Optimal location of resources and Steiner symmetry in a population dynamics model in heterogeneous environments

The subject of this paper is inspired by Cantrell and Cosner (1989) and Cosner, Cuccu and Porru (2013). Cantrell and Cosner (1989) investigate the dynamics of a population in heterogeneous environments by means of diffusive logistic equations. An important part of their study consists in finding sufficient conditions which guarantee the survival of the species. Mathematically, this task leads to the weighted eigenvalue problem \(-\Delta u =\lambda m u \) in a bounded smooth domain \(\Omega\subset \mathbb{R}^N\), \(N\geq 1\), under homogeneous Dirichlet boundary conditions, where \(\lambda \in \mathbb{R}\) and \(m\in L^\infty(\Omega)\). The domain \(\Omega\) represents the environment and \(m(x)\), called the local growth rate, says where the favourable and unfavourable habitats are located. Then, Cantrell and Cosner (1989) consider a class of weights \(m(x)\) corresponding to environments where the total sizes of favourable and unfavourable habitats are fixed, but their spatial arrangement is allowed to change; they determine the best choice among them for the population to survive. In our work we consider a sort of refinement of the result above. We write the weight \(m(x)\) as sum of two (or more) terms, i.e. \(m(x)=f_1(x)+f_2(x)\), where \(f_1(x)\) and \(f_2(x)\) represent the spatial densities of the two resources which contribute to form the local growth rate \(m(x)\). Then, we fix the total size of each resource allowing its spatial location to vary. As our first main result, we show that there exists an optimal choice of \(f_1(x)\) and \(f_2(x)\) and find the form of the optimizers. Our proof relies on some results in Cosner, Cuccu and Porru (2013) and on a new property (to our knowledge) about the classes of rearrangements of functions. Moreover, we show that if \(\Omega\) is Steiner symmetric, then the best arrangement of the resources inherits the same kind of symmetry. (Actually, this is proved in the more general context of the classes of rearrangements of measurable functions.

SHAT: A Novel Asynchronous Training Algorithm That Provides Fast Model Convergence in Distributed Deep Learning

The recent unprecedented success of deep learning (DL) in various fields is underlied by its use of large-scale data and models. Training a large-scale deep neural network (DNN) model with large-scale data, however, is time-consuming. To speed up the training of massive DNN models, data-parallel distributed training based on the parameter server (PS) has been widely applied. In general, a synchronous PS-based training suffers from the synchronization overhead, especially in heterogeneous environments. To reduce the synchronization overhead, asynchronous PS-based training employs the asynchronous communication between PS and workers so that PS processes the request of each worker independently without waiting. Despite the performance improvement of asynchronous training, however, it inevitably incurs the difference among the local models of workers, where such a difference among workers may cause slower model convergence. Fro addressing this problem, in this work, we propose a novel asynchronous PS-based training algorithm, SHAT that considers (1) the scale of distributed training and (2) the heterogeneity among workers for successfully reducing the difference among the local models of workers. The extensive empirical evaluation demonstrates that (1) the model trained by SHAT converges to the higher accuracy up to 5.22% than state-of-the-art algorithms, and (2) the model convergence of SHAT is robust under various heterogeneous environments.

Living in a Fluctuating Environment Increases Tolerance to Marine Heatwaves in the Free-Living Coralline Alga Phymatolithon lusitanicum

Recently, increased attention is being paid to the importance of environmental history in species’ responses to climate-change related stressors, as more variable and heterogeneous environments are expected to select for higher levels of plasticity in species tolerance traits, compared to stable conditions. For example, organisms inhabiting environments with highly fluctuating thermal regimes might be less susceptible to the increasing frequency and intensity of marine heatwaves (MHWs). In this study, we assessed the metabolic and calcification responses of the rhodolith-bed forming Phymatolithon lusitanicum, from a coastal region that is strongly influenced by frequent changes between upwelling and downwelling conditions, to a simulated MHW scenario, with and without prior exposure to a moderate thermal stress. This allowed determining not only the influence of the species’ long-term thermal history on its resilience against MHWs, but also the rhodoliths capacity for short-term thermal stress memory and its importance during posterior MHW-exposure. Our findings indicate that the rhodoliths experienced negative impacts on daily net primary production (DNP) and calcification (DNC) during the MHW. The effect on the former was only temporary at the beginning of the MHW, while DNC was highly impacted, but exhibited a quick recovery after the event, suggesting a high resilience of the species. Furthermore, prior exposure to a moderate temperature increase, such as those occurring frequently in the natural habitat of the species, mitigated the effects of a subsequent MHW on DNP, while promoting a faster recovery of DNC after the event. Thus, our findings (1) support the hypothesis that benthic organisms living in nearshore habitats may benefit from the natural short-term temperature fluctuations in these environments with an increased resistance to MHW impacts and (2) provide first-time evidence for thermally induced stress memory in coralline algae.

Nonhyperbolic normal moveout stretch correction with deep learning automation

Normal moveout (NMO) correction is a fundamental step in seismic data processing. It consists of mapping seismic data from recorded traveltimes to corresponding zero-offset times. This process produces wavelet stretching as an undesired byproduct. We address the NMO stretching problem with two methods: 1) an exact stretch-free NMO correction that prevents the stretching of primary reflections, and 2) an approximate post-NMO stretch correction. Our stretch-free NMO produces parallel moveout trajectories for primary reflections. Our post-NMO stretch correction calculates the moveout of stretched wavelets as a function of offset. Both methods are based on the generalized moveout approximation and are suitable for application in complex anisotropic or heterogeneous environments. We use new moveout equations and modify the original parameter functions to be constant over the primary reflections, and then interpolate the seismogram amplitudes at the calculated traveltimes. For fast and automatic modification of the parameter functions, we use deep learning. We design a deep neural network (DNN) using convolutional layers and residual blocks. To train the DNN, we generate a set of 40,000 synthetic NMO corrected common midpoint gathers and the corresponding desired outputs of the DNN. The data set is generated using different velocity profiles, wavelets, and offset vectors, and includes multiples, ground roll, and band-limited random noise. The simplicity of the DNN task –a 1D identification of primary reflections– improves the generalization in practice. We use the trained DNN and show successful applications of our stretch-correction method on synthetic and different real data sets.

An insect-scale robot reveals the effects of different body dynamics regimes during open-loop running in feature-laden terrain

The transition from the lab to natural environments is an archetypal challenge in robotics. While larger robots can manage complex limb-ground interactions using sensing and control, such strategies are difficult to implement on small platforms where space and power are limited. The Harvard Ambulatory Microrobot (HAMR) is an insect-scale quadruped capable of effective open-loop running on featureless, hard substrates. Inspired by the predominantly feedforward strategy of rapidly-running cockroaches on uneven terrain [Sponberg, 2007], we used HAMR to explore open-loop running on two 3D printed heterogeneous terrains generated using fractional Brownian motion. The ``pocked'' terrain had foot-scale features throughout while the ``jagged'' terrain features increased in height in the direction of travel. We measured the performance of trot and pronk gaits while varying limb amplitude and stride frequency. The frequencies tested encompassed different dynamics regimes: body resonance (10-25~Hz) and kinematic running (30-40~Hz), with dynamics typical of biological running and walking, respectively, and limb-transmission resonance (45-60~Hz). On the featureless and pocked terrains, low mechanical cost-of-transport (mCoT) kinematic running combinations performed best without systematic differences between trot and pronk; indicating that if terrain features are not too tall, a robot can transition from homo- to heterogeneous environments in open-loop. Pronk bypassed taller features than trot on the jagged terrain, and higher mCoT, lower frequency running was more often effective. While increasing input power to the robot improved performance in general, lower frequency pronking on jagged terrain allowed the robot to bypass taller features compared with the same input power at higher frequencies. This was correlated with the increased variation in center-of-mass orientation occurring at frequencies near body resonance. This study established that appropriate choice of robot dynamics, as mediated by gait, frequency, and limb amplitude, can expand the terrains accessible to microrobots without the addition of sensing or closed-loop control.

A Comprehensive Assessment on IOT Devices with Data Mining Techniques

Now at present development the entire world using vast variety of smart devices associated among sensors & handful of actuators. There is an enormous progress within the field of electronic communication; processing the data through devices and the bandwidth in internet technologies makes very easy to access and to interact with the variety of devices all over the whole world. There is a wide range research in the area of Internet of Things (IoT) along Cloud Technologies making to build incredible data which are creating from this type of heterogeneous environments and can be able to transform into a valuable knowledge with the help of data mining techniques. The knowledge that is generated will takes a crucial role in making intellectual decisions and also be a best possible resource management and services. In this paper we organized a comprehensive assessment on various data mining techniques engaged with small and large scale IoT applications to make the environment smart.

Dissolved Oxygen in Heterogeneous Environments Dictates the Metabolic Rate and Thermal Sensitivity of a Tropical Aquatic Crab

Oxygen availability, together with water temperature, greatly varies in coastal habitats, especially in those characterized by elevated primary production. In this study, we investigate the combined role of dissolved oxygen and temperature on the thermal physiological response of the mud crab Thalamita crenata living in an equatorial system of coastal habitats. We sampled temperature, oxygen and salinity in T. crenata habitats, mangrove creeks and fringes and seagrass meadows, at Gazi Bay (Kenya). We found that seagrass meadows exhibited higher temperature and oxygen saturation than the mangrove habitats during the day, creating conditions of oxygen supersaturation. By investigating the effect of different levels of oxygen saturation on the thermal response of T. crenata, we demonstrated that the respiratory physiology of this ectotherm has a pronounced resistance to heat, directly influenced by the amount of dissolved oxygen in the water. Under low oxygen saturation levels, the mud crab significantly reduced its metabolism, becoming temperature-independent. This result shows that aquatic species can modulate their thermal response in a stringent dependency with water oxygen saturation, corroborating previous findings on the thermal response of T. crenata under supersaturation. This contribution provides further support for the need to adopt an ecologically-relevant approach to forecast the effect of climate change on marine ectothermal species.