23,138 research outputs found

    Optimal universal quantum circuits for unitary complex conjugation

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    Let UdU_d be a unitary operator representing an arbitrary dd-dimensional unitary quantum operation. This work presents optimal quantum circuits for transforming a number kk of calls of UdU_d into its complex conjugate Udˉ\bar{U_d}. Our circuits admit a parallel implementation and are proven to be optimal for any kk and dd with an average fidelity of ⟨F⟩=k+1d(d−k)\left\langle{F}\right\rangle =\frac{k+1}{d(d-k)}. Optimality is shown for average fidelity, robustness to noise, and other standard figures of merit. This extends previous works which considered the scenario of a single call (k=1k=1) of the operation UdU_d, and the special case of k=d−1k=d-1 calls. We then show that our results encompass optimal transformations from kk calls of UdU_d to f(Ud)f(U_d) for any arbitrary homomorphism ff from the group of dd-dimensional unitary operators to itself, since complex conjugation is the only non-trivial automorphisms on the group of unitary operators. Finally, we apply our optimal complex conjugation implementation to design a probabilistic circuit for reversing arbitrary quantum evolutions.Comment: 19 pages, 5 figures. Improved presentation, typos corrected, and some proofs are now clearer. Closer to the published versio

    CoRe-Sleep: A Multimodal Fusion Framework for Time Series Robust to Imperfect Modalities

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    Sleep abnormalities can have severe health consequences. Automated sleep staging, i.e. labelling the sequence of sleep stages from the patient's physiological recordings, could simplify the diagnostic process. Previous work on automated sleep staging has achieved great results, mainly relying on the EEG signal. However, often multiple sources of information are available beyond EEG. This can be particularly beneficial when the EEG recordings are noisy or even missing completely. In this paper, we propose CoRe-Sleep, a Coordinated Representation multimodal fusion network that is particularly focused on improving the robustness of signal analysis on imperfect data. We demonstrate how appropriately handling multimodal information can be the key to achieving such robustness. CoRe-Sleep tolerates noisy or missing modalities segments, allowing training on incomplete data. Additionally, it shows state-of-the-art performance when testing on both multimodal and unimodal data using a single model on SHHS-1, the largest publicly available study that includes sleep stage labels. The results indicate that training the model on multimodal data does positively influence performance when tested on unimodal data. This work aims at bridging the gap between automated analysis tools and their clinical utility.Comment: 10 pages, 4 figures, 2 tables, journa

    TransFusionOdom: Interpretable Transformer-based LiDAR-Inertial Fusion Odometry Estimation

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    Multi-modal fusion of sensors is a commonly used approach to enhance the performance of odometry estimation, which is also a fundamental module for mobile robots. However, the question of \textit{how to perform fusion among different modalities in a supervised sensor fusion odometry estimation task?} is still one of challenging issues remains. Some simple operations, such as element-wise summation and concatenation, are not capable of assigning adaptive attentional weights to incorporate different modalities efficiently, which make it difficult to achieve competitive odometry results. Recently, the Transformer architecture has shown potential for multi-modal fusion tasks, particularly in the domains of vision with language. In this work, we propose an end-to-end supervised Transformer-based LiDAR-Inertial fusion framework (namely TransFusionOdom) for odometry estimation. The multi-attention fusion module demonstrates different fusion approaches for homogeneous and heterogeneous modalities to address the overfitting problem that can arise from blindly increasing the complexity of the model. Additionally, to interpret the learning process of the Transformer-based multi-modal interactions, a general visualization approach is introduced to illustrate the interactions between modalities. Moreover, exhaustive ablation studies evaluate different multi-modal fusion strategies to verify the performance of the proposed fusion strategy. A synthetic multi-modal dataset is made public to validate the generalization ability of the proposed fusion strategy, which also works for other combinations of different modalities. The quantitative and qualitative odometry evaluations on the KITTI dataset verify the proposed TransFusionOdom could achieve superior performance compared with other related works.Comment: Submitted to IEEE Sensors Journal with some modifications. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

    ENABLING EFFICIENT FLEET COMPOSITION SELECTION THROUGH THE DEVELOPMENT OF A RANK HEURISTIC FOR A BRANCH AND BOUND METHOD

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    In the foreseeable future, autonomous mobile robots (AMRs) will become a key enabler for increasing productivity and flexibility in material handling in warehousing facilities, distribution centers and manufacturing systems. The objective of this research is to develop and validate parametric models of AMRs, develop ranking heuristic using a physics-based algorithm within the framework of the Branch and Bound method, integrate the ranking algorithm into a Fleet Composition Optimization (FCO) tool, and finally conduct simulations under various scenarios to verify the suitability and robustness of the developed tool in a factory equipped with AMRs. Kinematic-based equations are used for computing both energy and time consumption. Multivariate linear regression, a data-driven method, is used for designing the ranking heuristic. The results indicate that the unique physical structures and parameters of each robot are the main factors contributing to differences in energy and time consumption. improvement on reducing computation time was achieved by comparing heuristic-based search and non-heuristic-based search. This research is expected to significantly improve the current nested fleet composition optimization tool by reducing computation time without sacrificing optimality. From a practical perspective, greater efficiency in reducing energy and time costs can be achieved.Ford Motor CompanyNo embargoAcademic Major: Aerospace Engineerin

    Harmonic structure of the nonlinear force on a fixed ship-shaped floating production, storage and offloading vessel under dispersive phase-focused wave groups

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    This paper presents a numerical investigation on the harmonic structure of hydrodynamic forces on a fixed and simplified representative floating production, storage and offloading (FPSO) vessel hull under dispersive phase-focused wave groups. The high-fidelity numerical model utilizes the two-phase flow solver in the open-source toolbox OpenFOAM. A series of cases were computed using the numerical model, where the effects of wave steepness, bow diameter, and length of the FPSO are investigated. It is found that given an FPSO under different wave steepness, the non-dimensional inline force exhibits remarkable similarity in terms of the temporal development. The harmonic structure of the inline force is only weakly dependent on the steepness of the incident wave group and the bow diameter, but strongly dependent on the FPSO length. When [Formula: see text], where L is the length of the FPSO and kp is the wave number at peak frequency, the incident wave group is diffracted significantly by the FPSO. The entire wave–structure interaction process is largely linear, where transfer between different harmonics is rarely seen. However, when kpL is further reduced to 0.57, globally the disturbance of the FPSO on the far field incident wave group is reduced, but locally a strongly nonlinear flow occurs at the rear of the FPSO, where severe run-up occurs at the downstream stagnation point. Higher-order harmonics of inline forces are excited, and the interaction process becomes much more nonlinear

    Advancing Model Pruning via Bi-level Optimization

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    The deployment constraints in practical applications necessitate the pruning of large-scale deep learning models, i.e., promoting their weight sparsity. As illustrated by the Lottery Ticket Hypothesis (LTH), pruning also has the potential of improving their generalization ability. At the core of LTH, iterative magnitude pruning (IMP) is the predominant pruning method to successfully find 'winning tickets'. Yet, the computation cost of IMP grows prohibitively as the targeted pruning ratio increases. To reduce the computation overhead, various efficient 'one-shot' pruning methods have been developed, but these schemes are usually unable to find winning tickets as good as IMP. This raises the question of how to close the gap between pruning accuracy and pruning efficiency? To tackle it, we pursue the algorithmic advancement of model pruning. Specifically, we formulate the pruning problem from a fresh and novel viewpoint, bi-level optimization (BLO). We show that the BLO interpretation provides a technically-grounded optimization base for an efficient implementation of the pruning-retraining learning paradigm used in IMP. We also show that the proposed bi-level optimization-oriented pruning method (termed BiP) is a special class of BLO problems with a bi-linear problem structure. By leveraging such bi-linearity, we theoretically show that BiP can be solved as easily as first-order optimization, thus inheriting the computation efficiency. Through extensive experiments on both structured and unstructured pruning with 5 model architectures and 4 data sets, we demonstrate that BiP can find better winning tickets than IMP in most cases, and is computationally as efficient as the one-shot pruning schemes, demonstrating 2-7 times speedup over IMP for the same level of model accuracy and sparsity.Comment: Thirty-sixth Conference on Neural Information Processing Systems (NeurIPS 2022

    Qluster: An easy-to-implement generic workflow for robust clustering of health data

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    The exploration of heath data by clustering algorithms allows to better describe the populations of interest by seeking the sub-profiles that compose it. This therefore reinforces medical knowledge, whether it is about a disease or a targeted population in real life. Nevertheless, contrary to the so-called conventional biostatistical methods where numerous guidelines exist, the standardization of data science approaches in clinical research remains a little discussed subject. This results in a significant variability in the execution of data science projects, whether in terms of algorithms used, reliability and credibility of the designed approach. Taking the path of parsimonious and judicious choice of both algorithms and implementations at each stage, this article proposes Qluster, a practical workflow for performing clustering tasks. Indeed, this workflow makes a compromise between (1) genericity of applications (e.g. usable on small or big data, on continuous, categorical or mixed variables, on database of high-dimensionality or not), (2) ease of implementation (need for few packages, few algorithms, few parameters, ...), and (3) robustness (e.g. use of proven algorithms and robust packages, evaluation of the stability of clusters, management of noise and multicollinearity). This workflow can be easily automated and/or routinely applied on a wide range of clustering projects. It can be useful both for data scientists with little experience in the field to make data clustering easier and more robust, and for more experienced data scientists who are looking for a straightforward and reliable solution to routinely perform preliminary data mining. A synthesis of the literature on data clustering as well as the scientific rationale supporting the proposed workflow is also provided. Finally, a detailed application of the workflow on a concrete use case is provided, along with a practical discussion for data scientists. An implementation on the Dataiku platform is available upon request to the authors

    Chiral active fluids: Odd viscosity, active turbulence, and directed flows of hydrodynamic microrotors

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    While the number of publications on rotating active matter has rapidly increased in recent years, studies on purely hydrodynamically interacting rotors on the microscale are still rare, especially from the perspective of particle based hydrodynamic simulations. The work presented here targets to fill this gap. By means of high-performance computer simulations, performed in a highly parallelised fashion on graphics processing units, the dynamics of ensembles of up to 70,000 rotating colloids immersed in an explicit mesoscopic solvent consisting out of up to 30 million fluid particles, are investigated. Some of the results presented in this thesis have been worked out in collaboration with experimentalists, such that the theoretical considerations developed in this thesis are supported by experiments, and vice versa. The studied system, modelled in order to resemble the essential physics of the experimentally realisable system, consists out of rotating magnetic colloidal particles, i.e., (micro-)rotors, rotating in sync to an externally applied magnetic field, where the rotors solely interact via hydrodynamic and steric interactions. Overall, the agreement between simulations and experiments is very good, proving that hydrodynamic interactions play a key role in this and related systems. While already an isolated rotating colloid is driven out of equilibrium, only collections of two or more rotors have experimentally shown to be able to convert the rotational energy input into translational dynamics in an orbital rotating fashion. The rotating colloids inject circular flows into the fluid, such that detailed balance is broken, and it is not a priori known whether equilibrium properties of colloids can be extended to isolated rotating colloids. A joint theoretical and experimental analysis of isolated, pairs, and small groups of hydrodynamically interacting rotors is given in chapter 2. While the translational dynamics of isolated rotors effectively resemble the dynamics of non-rotating colloids, the orbital rotation of pairs of rotors can be described with leading order hydrodynamics and a two-dimensional analogy of Faxén’s law is derived. In chapter 3, a homogeneously distributed ensemble of rotors (bulk) as a realisation of a chiral active fluid is studied and it is explicitly shown computationally and experimentally that it carries odd viscosity. The mutual orbital translation of rotors and an increase of the effective solvent viscosity with rotor density lead to a non-monotonous behaviour of the average translational velocity. Meanwhile, the rotor suspension bears a finite osmotic compressibility resulting from the long-ranged nature of hydrody- namic interactions such that rotational and odd stresses are transmitted through the solvent also at small and intermediate rotor densities. Consequently, density inhomogeneities predicted for chiral active fluids with odd viscosity can be found and allow for an explicit measurement of odd viscosity in simulations and experiments. At intermediate densities, the collective dynamics shows the emergence of multi-scale vortices and chaotic motion which is identified as active turbulence with a self-similar power-law decay in the energy spectrum, showing that the injected energy on the rotor scale is transported to larger scales, similar to the inverse energy cascade of clas- sical two-dimensional turbulence. While either odd viscosity or active turbulence have been reported in chiral active matter previously, the system studied here shows that the emergence of both simultaneously is possible resulting from the osmotic compressibility and hydrodynamic mediation of odd and active stresses. The collective dynamics of colloids rotating out of phase, i.e., where a constant torque instead of a constant angular velocity is applied, is shown to be qualitatively very similar. However, at smaller densities, local density inhomogeneities imply position dependent angular velocities of the rotors resulting from inter-rotor friction. While the friction of a quasi-2D layer of active colloids with the substrate is often not easily modifiable in experiments, the incorporation of substrate friction into the simulation models typically implies a considerable increase in computational effort. In chapter 4, a very efficient way of incorporating the friction with a substrate into a two-dimensional multiparticle collision dynamics solvent is introduced, allowing for an explicit investigation of the influences of substrate on active dynamics. For the rotor fluid, it is explicitly shown that the influence of the substrate friction results in a cutoff of the hydrodynamic interaction length, such that the maximum size of the formed vortices is controlled by the substrate friction, also resulting in a cutoff in the energy spectrum, because energy is taken out of the system at the respective length. These findings are in agreement with the experiments. Since active particles in confinement are known to organise in states of collective dynamics, ensembles of rotationally actuated colloids are studied in circular confinement and in the presence of periodic obstacle lattices in chapters 5 and 6, respectively. The results show that the chaotic active turbulent transport of rotors in suspension can be enhanced and guided resulting from edge flows generated at the boundaries, as has recently been reported for a related chiral active system. The consequent collective rotor dynamics can be regarded as a superposition of active turbulent and imposed flows, leading to on average stationary flows. In contrast to the bulk dynamics, the imposed flows inject additional energy into the system on the long length scales, and the same scaling behaviour of the energy spectrum as in bulk is only obtained if the energy injection scales, due to the mutual generation of rotor translational dynamics throughout the system and the edge flows, are well separated. The combination of edge flow and entropic layering at the boundaries leads to oscillating hydrodynamic stresses and consequently to an oscillating vorticity profile. In the presence of odd viscosity, this consequently leads to non-trivial steady-state density modulations at the boundary, resulting from a balance of osmotic pressure and odd stresses. Relevant for the efficient dispersion and mixing of inert particles on the mesoscale by means of active turbulent mixing powered by rotors, a study of the dynamics of a binary mixture consisting out of rotors and passive particles is presented in chapter 7. Because the rotors are not self-propelled, but the translational dynamics is induced by the surrounding rotors, the passive particles, which do not inject further energy into the system, are transported according to the same mechanism as the rotors. The collective dynamics thus resembles the pure rotor bulk dynamics at the respective density of only rotors. However, since no odd stresses act between the passive particles, only mutual rotor interactions lead to odd stresses leading to the accumulation of rotors in the regions of positive vorticity. This density increase is associated with a pressure increase, which balances the odd stresses acting on the rotors. However, the passive particles are only subject to the accumulation induced pressure increase such that these particles are transported into the areas of low rotor concentration, i.e., the regions of negative vorticity. Under conditions of sustained vortex flow, this results in segregation of both particle types. Since local symmetry breaking can convert injected rotational into translational energy, microswimmers can be constructed out of rotor materials when a suitable breaking of symmetry is kept in the vicinity of a rotor. One hypothetical realisation, i.e., a coupled rotor pair consisting out of two rotors of opposite angular velocity and of fixed distance, termed a birotor, are studied in chapter 8. The birotor pumps the fluid into one direction and consequently translates into the opposite direction, and creates a flow field reminiscent of a source doublet, or sliplet flow field. Fixed in space the birotor might be an interesting realisation of a microfluidic pump. The trans- lational dynamics of a birotor can be mapped onto the active Brownian particle model for single swimmers. However, due to the hydrodynamic interactions among the rotors, the birotor ensemble dynamics do not show the emergence of stable motility induced clustering. The reason for this is the flow created by birotor in small aggregates which effectively pushes further arriving birotors away from small aggregates, which eventually are all dispersed by thermal fluctuations

    Properties of a model of sequential random allocation

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    Probabilistic models of allocating shots to boxes according to a certain probability distribution have commonly been used for processes involving agglomeration. Such processes are of interest in many areas of research such as ecology, physiology, chemistry and genetics. Time could be incorporated into the shots-and-boxes model by considering multiple layers of boxes through which the shots move, where the layers represent the passing of time. Such a scheme with multiple layers, each with a certain number of occupied boxes is naturally associated with a random tree. It lends itself to genetic applications where the number of ancestral lineages of a sample changes through the generations. This multiple-layer scheme also allows us to explore the difference in the number of occupied boxes between layers, which gives a measure of how quickly merges are happening. In particular, results for the multiple-layer scheme corresponding to those known for a single-layer scheme, where, under certain conditions, the limiting distribution of the number of occupied boxes is either Poisson or normal, are derived. To provide motivation and demonstrate which methods work well, a detailed study of a small, finite example is provided. A common approach for establishing a limiting distribution for a random variable of interest is to first show that it can be written as a sum of independent Bernoulli random variables as this then allows us to apply standard central limit theorems. Additionally, it allows us to, for example, provide an upper bound on the distance to a Poisson distribution. One way of showing that a random variable can be written as a sum of independent Bernoulli random variables is to show that its probability generating function (p.g.f.) has all real roots. Various methods are presented and considered for proving the p.g.f. of the number of occupied boxes in any given layer of the scheme has all real roots. By considering small finite examples some of these methods could be ruled out for general N. Finally, the scheme for general N boxes and n shots is considered, where again a uniform allocation of shots is used. It is shown that, under certain conditions, the distribution of the number of occupied boxes tends towards either a normal or Poisson limit. Equivalent results are also demonstrated for the distribution of the difference in the number of occupied boxes between consecutive layers
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