Fast Descent Method Research Articles

Distributed soft video transmission based on hybrid digital and analog scheme

This study presents a novel distributed soft video delivery scheme using hybrid digital and analog framework, which realizes a relatively lightweight encoder as well as good robustness. Specifically, after applying scalar quantization to the interframes, the scaled analog information (quantization error) and the scaled digital information (quantized source) are superimposed and then transmitted. In this way, the proposed scheme directly delivers pseudo-analog symbols over the orthogonal frequency division multiplexing (OFDM) channels and involves no complicated digital codec. Moreover, we utilize cross-frame correlation to implement a distributed paradigm which further reduces the encoder complexity since the complex motion estimation and compensation algorithms are transferred to the decoder. Accordingly, the power distortion optimization scheme, which resolve the allocation of power and the parameters optimization to achieve minimum transmission distortion, is proposed. To solve it, first, we formulate the power distortion expressions regarding quantization parameters and power allocation coefficients. Subsequently, we divide the problem into two sub-problems based on the fast coordinate descent method and further propose a greedy iterative algorithm to optimize them. We also develop a data-driven optimization algorithm based on deep learning that reduces the additional delay brought by the iterative optimization method. At the receiver, we estimate the quantization output and quantization error by the modified linear least squares estimation with the virtual noise variance. Based on the simulation results, the proposed framework has a better performance in terms of peak signal-to-noise ratio and structural similarity than the relevant cutting-edge schemes while maintaining good robustness.

Impact of Non-Gaussian Noise and Time Delay on Stability and Stochastic Resonance for a FitzHugh-Nagumo Neural System Subjected to a Multiplicative Periodic Signal

In this paper, we focus on the investigations on the stochastic stability and the stochastic resonance (SR) phenomena for a FitzHugh-Nagumo system with time delay induced by a multiplicative non-Gaussian colored noise and an additive Gaussian colored noise. By use of the fast descent method, the unified colored noise approximation and the two-state theory for the SR, the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) caused by different noise terms and time delay are explored. The investigation results indicate that the two noise intensities, time delay and the departure parameter from the Gaussian noise can all reduce the probability density around the two stable states and destroy the stability of the neural system; while the two noise correlation times [Formula: see text] and [Formula: see text] can both improve the probability density around both stable states and reinforce the biological stability of the neural system. As regards the SNR, it is found that the two noise intensities and the departure coefficient can all weaken the SR effect, while time delay [Formula: see text] and the correlation time [Formula: see text] of the multiplicative noise will always magnify the SR phenomenon. It is worth to mention that the correlation time [Formula: see text] of the additive noise can stimulate the SR effect, but not alter the maximum of the SNR.

GPU-based simulation of cloth wrinkles at submillimeter levels

In this paper, we study physics-based cloth simulation in a very high resolution setting, presumably at submillimeter levels with millions of vertices, to meet perceptual precision of our human eyes. State-of-the-art simulation techniques, mostly developed for unstructured triangular meshes, can hardly meet this demand due to their large computational costs and memory footprints. We argue that in a very high resolution, it is more plausible to use regular meshes with an underlying grid structure, which can be highly compatible with GPU acceleration like high-resolution images. Based on this idea, we formulate and solve the nonlinear optimization problem for simulating high-resolution wrinkles, by a fast block-based descent method with reduced memory accesses. We also investigate the development of the collision handling component in our system, whose performance benefits greatly from the grid structure. Finally, we explore various issues related to the applications of our system, including initialization for fast convergence and temporal coherence, gathering effects, inflation and stuffing models, and mesh simplification. We can treat our system as a quasistatic wrinkle synthesis tool, run it as a standalone dynamic simulator, or integrate it into a multi-resolution solver as an additional component. The experiment demonstrates the capability, efficiency and flexibility of our system in producing a variety of high-resolution wrinkles effects.

Stochastic delayed dynamics for a metapopulation system induced by non-Gaussian noise and a multiplicative periodic signal

In this paper, we focus on shedding light on the stochastic stability, the MFPT and stochastic resonance (SR) phenomena for a metapopulation system in the presence of time delay, the colored cross-correlated multiplicative non-Gaussian noise and the additive Gaussian colored noise. By use of the fast descent method and the approximation of the unified colored noise, the dynamical behaviors for the modified potential function and the signal-to-noise ratio (SNR) are analyzed in detail. It is discovered that the additive Gaussian colored noise, the noise correlation strength as well as its self-correlation time can all impair the stability of the population system and speed up the population decline. Conversely, the two self-correlation times of the external and internal noises can both consolidate the stability of the biological system and prolong the survival time of the population. With regard to the SNR for the metapopulation system caused by the noise terms and time delay, it is revealed that time delay, the noise correlation strength and its correlation time can all along weaken the SR phenomenon. On the contrary, two noise self-correlation times are able to amplify effectively the resonance effect. It is worth noting that the parameter of non-Gaussianity $$ q $$ in the SNR- $$ \tau $$ and SNR- $$ \lambda $$ plots can initially weaken the SR phenomena and then enhance the maximum of the SNR as it is further increased.

Convergence analysis of the Fast Subspace Descent method for convex optimization problems

Author(s): Chen, L; Hu, X; Wise, SM | Abstract: The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed. The new method, the fast subspace descent (FASD) scheme, which generalizes classical FAS, can be recast as an inexact version of nonlinear multigrid methods based on space decomposition and subspace correction. The local problem in each subspace can be simplified to be linear and one gradient descent iteration (with an appropriate step size) is enough to ensure a global linear (geometric) convergence of FASD for convex optimization problems.

Local Algorithms for Minimizing the Force Field for 3D Representation of Macromolecules

The majority of problems in structural computational biology require minimization of the energy function (force field) defined on the molecule geometry. This makes it possible to determine properties of molecules, predict the correct arrangement of protein chains, find the best molecular docking for complex formation, verify hypotheses concerning the protein design, and solve other problems arising in modern drug development. In the case of low-molecular compounds (consisting of less than 250 atoms), the problem of finding the geometry that minimizes the energy function is well studied. The minimization of macromolecules (in particular, proteins) consisting of tens of thousands of atoms is more difficult. However, a distinctive feature of statements of these problems is that initial approximations that are close to the solution are often available. Therefore, the original problem can be formulated as a problem of nonconvex optimization in the space of about $${{10}^{4}}$$ variables. The complexity of computing the function and its gradient is quadratic in the number variables. A comparative analysis of gradient-free methods with gradient-type methods (gradient descent, fast gradient descent, conjugate gradient, and quasi-Newton methods) in their GPU implementations is carried out.

Stochastic Kinetics for a FitzHugh–Nagumo Neural System with Time Delay Driven by Non-Gaussian Noise and a Multiplicative Periodic Signal

In the present paper, the stability and the phenomena of stochastic resonance (SR) for a FitzHugh–Nagumo (FHN) system with time delay driven by a multiplicative non-Gaussian noise and an additive Gaussian white noise are investigated. By using the fast descent method, unified colored noise approximation and the two-state theory for the SR, the expressions for the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) are obtained. The research results show that the two noise intensities and time delay can always decrease the probability density at the two stable states and impair the stability of the neural system; while the noise correlation time [Formula: see text] can increase the probability density around both stable states and consolidate the stability of the neural system. Furthermore, the other noise correlation time [Formula: see text] can increase the probability at the resting state, but reduce that around the excited state. With respect to the SNR, it is discovered that the two noise strengths can both weaken the SR effect, while time delay [Formula: see text] and the departure parameter [Formula: see text] will always amplify the SR phenomenon. Moreover, the noise correlation time [Formula: see text] can motivate the SR effect, but not alter the peak value of the SNR. What’s most interesting is that the other noise correlation time [Formula: see text] can not only stimulate the SR phenomenon, but also results in the occurrence of two resonant peaks, whose heights are simultaneously improved because of the action of [Formula: see text].

Impact of Time Delay and Non-Gaussian Noise on Stochastic Resonance and Stability for a Stochastic Metapopulation System Driven by a Multiplicative Periodic Signal

In the present paper, the stability of the population system and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by the terms of time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal are investigated in detail. By applying the fast descent method, the unified colored noise approximation and the SR theory, the expressions of the steady-state probability function and the SNR are derived. It is shown that multiplicative non-Gaussian noise, the additive Gaussian noise and time delay can all weaken the stability of the population system, and even result in population extinction. Conversely, the two noise correlation times can both strengthen the stability of the biological system and contribute to group survival. In regard to the SNR for the metapopulation system impacted by the noise terms and time delay, it is revealed that the correlation time of the multiplicative noise can improve effectively the SR effect, while time delay would all along restrain the SR phenomena. On the other hand, although the additive noise and its correlation time can stimulate easily the SR effect, they cannot change the maximum of the SNR. In addition, the departure parameter from the Gaussian noise and the multiplicative noise play the opposite roles in motivating the SR effect in different cases.

Fast Gradient Descent for Convex Minimization Problems with an Oracle Producing a (δ, L)-Model of Function at the Requested Point

A new concept of $$(\delta ,L)$$ -model of a function that is a generalization of the Devolder–Glineur–Nesterov $$(\delta ,L)$$ -oracle is proposed. Within this concept, the gradient descent and fast gradient descent methods are constructed and it is shown that constructs of many known methods (composite methods, level methods, conditional gradient and proximal methods) are particular cases of the methods proposed in this paper.

A Constrained Sparse-Representation-Based Binary Hypothesis Model for Target Detection in Hyperspectral Imagery

In this paper, we propose a novel constrained sparse-representation-based binary hypothesis model for target detection in hyperspectral imagery. This model is based on the concept that a target pixel can only be linearly represented by the union dictionary combined by the background dictionary and target dictionary, while a background pixel can be linearly represented by both the background dictionary and the union dictionary. To be physically meaningful, the non-negativity constraint is imposed to the weight vector. To suppress the target signals in the background dictionary, the upper bound constraint is also imposed to the weight vector. These upper bounds are adaptively estimated by the similarities between the atoms in the background dictionary and target. Then, the weight vectors under different hypotheses are recovered by a fast coordinate descent method. Finally, both the residual difference and weight difference between the two hypotheses are used to perform the target detection. An important advantage of the proposed method is the robustness to varying target contamination. Extensive experiments conducted on real and synthetic hyperspectral datasets have demonstrated the superiority of the proposed detector in detection performance and computational cost. Specifically, for the Avon dataset, our method achieves the highest area under the receiver operating characteristic (ROC) curve of 99.91%, and achieves the shortest runtime of 109.76 s.

Time delay and cross-correlated Gaussian noises-induced stochastic stability and regime shift between steady states for an insect outbreak system

In this paper, we focus on investigating the stochastic stability and the regime transition between the endangered state and the boom state for a time-delayed insect growth system driven by correlated external and internal noises. By use of the Fokker–Planck equation, the method of small time delay approximation and the fast descent method, we explore in detail the joint action of noise terms and time delay on the mean reproduction and depression time for the insect population. Our investigations indicate that the pseudo-resonance phenomenon of the mean first-passage time (MFPT) occurs because of the impact of different noises and time delay. Through the numerical calculation, it is discovered that multiplicative noise can speed up the shift of the insect population from the boom state to the endangered one, while the noise correlation and time delay can propel the insect system to evolve from the endangered state to the boom state and improve the biological stability. In addition, the impact of the additive noise on the stability of the biological system depends on the positive and negative situation of the noise correlation. On the other hand, during the process of suppressing the insect explosion, it is beneficial to the pest control to amplify the association noise strength and weaken the intensities of the multiplicative, additive noises and time delay. However, during the process of eliminating the pests, it can produce nice effect on the disinsection to increase time delay, the intensities of multiplicative and additive noises and weaken the strength of noise correlation.

Text Image Deblurring Using Kernel Sparsity Prior.

Previous methods on text image motion deblurring seldom consider the sparse characteristics of the blur kernel. This paper proposes a new text image motion deblurring method by exploiting the sparse properties of both text image itself and kernel. It incorporates the L 0 -norm for regularizing the blur kernel in the deblurring model, besides the L 0 sparse priors for the text image and its gradient. Such a L 0 -norm-based model is efficiently optimized by half-quadratic splitting coupled with the fast conjugate descent method. To further improve the quality of the recovered kernel, a structure-preserving kernel denoising method is also developed to filter out the noisy pixels, yielding a clean kernel curve. Experimental results show the superiority of the proposed method. The source code and results are available at: https://github.com/shenjianbing/text-image-deblur.

Scalable Discrete Supervised Multimedia Hash Learning With Clustering

The hashing method maps similar data of various types to binary hashcodes with smaller hamming distance, and it has received broad attention due to its low-storage cost and fast retrieval speed. However, the existing limitations make the present algorithms difficult to deal with for large-scale data sets: 1) discrete constraints are involved in the learning of the hash function and 2) pairwise or triplet similarity is adopted to generate efficient hashcodes, resulting in both time and space complexity greater than $O(n^{2})$ . To address these issues, we propose a novel discrete supervised hash learning framework that can be scalable to large-scale data sets of various types. First, the discrete learning procedure is decomposed into a binary classifier learning scheme and binary codes learning scheme, which makes the learning procedure more efficient. Second, by adopting the asymmetric low-rank matrix factorization , we propose the fast clustering-based batch coordinate descent method, such that the time and space complexity are reduced to $O(n)$ . The proposed framework also provides a flexible paradigm to incorporate with arbitrary hash function, including deep neural networks and kernel methods, as well as any types of data to hash, including images and videos. Experiments on large-scale data sets demonstrate that the proposed method is superior or comparable with the state-of-the-art hashing algorithms.

Time delay and non-Gaussian noise-induced stochastic stability and stochastic resonance for a metapopulation system subjected to a multiplicative periodic signal

In this paper, the stable state transformation and the effect of the stochastic resonance (SR) for a metapopulation system are investigated, which is disturbed by time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal. By use of the fast descent method, the approximation of the unified colored noise and the SR theory, the dynamical behaviors for the steady-state probability function and the SNR are analyzed. It is found that non-Gaussian noise, the colored Gaussian noise and time delay can all reduce the stability of the biological system, and even lead to the population extinction. Inversely, the self-correlation times of two noises can both increase the stability of the population system and be in favor of the population reproduction. As regards the SNR for the metapopulation system induced by the noise terms and time delay, it is discovered that time delay and the correlation time of the multiplicative noise can effectively enhance the SR effect, while the multiplicative noise and the correlation time of the additive noise would all the time suppress the SR phenomena. In addition, the additive noise can effectively motivate the SR effect, but not alter the peak value of the SNR. It is worth noting that the departure parameter from the Gaussian noise plays the diametrical roles in stimulating the SR effect in different cases.

Impact of colored cross-correlated noises on stochastic resonance and mean extinction rate for a metapopulation system with a multiplicative periodic signal

In this paper, we aim to explore the mean extinction rate and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by a multiplicative periodic signal, colored cross-correlated multiplicative and additive Gaussian noises. By use of the fast descent method and the adiabatic approximation theory for the signal-to-noise ratio, we obtain the expression of the signal-to-noise ratio (SNR). Numerical results indicate that the various SR phenomena occur in the metapopulation system due to the variation of the noise terms and the correlation time. Specifically, the noise correlation always plays a critical role in motivating the SR phenomenon, while the multiplicative noise exerts the inhibition effect on the SR. Interestingly, the weak additive noise can stimulate the resonant peak of the SNR, while the further increase of the noise intensity will lead to the reduction of the SR effect. On the other hand, the noise correlation time τ plays antipodal roles in motivating the SR phenomenon under different circumstances. With regard to the mean extinction rate of the population from the boom state to the extinction one, by performing the numerical calculations, it is found that the additive noise always accelerate the extinction of the population, while the correlation noise will slow down the decline for the population. The role that the noise correlation time plays in the population extinction depends on the values that λ takes.

Double time-delays induced stochastic dynamical characteristics for a metapopulation system subjected to the associated noises and a multiplicative periodic signal

In this paper, we aim to investigating in detail the stability of the system, the mean extinction time and stochastic resonance (SR) phenomena caused by a multiplicative periodic signal for a dual time-delayed metapopulation system subjected to cross-correlated noises. By use of the fast descent method, the small time delay approximation method and the SR theory, we obtain the expressions of the steady state probability distribution function, the mean first-passage time and signal-to-noise ratio (SNR). Numerical results indicate that the multiplicative, additive and association noises together with time delay τ can all accelerate the transition from the stable state of big density to the extinction one and play significant roles in weakening the stability and shortening the mean extinction time of the metapopulation. In particular, the additive noise and time delay τ can result in the crash of the system, while another time delay θ can strengthen the biological system stability and extend the declining time for the population. On the other hand, with respect to the SNR, the figures show that time delay τ plays entirely antipodal roles in motivating stochastic resonance (SR) in a variety of different situations. Conversely, the multiplicative noise intensity Q and time delay θ all along produce negative effect on exciting the SR. Meanwhile, the increase of the weak additive noise intensity M can stimulate the SR phenomenon, but the bigger values of M will suppress the SNR and SR phenomenon. The strength of the noise correlation λ plays an important role in restraining the SR in most cases except that it does in the plot of SNR-Q.

Stability and Stochastic Resonance for a Time-Delayed Cancer Development System Subjected to Noises and Multiplicative Periodic Signal

In this paper, the stability and the phenomenon of stochastic resonance (SR) for a stochastic time-delayed cancer development system that is induced by the multiplicative periodic signal, the multiplicative and the additive noises are investigated. By using the fast descent method, small time delay method and the two-state theory, the expressions of the steady state probability distribution function and the signal-to-noise ratio (SNR) are obtained. Numerical results reflect that the multiplicative and additive noise always restrain the diffusion of the cancer cells. Whereas, the time delay can not only control the spread of the tumor cells, but also suppress the extinction of cancer cells. Meanwhile, the conventional SR occurs in the tumor cell growth model under the excitation of different noises and time delay. In conclusion, the multiplicative noise always plays a critical role in restraining SR, a smaller additive noise can stimulate the SR, but the larger additive noise can weaken the SR and SNR. In particular, the time delay displays relatively complicated effects on the SR phenomenon of the system. It plays different roles in motivating or suppressing SR under the different conditions of parameters.

Stochastic resonance for a forest growth system subjected to non-Gaussian noises and a multiplicative periodic signal

In this paper, the stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a forest growth system which is excited by additive Gaussian noise, multiplicative non-Gaussian noise and noise correlation time is investigated. According to the fast descent method, the unified colored noise approximation and the SR theory, the analytical expression of the signal-to-noise ratio (SNR)is derived in the adiabatic limit. Via numerical calculations, each effect of the addictive noise intensity, the multiplicative noise intensity and the departure parameter from the Gaussian noise upon the signal-to-noise ratio (SNR) is discussed. It is shown that the addictive noise intensity always plays a significant role in stimulating the SR phenomenon. Conversely, the multiplicative noise intensity generally plays a remarkable role in restraining the effect of SR in most cases except for the case of M=0.01. Moreover, the noise correlation time can also excite the SR effect. On the other hand, the departure parameter from the Gaussian noise and the forest growth rate can produce entirely different effects on the SNR under the different conditions of the system parameters.

Impact of two types of time delays and cross-correlated multiplicative and additive noises on stability and stochastic resonance for a metapopulation system

In this paper, we investigate the stability and the shift between the extinction state and the stable one of a large density and the stochastic resonance (SR) for a metapopulation system subjected to two types of time delay terms, cross-correlation noises and multiplicative signal. By using the fast descent method and the method of small delay approximation, the expressions of the effective potential function and the signal-to-noise ratio (SNR) are obtained. We denote by Q the intensity of the multiplicative noise, and M the intensity of the additive noise, θ and τ the two time delay terms introduced into the metapopulation system. Our main results show some facts that time delay θ and the strength of correlation noise λ can restrain the development of the metapopulation, while the other term of time delay τ can accelerate the expansion of the population from the extinction state to the large stable one. We discover that it is possible to enhance the signal-to-noise ratio by adjusting the intensities of the multiplicative, additive noises and the time delays of the stochastic metapopulation system

Combined action of time-delay and colored cross-associated multiplicative and additive noises on stability and stochastic resonance for a stochastic metapopulation system

In this paper, the transition between the stable state of a big density and the extinction state and stochastic resonance (SR) for a time-delayed metapopulation system disturbed by colored cross-correlated noises are investigated. By applying the fast descent method, the small time-delay approximation and McNamara and Wiesenfeld’s SR theory, we investigate the impacts of time-delay, the multiplicative, additive noises and colored cross-correlated noise on the SNR and the shift between the two states of the system. Numerical results show that the multiplicative, additive noises and time-delay can all speed up the transition from the stable state to the extinction state, while the correlation noise and its correlation time can slow down the extinction process of the population system. With respect to SNR, the multiplicative noise always weakens the SR effect, while noise correlation time plays a dual role in motivating the SR phenomenon. Meanwhile, time-delay mainly plays a negative role in stimulating the SR phenomenon. Conversely, it could motivate the SR effect to increase the strength of the cross-correlation noise in the SNR-β plot, while the increase of additive noise intensity will firstly excite SR, and then suppress the SR effect.