Near-constant Time Research Articles

GeodesicEmbedding (GE): A High-Dimensional Embedding Approach for Fast Geodesic Distance Queries.

In this article, we develop a novel method for fast geodesic distance queries. The key idea is to embed the mesh into a high-dimensional space, such that the euclidean distance in the high-dimensional space can induce the geodesic distance in the original manifold surface. However, directly solving the high-dimensional embedding problem is not feasible due to the large number of variables and the fact that the embedding problem is highly nonlinear. We overcome the challenges with two novel ideas. First, instead of taking all vertices as variables, we embed only the saddle vertices, which greatly reduces the problem complexity. We then compute a local embedding for each non-saddle vertex. Second, to reduce the large approximation error resulting from the purely euclidean embedding, we propose a cascaded optimization approach that repeatedly introduces additional embedding coordinates with a non-euclidean function to reduce the approximation residual. Using the precomputation data, our approach can determine the geodesic distance between any two vertices in near-constant time. Computational testing results show that our method is more desirable than previous geodesic distance queries methods.

Unsupervised Learning in Next-Generation Networks: Real-Time Performance Self-Diagnosis

This letter demonstrates the use of unsupervised machine learning to enable performance self-diagnosis of next-generation cellular networks. We propose two simplified applications of unsupervised learning that can enable real-time performance self-diagnosis on edge nodes such as the radio access network intelligent controller (RIC). The first application detects anomalous performance and finds its root cause of faults, configuration, or network procedure failures. The second application uses clustering to learn the relationship between two performance measures. Our proposed applications run in near-constant time complexity, making them, combined with subject-matter expertise validation, suitable real-time RIC applications for network diagnosis.

A New Discrete-Time Multi-Constrained $K$ -Winner-Take-All Recurrent Network and Its Application to Prioritized Scheduling

In this paper, we propose a novel discrete-time recurrent neural network aiming to resolve a new class of multi-constrained K-winner-take-all (K-WTA) problems. By facilitating specially designed asymmetric neuron weights, the proposed model is capable of operating in a fully parallel manner, thereby allowing true digital implementation. This paper also provides theorems that delineate the theoretical upper bound of the convergence latency, which is merely O(K). Importantly, via simulations, the average convergence time is close to O(1) in most general cases. Moreover, as the multi-constrained K-WTA problem degenerates to a traditional single-constrained problem, the upper bound becomes exactly two parallel iterations, which significantly outperforms the existing K-WTA models. By associating the neurons and neuron weights with routing paths and path priorities, respectively, we then apply the model to a prioritized flow scheduler for the data center networks. Through extensive simulations, we demonstrate that the proposed scheduler converges to the equilibrium state within near-constant time for different scales of networks while achieving maximal throughput, quality-of-service priority differentiation, and minimum energy consumption, subject to the flow contention-free constraints.

Monte Carlo MP2 on Many Graphical Processing Units.

In the Monte Carlo second-order many-body perturbation (MC-MP2) method, the long sum-of-product matrix expression of the MP2 energy, whose literal evaluation may be poorly scalable, is recast into a single high-dimensional integral of functions of electron pair coordinates, which is evaluated by the scalable method of Monte Carlo integration. The sampling efficiency is further accelerated by the redundant-walker algorithm, which allows a maximal reuse of electron pairs. Here, a multitude of graphical processing units (GPUs) offers a uniquely ideal platform to expose multilevel parallelism: fine-grain data-parallelism for the redundant-walker algorithm in which millions of threads compute and share orbital amplitudes on each GPU; coarse-grain instruction-parallelism for near-independent Monte Carlo integrations on many GPUs with few and infrequent interprocessor communications. While the efficiency boost by the redundant-walker algorithm on central processing units (CPUs) grows linearly with the number of electron pairs and tends to saturate when the latter exceeds the number of orbitals, on a GPU it grows quadratically before it increases linearly and then eventually saturates at a much larger number of pairs. This is because the orbital constructions are nearly perfectly parallelized on a GPU and thus completed in a near-constant time regardless of the number of pairs. In consequence, an MC-MP2/cc-pVDZ calculation of a benzene dimer is 2700 times faster on 256 GPUs (using 2048 electron pairs) than on two CPUs, each with 8 cores (which can use only up to 256 pairs effectively). We also numerically determine that the cost to achieve a given relative statistical uncertainty in an MC-MP2 energy increases as O(n3) or better with system size n, which may be compared with the O(n5) scaling of the conventional implementation of deterministic MP2. We thus establish the scalability of MC-MP2 with both system and computer sizes.

Scheduled approximation for Personalized PageRank with Utility-based Hub Selection

As Personalized PageRank has been widely leveraged for ranking on a graph, the efficient computation of Personalized PageRank Vector (PPV) becomes a prominent issue. In this paper, we propose FastPPV, an approximate PPV computation algorithm that is incremental and accuracy-aware. Our approach hinges on a novel paradigm of scheduled approximation: the computation is partitioned and scheduled for processing in an “organized” way, such that we can gradually improve our PPV estimation in an incremental manner and quantify the accuracy of our approximation at query time. Guided by this principle, we develop an efficient hub-based realization, where we adopt the metric of hub length to partition and schedule random walk tours so that the approximation error reduces exponentially over iterations. In addition, as tours are segmented by hubs, the shared substructures between different tours (around the same hub) can be reused to speed up query processing both within and across iterations. Given the key roles played by the hubs, we further investigate the problem of hub selection. In particular, we develop a conceptual model to select hubs based on the two desirable properties of hubs—sharing and discriminating, and present several different strategies to realize the conceptual model. Finally, we evaluate FastPPV over two real-world graphs, and show that it not only significantly outperforms two state-of-the-art baselines in both online and offline phrases, but also scales well on larger graphs. In particular, we are able to achieve near-constant time online query processing irrespective of graph size.

Incremental and accuracy-aware personalized pagerank through scheduled approximation

As Personalized PageRank has been widely leveraged for ranking on a graph, the efficient computation of Personalized PageRank Vector (PPV) becomes a prominent issue. In this paper, we propose FastPPV, an approximate PPV computation algorithm that is incremental and accuracy-aware. Our approach hinges on a novel paradigm of scheduled approximation: the computation is partitioned and scheduled for processing in an "organized" way, such that we can gradually improve our PPV estimation in an incremental manner, and quantify the accuracy of our approximation at query time. Guided by this principle, we develop an efficient hub based realization, where we adopt the metric of hub-length to partition and schedule random walk tours so that the approximation error reduces exponentially over iterations. Furthermore, as tours are segmented by hubs, the shared substructures between different tours (around the same hub) can be reused to speed up query processing both within and across iterations. Finally, we evaluate FastPPV over two real-world graphs, and show that it not only significantly outperforms two state-of-the-art baselines in both online and offline phrases, but also scale well on larger graphs. In particular, we are able to achieve near-constant time online query processing irrespective of graph size.

Real-Time Trajectory Generation for Target Localization Using Micro Air Vehicles

This thesis presents an approach to near-optimal target localization for small and micro unmanned aerial vehicles using a family of pre-computed parameterized trajectories. These trajectories are pre-computed for a set of nominal target locations uniformly distributed over the sensor field of view and stored offline in a non-dimensionalized form. In the first part of this research, the trajectories are parameterized and stored as a sequence of turn-rate commands. In the second part of this research, the trajectories are parameterized and stored as a sequence of non-dimensional waypoints. Upon target detection, a trajectory corresponding to the nearest nominal target location is selected and dimensionalized. An onboard navigation controller follows the dimensionalized trajectory. Thus, trajectory generation occurs in near-constant time, which allows for fast adaptation as the target state estimate is refined. Non-dimensionalization of the trajectories with respect to relative vehicle speed, sensor range, and sensor update rate allows the same table to be used for various combinations of sensor package and vehicle or vehicle operating conditions.

Near-constant time delay response of fiber grating Sagnac loop filters

A theoretical and experimental investigation of the time delay characteristics of fiber Bragg grating-based Sagnac loops (FBGSLs) is presented. Analytic expressions for the phase and time delay of the FBGSL have been derived and excellent agreement is found between their predictions and experimental results for configurations incorporating uniform-period and chirped-period gratings. For symmetrical grating structures, it is found that the FBGSL time delay response is similar to that of the incorporated grating; with asymmetrical gratings, the FBGSL response is quite different. It is shown that wavelength-division-multiplexing filters exhibiting near-zero dispersion characteristics can be implemented using FBGSLs.

Echocardiographic and hemodynamic correlates of diastolic closure of mitral valve and diastolic opening of aortic valve in severe aortic regurgitation

Acute severe aortic regurgitation (AR) is characterized by a steep increase in left ventricular end-diastolic pressure, exceeding left atrial pressure and occasionally equilibrating with aortic diastolic pressure. These pressure phenomena correlate with the M-mode echocardiographic (echo) findings of diastolic closure of the mitral valve (DCMV) and diastolic opening of the aortic valve (DOAV). Six men, aged 23 to 48 years, with recent-onset, severe AR were evaluated by M-mode echo and pressures at cardiac catheterization. DCMV was seen in all 6 patients and DOAV in 4. Near-constant time intervals from the preceding R wave of the electrocardiogram to DCMV and DOAV were seen, even in 3 patients with varying RR intervals (1 with atrial fibrillation and 2 with asynchronous and demand atrial pacing). When the RR intervals were shorter than these intervals, DCMV and DOAV did not occur. Increasing the heart rate in the 2 patients by atrial pacing resulted in a marked decrease in left ventricular end-diastolic pressure. In conclusion, (1) DCMV and DOAV have a near constant relation to the preceding R wave of the electrocardiogram, (2) DCMV with competence of the mitral valve must be present for DOAV to occur, (3) DOAV indicates that the diastolic blood pressure equals left ventricular end-diastolic pressure, and (4) heart rate is an important factor influencing the hemodynamic and echocardiographic parameters in recent-onset, severe AR.