Reduced Dimension, Biophysical Neuron Models Constructed From Observed Data

Using methods from nonlinear dynamics and interpolation techniques from applied mathematics, we show how to use data alone to construct discrete time dynamical rules that forecast observed neuron properties. These data may come from from simulations of a Hodgkin-Huxley (HH) neuron model or from laboratory current clamp experiments. In each case the reduced dimension data driven forecasting (DDF) models are shown to predict accurately for times after the training period.When the available observations for neuron preparations are, for example, membrane voltage V(t) only, we use the technique of time delay embedding from nonlinear dynamics to generate an appropriate space in which the full dynamics can be realized.The DDF constructions are reduced dimension models relative to HH models as they are built on and forecast only observables such as V(t). They do not require detailed specification of ion channels, their gating variables, and the many parameters that accompany an HH model for laboratory measurements, yet all of this important information is encoded in the DDF model.As the DDF models use only voltage data and forecast only voltage data they can be used in building networks with biophysical connections. Both gap junction connections and ligand gated synaptic connections among neurons involve presynaptic voltages and induce postsynaptic voltage response. Biophysically based DDF neuron models can replace other reduced dimension neuron models, say of the integrate-and-fire type, in developing and analyzing large networks of neurons.When one does have detailed HH model neurons for network components, a reduced dimension DDF realization of the HH voltage dynamics may be used in network computations to achieve computational efficiency and the exploration of larger biological networks.

Alpenprojekt

Alpenprojekt videos register the action of cutting the skyline in the alpine mountains. The footage was taken at different sites in the Alps. The cutouts evoke the European tradition from the 18th century to depict portraits with scissors and paper. A deliberate intent to apprehend the landscape within a unique line in a reduced dimension is the main issue in Alpenprojekt I and II. To react in the face of this specific landscape as an effort to embrace what is not controllable became a fundamental issue in the Alpenprojekt series of works. Alpenprojekt began with artistic research related to the southern German region closely connected with its physical landscape. Its representation was then perceived as a memory heritage of historical facts, either forgotten or intentionally lost. The entire project is called Trilogy of the Mountains, and it is related to memory and history. Trilogy of the Mountains comprises three phases: Alpenprojekt, based on the alpine landscape; the second one approaches Beckton Alps, an artificial mountain in east London; and the third part is related to artificial mountains made with war debris in Germany. Each piece of the Trilogy comprises a series of works. The project was initially developed based on landscapes where the notion of Romanticism is still present. Then the project was set toward the post-industrialization period—and finally related to reshaping the topography in Germany after WWII. In Trilogy of Mountains, the tension between natural and artificial is a central issue, being rather complementary than the opposite.

The structure of the local detector of the reprint model of the object in the image

Currently, methods for recognizing objects in images work poorly and use intellectually unsatisfactory methods. The existing identification systems and methods do not completely solve the problem of identification, namely, identification in difficult conditions: interference, lighting, various changes on the face, etc. To solve these problems, a local detector for a reprint model of an object in an image was developed and described. A transforming autocoder (TA), a model of a neural network, was developed for the local detector. This neural network model is a subspecies of the general class of neural networks of reduced dimension. The local detector is able, in addition to determining the modified object, to determine the original shape of the object as well. A special feature of TA is the representation of image sections in a compact form and the evaluation of the parameters of the affine transformation. The transforming autocoder is a heterogeneous network (HS) consisting of a set of networks of smaller dimension. These networks are called capsules. Artificial neural networks should use local capsules that perform some rather complex internal calculations on their inputs, and then encapsulate the results of these calculations in a small vector of highly informative outputs. Each capsule learns to recognize an implicitly defined visual object in a limited area of viewing conditions and deformations. It outputs both the probability that the object is present in its limited area and a set of “instance parameters” that can include the exact pose, lighting, and deformation of the visual object relative to an implicitly defined canonical version of this object. The main advantage of capsules that output instance parameters is a simple way to recognize entire objects by recognizing their parts. The capsule can learn to display the pose of its visual object in a vector that is linearly related to the “natural” representations of the pose that are used in computer graphics. There is a simple and highly selective test for whether visual objects represented by two active capsules A and B have the correct spatial relationships for activating a higher-level capsule C. The transforming autoencoder solves the problem of identifying facial images in conditions of interference (noise), changes in illumination and angle.

Tensor-Based Reduced-Dimension MUSIC Method for Parameter Estimation in Monostatic FDA-MIMO Radar

Frequency diverse array (FDA) radar has attracted much attention due to the angle and range dependence of the beam pattern. Multiple-input-multiple-output (MIMO) radar has high degrees of freedom (DOF) and spatial resolution. The FDA-MIMO radar, a hybrid of FDA and MIMO radar, can be used for target parameter estimation. This paper investigates a tensor-based reduced-dimension multiple signal classification (MUSIC) method, which is used for target parameter estimation in the FDA-MIMO radar. The existing subspace methods deteriorate quickly in performance with small samples and a low signal-to-noise ratio (SNR). To deal with the deterioration difficulty, the sparse estimation method is then proposed. However, the sparse algorithm has high computation complexity and poor stability, making it difficult to apply in practice. Therefore, we use tensor to capture the multi-dimensional structure of the received signal, which can optimize the effectiveness and stability of parameter estimation, reduce computation complexity and overcome performance degradation in small samples or low SNR simultaneously. In our work, we first obtain the tensor-based subspace by the high-order-singular value decomposition (HOSVD) and establish a two-dimensional spectrum function. Then the Lagrange multiplier method is applied to realize a one-dimensional spectrum function, estimate the direction of arrival (DOA) and reduce computation complexity. The transmitting steering vector is obtained by the partial derivative of the Lagrange function, and automatic pairing of target parameters is then realized. Finally, the range can be obtained by using the least square method to process the phase of transmitting steering vector. Method analysis and simulation results prove the superiority and reliability of the proposed method.

Direct Position Determination of Noncircular Sources with Multiple Nested Arrays: Reduced Dimension Subspace Data Fusion

Direct position determination (DPD) of noncircular (NC) sources with multiple nested arrays (NA) is investigated in this paper. Noncircular sources are used to expand the dimension of the received signal matrix, so the number of identifiable information sources and the accuracy of direct position determination are improved. Furthermore, nested array increases spatial degree of freedom. In this paper, the high-dimensional search problem of noncircular sources is investigated. Therefore, we propose algorithm dimension reduction subspace data fusion (RD-SDF) to reduce complexity and increase positioning accuracy. Simulation results show that the proposed RD-SDF algorithm for multiple nested arrays with noncircular sources has improved positioning accuracy with higher spatial degree of freedom than SDF, Capon, and two-step algorithms with uniform linear array and circular sources (CS).

Reduced-cost construction of Jacobian matrices for high-resolution inversions of satellite observations of atmospheric composition

Global high-resolution observations of atmospheric composition from satellites can greatly improve our understanding of surface emissions through inverse analyses. Variational inverse methods can optimize surface emissions at any resolution but do not readily quantify the error and information content of the posterior solution. The information content of satellite data may be much lower than its coverage would suggest because of failed retrievals, instrument noise, and error correlations that propagate through the inversion. Analytical solution of the inverse problem provides closed-form characterization of posterior error statistics and information content but requires the construction of the Jacobian matrix that relates emissions to atmospheric concentrations. Building the Jacobian matrix is computationally expensive at high resolution because it involves perturbing each emission element, typically individual grid cells, in the atmospheric transport model used as the forward model for the inversion. We propose and analyze two methods, reduced dimension and reduced rank, to construct the Jacobian matrix at greatly decreased computational cost while retaining information content. Both methods are two-step iterative procedures that begin from an initial native-resolution estimate of the Jacobian matrix constructed at no computational cost by assuming that atmospheric concentrations are most sensitive to local emissions. The reduced-dimension method uses this estimate to construct a Jacobian matrix on a multiscale grid that maintains a high resolution in areas with high information content and aggregates grid cells elsewhere. The reduced-rank method constructs the Jacobian matrix at native resolution by perturbing the leading patterns of information content given by the initial estimate. We demonstrate both methods in an analytical Bayesian inversion of Greenhouse Gases Observing Satellite (GOSAT) methane data with augmented information content over North America in July 2009. We show that both methods reproduce the results of the native-resolution inversion while achieving a factor of 4 improvement in computational performance. The reduced-dimension method produces an exact solution at a lower spatial resolution, while the reduced-rank method solves the inversion at native resolution in areas of high information content and defaults to the prior estimate elsewhere.