 00:00:00 GMTRegular grid subgraphs of maximal girth
https://scholar.archive.org/work/flfmwwtqlve55c22x5dahri36q
The unit-distance graph on the n-dimensional integer lattice ℤ^n is called the n-dimensional grid. We attempt to maximize the girth of a k-regular (possibly induced) subgraph of the n-dimensional grid, and provide examples and bounds for selected values of n and k, along with more general results. A few cases involving alternative lattices are also considered.Jan Kristian Hauglandwork_flfmwwtqlve55c22x5dahri36qSun, 04 Sep 2022 00:00:00 GMTThe Neural Process Family: Survey, Applications and Perspectives
https://scholar.archive.org/work/lpfyllkwovcqvjcz354tq4pnv4
The standard approaches to neural network implementation yield powerful function approximation capabilities but are limited in their abilities to learn meta representations and reason probabilistic uncertainties in their predictions. Gaussian processes, on the other hand, adopt the Bayesian learning scheme to estimate such uncertainties but are constrained by their efficiency and approximation capacity. The Neural Processes Family (NPF) intends to offer the best of both worlds by leveraging neural networks for meta-learning predictive uncertainties. Such potential has brought substantial research activity to the family in recent years. Therefore, a comprehensive survey of NPF models is needed to organize and relate their motivation, methodology, and experiments. This paper intends to address this gap while digging deeper into the formulation, research themes, and applications concerning the family members. We shed light on their potential to bring several recent advances in other deep learning domains under one umbrella. We then provide a rigorous taxonomy of the family and empirically demonstrate their capabilities for modeling data generating functions operating on 1-d, 2-d, and 3-d input domains. We conclude by discussing our perspectives on the promising directions that can fuel the research advances in the field. Code for our experiments will be made available at https://github.com/srvCodes/neural-processes-survey.Saurav Jha, Dong Gong, Xuesong Wang, Richard E. Turner, Lina Yaowork_lpfyllkwovcqvjcz354tq4pnv4Thu, 01 Sep 2022 00:00:00 GMTA heuristic algorithm for the maximum happy vertices problem using tree decompositions
https://scholar.archive.org/work/uvo7gri46fdztnplmurxdlf564
We propose a new heuristic algorithm for the Maximum Happy Vertices problem, using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this procedure by integrating a parameter W that dictates the number of dynamic programming states to consider. We drop the exactness guarantee in favour of a shorter running time. However, if W is large enough such that all valid states are considered, our heuristic algorithm proves optimality of the constructed solution. Our algorithm more efficiently constructs an optimal solution for the Maximum Happy Vertices problem than the exact algorithm for graphs of bounded treewidth. Furthermore, our algorithm constructs higher quality solutions than state-of-the-art heuristic algorithms Greedy-MHV and Growth-MHV for instances of which at least 40 are initially coloured, at the cost of a larger running time.Louis Carpentier, Jorik Jooken, Jan Goedgebeurwork_uvo7gri46fdztnplmurxdlf564Wed, 31 Aug 2022 00:00:00 GMTOn the power of message passing for learning on graph-structured data
https://scholar.archive.org/work/ukhmzqtoeje4jcx4mopmkzd4ha
This thesis proposes novel approaches for machine learning on irregularly structured input data such as graphs, point clouds and manifolds. Specifically, we are breaking up with the regularity restriction of conventional deep learning techniques, and propose solutions in designing, implementing and scaling up deep end-to-end representation learning on graph-structured data, known as Graph Neural Networks (GNNs). GNNs capture local graph structure and feature information by following a neural message passing scheme, in which node representations are recursively updated in a trainable and purely local fashion. In this thesis, we demonstrate the generality of message passing through a unified framework suitable for a wide range of operators and learning tasks. Specifically, we analyze the limitations and inherent weaknesses of GNNs and propose efficient solutions to overcome them, both theoretically and in practice, e.g., by conditioning messages via continuous B-spline kernels, by utilizing hierarchical message passing, or by leveraging positional encodings. In addition, we ensure that our proposed methods scale naturally to large input domains. In particular, we propose novel methods to fully eliminate the exponentially increasing dependency of nodes over layers inherent to message passing GNNs. Lastly, we introduce PyTorch Geometric, a deep learning library for implementing and working with graph-based neural network building blocks, built upon PyTorch.Matthias Fey, Technische Universität Dortmundwork_ukhmzqtoeje4jcx4mopmkzd4haWed, 31 Aug 2022 00:00:00 GMTIntegrating silicon carbide spintronics quantum systems
https://scholar.archive.org/work/3l5izaoo6fffjj3ak5wivphnq4
As the second quantum revolution is unfolding, the investigation and development of individual quantum systems best-suited to lead this revolution is thriving. In the surge of new platforms, our work aims to decipher the role that silicon carbide's color centers could play in the near-future. In this dissertation, we demonstrate that ion-assisted implantation and integration in nanophotonic waveguides preserve the silicon vacancy center spin-optical properties. Further, high-fidelity coherent manipulation of integrated nuclear spins via decoupling sequences is shown, which is a critical ressource for mutli-qubit local registers. Our work paves the way towards integration into nanophotonic resonators, overcoming the inherent low light collection efficiency of optically active spins in the solid.Charles Babin, Universität Stuttgartwork_3l5izaoo6fffjj3ak5wivphnq4Mon, 29 Aug 2022 00:00:00 GMTFitting Metrics and Ultrametrics with Minimum Disagreements
https://scholar.archive.org/work/7zgl4rvk5bgspa5cer3izquik4
Given x ∈ (ℝ_≥ 0)^[n]2 recording pairwise distances, the METRIC VIOLATION DISTANCE (MVD) problem asks to compute the ℓ_0 distance between x and the metric cone; i.e., modify the minimum number of entries of x to make it a metric. Due to its large number of applications in various data analysis and optimization tasks, this problem has been actively studied recently. We present an O(log n)-approximation algorithm for MVD, exponentially improving the previous best approximation ratio of O(OPT^1/3) of Fan et al. [ SODA, 2018]. Furthermore, a major strength of our algorithm is its simplicity and running time. We also study the related problem of ULTRAMETRIC VIOLATION DISTANCE (UMVD), where the goal is to compute the ℓ_0 distance to the cone of ultrametrics, and achieve a constant factor approximation algorithm. The UMVD can be regarded as an extension of the problem of fitting ultrametrics studied by Ailon and Charikar [SIAM J. Computing, 2011] and by Cohen-Addad et al. [FOCS, 2021] from ℓ_1 norm to ℓ_0 norm. We show that this problem can be favorably interpreted as an instance of Correlation Clustering with an additional hierarchical structure, which we solve using a new O(1)-approximation algorithm for correlation clustering that has the structural property that it outputs a refinement of the optimum clusters. An algorithm satisfying such a property can be considered of independent interest. We also provide an O(log n loglog n) approximation algorithm for weighted instances. Finally, we investigate the complementary version of these problems where one aims at choosing a maximum number of entries of x forming an (ultra-)metric. In stark contrast with the minimization versions, we prove that these maximization versions are hard to approximate within any constant factor assuming the Unique Games Conjecture.Vincent Cohen-Addad, Chenglin Fan, Euiwoong Lee, Arnaud de Mesmaywork_7zgl4rvk5bgspa5cer3izquik4Mon, 29 Aug 2022 00:00:00 GMTLifted edges as connectivity priors for multicut and disjoint paths
https://scholar.archive.org/work/edizj43isvflhhihrsapdwjlhu
This work studies graph decompositions and their representation by 0/1 labeling of edges. We study two problems. The first is multicut (MC) which represents decompositions of undirected graphs (clustering of nodes into connected components). The second is disjoint paths (DP) in directed acyclic graphs where the clusters correspond to nodedisjoint paths. Unlike an alternative representation by node labeling, the number of clusters is not part of the input but is fully determined by the costs of edges. I would like to thank all my co-authors for a pleasant and constructive cooperation. Besides my supervisor Paul Swoboda, I would like to name especially Roberto Henschel, Timo Kaiser, Bjoern Andres, and Jan-Hendrik Lange for their major contribution to the shared publications that are part of this thesis. The publications could not be realized without their part of the work. I would like to thank Bjoern Andres for his supervision and help during the work on our common paper. I would like to mention also Michal Rolinek who helped us with our latest publication. I would like to thank Jiles Vreeken, Marcel Schulz and Markus List who cooperated with me on a research project that is not part of this thesis. I am very grateful to Bernt Schiele, the director of our department, who provided me with good working conditions, fully supported me in combining my working duties with family, and found a solution in the difficult stage of my PhD study by finding a new supervisor. Also, other people at MPI and Saarland University helped me to organize my work and family life and helped me with administrative issues.Andrea Hornakova, Universität Des Saarlandeswork_edizj43isvflhhihrsapdwjlhuMon, 29 Aug 2022 00:00:00 GMTIntroduction to Quantum Error Correction and Fault Tolerance
https://scholar.archive.org/work/zet4iouwvrdldga5e7jqfcqk74
These lecture notes from the 2019 Les Houches Summer School on 'Quantum Information Machines' are intended to provide an introduction to classical and quantum error correction with bits and qubits, and with continuous variable systems (harmonic oscillators). The focus on the latter will be on practical examples that can be realized today or in the near future with a modular architecture based on superconducting electrical circuits and microwave photons. The goal and vision is 'hardware-efficient' quantum error correction that does not require exponentially large hardware overhead in order to achieve practical and useful levels of fault tolerance and circuit depth.Steven M. Girvinwork_zet4iouwvrdldga5e7jqfcqk74Sun, 28 Aug 2022 00:00:00 GMT