亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Dijkstra's algorithm is one of the most popular classic path planning algorithms, achieving optimal solutions across a wide range of challenging tasks. However, it only calculates the shortest distance from one vertex to another, which is hard to directly apply to the Dynamic Multi-Sources to Single-Destination (DMS-SD) problem. This paper proposes a modified Dijkstra algorithm to address the DMS-SD problem, where the destination can be dynamically changed. Our method deploys the concept of Adjacent Matrix from Floyd's algorithm and achieves the goal with mathematical calculations. We formally show that all-pairs shortest distance information in Floyd's algorithm is not required in our algorithm. Extensive experiments verify the scalability and optimality of the proposed method.

Integrated information theory (IIT) is a theoretical framework that provides a quantitative measure to estimate when a physical system is conscious, its degree of consciousness, and the complexity of the qualia space that the system is experiencing. Formally, IIT rests on the assumption that if a surrogate physical system can fully embed the phenomenological properties of consciousness, then the system properties must be constrained by the properties of the qualia being experienced. Following this assumption, IIT represents the physical system as a network of interconnected elements that can be thought of as a probabilistic causal graph, $\mathcal{G}$, where each node has an input-output function and all the graph is encoded in a transition probability matrix. Consequently, IIT's quantitative measure of consciousness, $\Phi$, is computed with respect to the transition probability matrix and the present state of the graph. In this paper, we provide a random search algorithm that is able to optimize $\Phi$ in order to investigate, as the number of nodes increases, the structure of the graphs that have higher $\Phi$. We also provide arguments that show the difficulties of applying more complex black-box search algorithms, such as Bayesian optimization or metaheuristics, in this particular problem. Additionally, we suggest specific research lines for these techniques to enhance the search algorithm that guarantees maximal $\Phi$.

Graph Pattern Mining (GPM) is an important, rapidly evolving, and computation demanding area. GPM computation relies on subgraph enumeration, which consists in extracting subgraphs that match a given property from an input graph. Graphics Processing Units (GPUs) have been an effective platform to accelerate applications in many areas. However, the irregularity of subgraph enumeration makes it challenging for efficient execution on GPU due to typical uncoalesced memory access, divergence, and load imbalance. Unfortunately, these aspects have not been fully addressed in previous work. Thus, this work proposes novel strategies to design and implement subgraph enumeration efficiently on GPU. We support a depth-first search style search (DFS-wide) that maximizes memory performance while providing enough parallelism to be exploited by the GPU, along with a warp-centric design that minimizes execution divergence and improves utilization of the computing capabilities. We also propose a low-cost load balancing layer to avoid idleness and redistribute work among thread warps in a GPU. Our strategies have been deployed in a system named DuMato, which provides a simple programming interface to allow efficient implementation of GPM algorithms. Our evaluation has shown that DuMato is often an order of magnitude faster than state-of-the-art GPM systems and can mine larger subgraphs (up to 12 vertices).

Expander graphs play a central role in graph theory and algorithms. With a number of powerful algorithmic tools developed around them, such as the Cut-Matching game, expander pruning, expander decomposition, and algorithms for decremental All-Pairs Shortest Paths (APSP) in expanders, to name just a few, the use of expanders in the design of graph algorithms has become ubiquitous. Specific applications of interest to us are fast deterministic algorithms for cut problems in static graphs, and algorithms for dynamic distance-based graph problems, such as APSP. Unfortunately, the use of expanders in these settings incurs a number of drawbacks. For example, the best currently known algorithm for decremental APSP in constant-degree expanders can only achieve a $(\log n)^{O(1/\epsilon^2)}$-approximation with $n^{1+O(\epsilon)}$ total update time for any $\epsilon$. All currently known algorithms for the Cut Player in the Cut-Matching game are either randomized, or provide rather weak guarantees. This, in turn, leads to somewhat weak algorithmic guarantees for several central cut problems: for example, the best current almost linear time deterministic algorithm for Sparsest Cut can only achieve approximation factor $(\log n)^{\omega(1)}$. Lastly, when relying on expanders in distance-based problems, such as dynamic APSP, via current methods, it seems inevitable that one has to settle for approximation factors that are at least $\Omega(\log n)$. In this paper we propose the use of well-connected graphs, and introduce a new algorithmic toolkit for such graphs that, in a sense, mirrors the above mentioned algorithmic tools for expanders. One of these new tools is the Distanced Matching game, an analogue of the Cut-Matching game for well-connected graphs. We demonstrate the power of these new tools by obtaining better results for several of the problems mentioned above.

Pose graph optimization is a special case of the simultaneous localization and mapping problem where the only variables to be estimated are pose variables and the only measurements are inter-pose constraints. The vast majority of pose graph optimization techniques are vertex based (variables are robot poses), but recent work has parameterized the pose graph optimization problem in a relative fashion (variables are the transformations between poses) that utilizes a minimum cycle basis to maximize the sparsity of the problem. We explore the construction of a cycle basis in an incremental manner while maximizing the sparsity. We validate an algorithm that constructs a sparse cycle basis incrementally and compare its performance with a minimum cycle basis. Additionally, we present an algorithm to approximate the minimum cycle basis of two graphs that are sparsely connected as is common in multi-agent scenarios. Lastly, the relative parameterization of pose graph optimization has been limited to using rigid body transforms on SE(2) or SE(3) as the constraints between poses. We introduce a methodology to allow for the use of lower-degree-of-freedom measurements in the relative pose graph optimization problem. We provide extensive validation of our algorithms on standard benchmarks, simulated datasets, and custom hardware.

Influence diagnostics such as influence functions and approximate maximum influence perturbations are popular in machine learning and in AI domain applications. Influence diagnostics are powerful statistical tools to identify influential datapoints or subsets of datapoints. We establish finite-sample statistical bounds, as well as computational complexity bounds, for influence functions and approximate maximum influence perturbations using efficient inverse-Hessian-vector product implementations. We illustrate our results with generalized linear models and large attention based models on synthetic and real data.

Gradient-based first-order convex optimization algorithms find widespread applicability in a variety of domains, including machine learning tasks. Motivated by the recent advances in fixed-time stability theory of continuous-time dynamical systems, we introduce a generalized framework for designing accelerated optimization algorithms with strongest convergence guarantees that further extend to a subclass of non-convex functions. In particular, we introduce the \emph{GenFlow} algorithm and its momentum variant that provably converge to the optimal solution of objective functions satisfying the Polyak-{\L}ojasiewicz (PL) inequality, in a fixed-time. Moreover for functions that admit non-degenerate saddle-points, we show that for the proposed GenFlow algorithm, the time required to evade these saddle-points is bounded uniformly for all initial conditions. Finally, for strongly convex-strongly concave minimax problems whose optimal solution is a saddle point, a similar scheme is shown to arrive at the optimal solution again in a fixed-time. The superior convergence properties of our algorithm are validated experimentally on a variety of benchmark datasets.

In this paper, a hyperparameter tuning based Bayesian optimization of digital twins is carried out to diagnose various faults in grid connected inverters. As fault detection and diagnosis require very high precision, we channelize our efforts towards an online optimization of the digital twins, which, in turn, allows a flexible implementation with limited amount of data. As a result, the proposed framework not only becomes a practical solution for model versioning and deployment of digital twins design with limited data, but also allows integration of deep learning tools to improve the hyperparameter tuning capabilities. For classification performance assessment, we consider different fault cases in virtual synchronous generator (VSG) controlled grid-forming converters and demonstrate the efficacy of our approach. Our research outcomes reveal the increased accuracy and fidelity levels achieved by our digital twin design, overcoming the shortcomings of traditional hyperparameter tuning methods.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.