14 research outputs found
Identifying manifolds underlying group motion in Vicsek agents
Collective motion of animal groups often undergoes changes due to
perturbations. In a topological sense, we describe these changes as switching
between low-dimensional embedding manifolds underlying a group of evolving
agents. To characterize such manifolds, first we introduce a simple mapping of
agents between time-steps. Then, we construct a novel metric which is
susceptible to variations in the collective motion, thus revealing distinct
underlying manifolds. The method is validated through three sample scenarios
simulated using a Vicsek model, namely switching of speed, coordination, and
structure of a group. Combined with a dimensionality reduction technique that
is used to infer the dimensionality of the embedding manifold, this approach
provides an effective model-free framework for the analysis of collective
behavior across animal species.Comment: 12 pages, 6 figures, journal articl
Modeling the lowest-cost splitting of a herd of cows by optimizing a cost function
Animals live in groups to defend against predation and to obtain food.
However, for some animals --- especially ones that spend long periods of time
feeding --- there are costs if a group chooses to move on before their
nutritional needs are satisfied. If the conflict between feeding and keeping up
with a group becomes too large, it may be advantageous to some animals to split
into subgroups of animals with similar nutritional needs. We model the costs
and benefits of splitting by a herd of cows using a cost function (CF) that
quantifies individual variation in hunger, desire to lie down, and predation
risk. We model the costs associated with hunger and lying desire as the
standard deviations of individuals within a group, and we model predation risk
as an inverse exponential function of group size. We minimize the cost function
over all plausible groups that can arise from a given herd and study the
dynamics of group splitting. We explore our model using two examples: (1) we
consider group switching and group fission in a herd of relatively homogeneous
cows; and (2) we examine a herd with an equal number of adult males (larger
animals) and adult females (smaller animals).Comment: 19 pages, 10 figure
Efficient Noise Filtration of Images by Low-Rank Singular Vector Approximations of Geodesics' Gramian Matrix
Modern society is interested in capturing high-resolution and fine-quality
images due to the surge of sophisticated cameras. However, the noise
contamination in the images not only inferior people's expectations but also
conversely affects the subsequent processes if such images are utilized in
computer vision tasks such as remote sensing, object tracking, etc. Even though
noise filtration plays an essential role, real-time processing of a
high-resolution image is limited by the hardware limitations of the
image-capturing instruments. Geodesic Gramian Denoising (GGD) is a
manifold-based noise filtering method that we introduced in our past research
which utilizes a few prominent singular vectors of the geodesics' Gramian
matrix for the noise filtering process. The applicability of GDD is limited as
it encounters when denoising a given image of size since GGD computes the prominent singular vectors of a data
matrix that is implemented by singular value decomposition (SVD). In this
research, we increase the efficiency of our GGD framework by replacing its SVD
step with four diverse singular vector approximation techniques. Here, we
compare both the computational time and the noise filtering performance between
the four techniques integrated into GGD.Comment: 19 pages, 3 figures, submitted to ACM Transactions on Architecture
and Code Optimizatio
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Real-time forecasting of time series in financial markets using sequentially trained many-to-one LSTMs
Financial markets are highly complex and volatile; thus, learning about such markets for the sake of making predictions is vital to make early alerts about crashes and subsequent recoveries. People have been using learning tools from diverse fields such as financial mathematics and machine learning in the attempt of making trustworthy predictions on such markets. However, the accuracy of such techniques had not been adequate until artificial neural network (ANN) frameworks were developed. Moreover, making accurate real time predictions of financial time series is highly subjective to the ANN architecture in use and the procedure of training it. Long short-term memory (LSTM) is a member of the recurrent neural network family which has been widely utilized for time series predictions. Especially, we train two LSTMs with a known length, say T time steps, of previous data and predict only one time step ahead. At each iteration, while one LSTM is employed to find the best number of epochs, the second LSTM is trained only for the best number of epochs to make predictions. We treat the current prediction as in the training set for the next prediction and train the same LSTM. While classic ways of training result in more error when the predictions are made further away in the test period, our approach is capable of maintaining a superior accuracy as training increases when it proceeds through the testing period. The forecasting accuracy of our approach is validated using three time series from each of the three diverse financial markets: stock, cryptocurrency, and commodity. The results are compared with those of an extended Kalman filter, an autoregressive model, and an autoregressive integrated moving average model
Geodesic Gramian denoising applied to the images contaminated with noise sampled from diverse probability distributions
Abstract As quotidian use of sophisticated cameras surges, people in modern society are more interested in capturing fineāquality images. However, the quality of the images might be inferior to people's expectations due to the noise contamination in the images. Thus, filtering out the noise while preserving vital image features is an essential requirement. Existing denoising methods have assumptions, on the probability distribution in which the contaminated noise is sampled, for the method to attain its expected denoising performance. In this paper, the recent Gramianābased filtering scheme to remove noise sampled from five prominent probability distributions from selected images is utilized. This method preserves image smoothness by adopting patches partitioned from the image, rather than pixels, and retains vital image features by performing denoising on the manifold underlying the patch space rather than in the image domain. Its denoising performance is validated, using six benchmark computer vision test images applied to two stateāofātheāart denoising methods, namely BM3D andĀ KāSVD