Spatial nonhomogeneous periodic solutions induced by nonlocal prey competition in a diffusive predator-prey model

The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatial nonhomogeneous periodic solutions, which is induced by nonlocal prey competition. In particular, the constant positive steady state can lose the stability through Hopf bifurcation when the given parameter passes through some critical values, and the bifurcating periodic solutions near such values can be spatially nonhomogeneous and orbitally asymptotically stable. This phenomenon is different from that in models without nonlocal effect.Comment: 28 pages, 8 figure

Hopf bifurcation in a delayed reaction-diffusion-advection population model

In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our result implies that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation.Comment: 29 page

Dynamics of a diffusive predator-prey model: the effect of conversion rate

A general diffusive predator-prey model is investigated in this paper. We prove the global attractivity of constant equilibria when the conversion rate is small, and the non-existence of non-constant positive steady states when the conversion rate is large. The results are applied to several predator-prey models and give some ranges of parameters where complex pattern formation cannot occur.Comment: 27 page

Hopf bifurcation for a delayed diffusive logistic population model in the advective heterogeneous environment

In this paper, we investigate a delayed reaction-diffusion-advection equation, which models the population dynamics in the advective heterogeneous environment. The existence of the nonconstant positive steady state and associated Hopf bifurcation are obtained. A weighted inner product associated with the advection rate is introduced to compute the normal forms, which is the main difference between Hopf bifurcation for delayed reaction-diffusion-advection model and that for delayed reaction-diffusion model. Moreover, we find that the spatial scale and advection can affect Hopf bifurcation in the heterogenous environment.Comment: 30 page

Randomized Structural Sparsity based Support Identification with Applications to Locating Activated or Discriminative Brain Areas: A Multi-center Reproducibility Study

In this paper, we focus on how to locate the relevant or discriminative brain regions related with external stimulus or certain mental decease, which is also called support identification, based on the neuroimaging data. The main difficulty lies in the extremely high dimensional voxel space and relatively few training samples, easily resulting in an unstable brain region discovery (or called feature selection in context of pattern recognition). When the training samples are from different centers and have betweencenter variations, it will be even harder to obtain a reliable and consistent result. Corresponding, we revisit our recently proposed algorithm based on stability selection and structural sparsity. It is applied to the multi-center MRI data analysis for the first time. A consistent and stable result is achieved across different centers despite the between-center data variation while many other state-of-the-art methods such as two sample t-test fail. Moreover, we have empirically showed that the performance of this algorithm is robust and insensitive to several of its key parameters. In addition, the support identification results on both functional MRI and structural MRI are interpretable and can be the potential biomarkers.Comment: arXiv admin note: text overlap with arXiv:1410.465

Being Rational or Aggressive? A Revisit to Dunbar's Number in Online Social Networks

Recent years have witnessed the explosion of online social networks (OSNs). They provide powerful IT-innovations for online social activities such as organizing contacts, publishing contents, and sharing interests between friends who may never meet before. As more and more people become the active users of online social networks, one may ponder questions such as: (1) Do OSNs indeed improve our sociability? (2) To what extent can we expand our offline social spectrum in OSNs? (3) Can we identify some interesting user behaviors in OSNs? Our work in this paper just aims to answer these interesting questions. To this end, we pay a revisit to the well-known Dunbar's number in online social networks. Our main research contributions are as follows. First, to our best knowledge, our work is the first one that systematically validates the existence of the online Dunbar's number in the range of [200,300]. To reach this, we combine using local-structure analysis and user-interaction analysis for extensive real-world OSNs. Second, we divide OSNs users into two categories: rational and aggressive, and find that rational users intend to develop close and reciprocated relationships, whereas aggressive users have no consistent behaviors. Third, we build a simple model to capture the constraints of time and cognition that affect the evolution of online social networks. Finally, we show the potential use of our findings in viral marketing and privacy management in online social networks

Learning to Cluster Faces on an Affinity Graph

Face recognition sees remarkable progress in recent years, and its performance has reached a very high level. Taking it to a next level requires substantially larger data, which would involve prohibitive annotation cost. Hence, exploiting unlabeled data becomes an appealing alternative. Recent works have shown that clustering unlabeled faces is a promising approach, often leading to notable performance gains. Yet, how to effectively cluster, especially on a large-scale (i.e. million-level or above) dataset, remains an open question. A key challenge lies in the complex variations of cluster patterns, which make it difficult for conventional clustering methods to meet the needed accuracy. This work explores a novel approach, namely, learning to cluster instead of relying on hand-crafted criteria. Specifically, we propose a framework based on graph convolutional network, which combines a detection and a segmentation module to pinpoint face clusters. Experiments show that our method yields significantly more accurate face clusters, which, as a result, also lead to further performance gain in face recognition.Comment: 8 pages, 8 figures, CVPR 201

Deep Cocktail Network: Multi-source Unsupervised Domain Adaptation with Category Shift

Unsupervised domain adaptation (UDA) conventionally assumes labeled source samples coming from a single underlying source distribution. Whereas in practical scenario, labeled data are typically collected from diverse sources. The multiple sources are different not only from the target but also from each other, thus, domain adaptater should not be modeled in the same way. Moreover, those sources may not completely share their categories, which further brings a new transfer challenge called category shift. In this paper, we propose a deep cocktail network (DCTN) to battle the domain and category shifts among multiple sources. Motivated by the theoretical results in \cite{mansour2009domain}, the target distribution can be represented as the weighted combination of source distributions, and, the multi-source unsupervised domain adaptation via DCTN is then performed as two alternating steps: i) It deploys multi-way adversarial learning to minimize the discrepancy between the target and each of the multiple source domains, which also obtains the source-specific perplexity scores to denote the possibilities that a target sample belongs to different source domains. ii) The multi-source category classifiers are integrated with the perplexity scores to classify target sample, and the pseudo-labeled target samples together with source samples are utilized to update the multi-source category classifier and the feature extractor. We evaluate DCTN in three domain adaptation benchmarks, which clearly demonstrate the superiority of our framework.Comment: Accepted for publication in Conference on Computer Vision and Pattern Recognition(CVPR), 201

Dependency Graph Approach for Multiprocessor Real-Time Synchronization

Over the years, many multiprocessor locking protocols have been designed and analyzed. However, the performance of these protocols highly depends on how the tasks are partitioned and prioritized and how the resources are shared locally and globally. This paper answers a few fundamental questions when real-time tasks share resources in multiprocessor systems. We explore the fundamental difficulty of the multiprocessor synchronization problem and show that a very simplified version of this problem is ${\mathcal NP}$-hard in the strong sense regardless of the number of processors and the underlying scheduling paradigm. Therefore, the allowance of preemption or migration does not reduce the computational complexity. For the positive side, we develop a dependency-graph approach, that is specifically useful for frame-based real-time tasks, in which all tasks have the same period and release their jobs always at the same time. We present a series of algorithms with speedup factors between $2$ and $3$ under semi-partitioned scheduling. We further explore methodologies and tradeoffs of preemptive against non-preemptive scheduling algorithms and partitioned against semi-partitioned scheduling algorithms. The approach is extended to periodic tasks under certain conditions.Comment: accepted and to appear in IEEE Real-Time System Symposium (RTSS) 201

An Empirical Analysis of the Influence of Fault Space on Search-Based Automated Program Repair

Automated program repair (APR) has attracted great research attention, and various techniques have been proposed. Search-based APR is one of the most important categories among these techniques. Existing researches focus on the design of effective mutation operators and searching algorithms to better find the correct patch. Despite various efforts, the effectiveness of these techniques are still limited by the search space explosion problem. One of the key factors attribute to this problem is the quality of fault spaces as reported by existing studies. This motivates us to study the importance of the fault space to the success of finding a correct patch. Our empirical study aims to answer three questions. Does the fault space significantly correlate with the performance of search-based APR? If so, are there any indicative measurements to approximate the accuracy of the fault space before applying expensive APR techniques? Are there any automatic methods that can improve the accuracy of the fault space? We observe that the accuracy of the fault space affects the effectiveness and efficiency of search-based APR techniques, e.g., the failure rate of GenProg could be as high as $60\%$ when the real fix location is ranked lower than 10 even though the correct patch is in the search space. Besides, GenProg is able to find more correct patches and with fewer trials when given a fault space with a higher accuracy. We also find that the negative mutation coverage, which is designed in this study to measure the capability of a test suite to kill the mutants created on the statements executed by failing tests, is the most indicative measurement to estimate the efficiency of search-based APR. Finally, we confirm that automated generated test cases can help improve the accuracy of fault spaces, and further improve the performance of search-based APR techniques