Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample

In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We find that, due to coarse-graining, the entropy is a monotonic increasing function of the bin width for histogram or bandwidth for kernel estimation, which seems to be difficult to select an optimal bin width/bandwidth for computing the entropy. Fortunately, we notice that there exists a minimum of the first derivative of entropy for both histogram and kernel estimation, and this minimum point of the first derivative asymptotically points to the optimal bin width or bandwidth. We have verified these findings by large amounts of numerical experiments. Hence, we suggest that the minimum of the first derivative of entropy be used as a selector for the optimal bin width or bandwidth of density estimation. Moreover, the optimal bandwidth selected by the minimum of the first derivative of entropy is purely data-based, independent of the unknown underlying probability density distribution, which is obviously superior to the existing estimators. Our results are not restricted to one-dimensional, but can also be extended to multivariate cases. It should be emphasized, however, that we do not provide a robust mathematical proof of these findings, and we leave these issues with those who are interested in them.Comment: 8 pages, 6 figures, MNRAS, in the pres

Predicting Lower Extremity Joint Kinematics Using Multi-Modal Data in the Lab and Outdoor Environment

Predicting future walking joint kinematics is crucial for assistive device control, especially in variable walking environments. Traditional optical motion capture systems provide kinematics data but require laborious post-processing, whereas IMU based systems provide direct calculations but add delays due to data collection and algorithmic processes. Predicting future kinematics helps to compensate for these delays, enabling the system real-time. Furthermore, these predicted kinematics could serve as target trajectories for assistive devices such as exoskeletal robots and lower limb prostheses. However, given the complexity of human mobility and environmental factors, this prediction remains to be challenging. To address this challenge, we propose the Dual-ED-Attention-FAM-Net, a deep learning model utilizing two encoders, two decoders, a temporal attention module, and a feature attention module. Our model outperforms the state-of-the-art LSTM model. Specifically, for Dataset A, using IMUs and a combination of IMUs and videos, RMSE values decrease from 4.45° to 4.22° and from 4.52° to 4.15°, respectively. For Dataset B, IMUs and IMUs combined with pressure insoles result in RMSE reductions from 7.09° to 6.66° and from 7.20° to 6.77°, respectively. Additionally, incorporating other modalities alongside IMUs helps improve the performance of the model

Familial Clustering For Weakly-labeled Android Malware Using Hybrid Representation Learning

IEEE Labeling malware or malware clustering is important for identifying new security threats, triaging and building reference datasets. The state-of-the-art Android malware clustering approaches rely heavily on the raw labels from commercial AntiVirus (AV) vendors, which causes misclustering for a substantial number of weakly-labeled malware due to the inconsistent, incomplete and overly generic labels reported by these closed-source AV engines, whose capabilities vary greatly and whose internal mechanisms are opaque (i.e., intermediate detection results are unavailable for clustering). The raw labels are thus often used as the only important source of information for clustering. To address the limitations of the existing approaches, this paper presents ANDRE, a new ANDroid Hybrid REpresentation Learning approach to clustering weakly-labeled Android malware by preserving heterogeneous information from multiple sources (including the results of static code analysis, the metainformation of an app, and the raw-labels of the AV vendors) to jointly learn a hybrid representation for accurate clustering. The learned representation is then fed into our outlieraware clustering to partition the weakly-labeled malware into known and unknown families. The malware whose malicious behaviours are close to those of the existing families on the network, are further classified using a three-layer Deep Neural Network (DNN). The unknown malware are clustered using a standard density-based clustering algorithm. We have evaluated our approach using 5,416 ground-truth malware from Drebin and 9,000 malware from VIRUSSHARE (uploaded between Mar. 2017 and Feb. 2018), consisting of 3324 weakly-labeled malware. The evaluation shows that ANDRE effectively clusters weaklylabeled malware which cannot be clustered by the state-of-theart approaches, while achieving comparable accuracy with those approaches for clustering ground-truth samples

CaCu3Ti4O12: Low-Temperature Synthesis by Pyrolysis of an Organic Solution

The giant-dielectric-constant material CaCu3Ti4O12 (CCTO) has been synthesized by pyrolyzing an organic solution containing stoichiometric amounts of the metal cations, which is done at lower temperature and shorter reaction time than the conventional solid-state reaction. A stable solution was prepared by dissolving calcium nitrate, copper(II) nitrate, and titanium(IV) isopropoxide in 2-methoxyethanol. This solution was pyrolyzed and heat-treated to achieve single-phase CCTO. The phases, microstructures, and dielectric properties of intermediate and final samples were characterized by X-ray diffraction, scanning electron microscopy, and dielectric spectroscopy