We discuss the properties of causal LTI operators on weighted ？2 spaces for different choices of the weighting sequence {w（t）}t∈Z. Problems of closability of unstable causal LTI convolution operators are also disc...We discuss the properties of causal LTI operators on weighted ？2 spaces for different choices of the weighting sequence {w（t）}t∈Z. Problems of closability of unstable causal LTI convolution operators are also discussed. We shall provide a new type of argument concerning causal LTI operators and robust design that can be applied to a large class of weighted ？2 spaces on Z.展开更多
Analysis of a four-dimensional displacement vector on the fabric of space-time in the special or general case into two Four-dimensional vectors, according to specific conditions leads to the splitting of the total fab...Analysis of a four-dimensional displacement vector on the fabric of space-time in the special or general case into two Four-dimensional vectors, according to specific conditions leads to the splitting of the total fabric of space-time into a positive subspace-time that represents the space of causality and a negative subspace-time which represents a space without causality, thus, in the special case, we have new transformations for the coordinates of space and time modified from Lorentz transformations specific to each subspace, where the contraction of length disappears and the speed of light is no longer a universal constant. In the general case, we have new types of matric tensor, one for positive subspace-time and the other for negative subspace-time. We also find that the speed of the photon decreases in positive subspace-time until it reaches zero and increases in negative subspace-time until it reaches the speed of light when the photon reaches the Schwarzschild radius.展开更多
A causal-directed graphical space-time model has been suggested in which the recurrence phenomena that happen in history and science can be naturally explained. In this Ramsey theorem inspired model, the regular and r...A causal-directed graphical space-time model has been suggested in which the recurrence phenomena that happen in history and science can be naturally explained. In this Ramsey theorem inspired model, the regular and repeated patterns are interpreted as identical or semi-identical space-time causal chains. The “same colored paths and subgraphs” in the classical Ramsey theorem are interpreted as identical or semi-identical causal chains. In the framework of the model, Poincare recurrence and the cosmological recurrence arise naturally. We use Ramsey theorem to prove that there’s always a possibility of predictability no matter how chaotic the system is.展开更多
The distinctions between locality and non-locality as well as causality and excess correlation may be related to coupling between increments of space-time or to the total space-time within the universe as a unit. The ...The distinctions between locality and non-locality as well as causality and excess correlation may be related to coupling between increments of space-time or to the total space-time within the universe as a unit. The most likely candidates for the latter are the proton and the electron when related by Minkowski’s space-time. When two velocities: light in a vacuum for locality and the “entanglement” velocity based upon parameters that define the universe for non-locality, are considered the two times required to produce identities for the -v<sup>2</sup>t<sup>2</sup> components are frequencies whose energies approximate the neutral hydrogen line (primarily associated with shifts in electron spin direction) and the mass equivalence of a proton. The values for the additional three spatial dimensions required to produce a solution whose square root is not imaginary and greater than zero are within the domains of the surface areas of the human cerebrum. Detailed calculations converge to show that the proportions of energy that represent the electron’s Compton energy and the proton’s mass equivalent may be central to the condition of excess correlation within the cerebral volume. Proton channels within the neuronal cell plasma membranes whose pH-dependent specific currents produce the required magnetic field strengths could be the physical substrates by which excess correlations between brain activities of human subjects separated by non-local distances might occur. If protons are considered as the basic Eddington (number) units of the universe then Mach’s principle that any component of the universe is determined by all of its components may be testable empirically.展开更多
The proposed work handles the concept of fuzzy space as a set of real numbers with a set finite membership function. Extending standard arithmetic operations through a fuzzy space, the fuzzy Green’s function is creat...The proposed work handles the concept of fuzzy space as a set of real numbers with a set finite membership function. Extending standard arithmetic operations through a fuzzy space, the fuzzy Green’s function is created here with an analysis of its behavior inside and outside the light cone. The fuzzy causality principle is generalized to field models. Also, this work demonstrates the ability to use fuzzy space to regularize divergences in quantum field theory. The passage to the limit to a system of interacting particles enables the obtaining of the dissipative projection operator, represented earlier. The Liouville equation is solved here by successive approximations in the range of times much larger than the typical scale of fuzziness, by assuming the interaction as a small parameter. As well, here was applied the standard diagram technique.展开更多
目的 图像复原是计算机视觉领域的经典研究问题。选择性状态空间模型(selective state space model,selective SSM)因其高效的序列建模能力,广泛应用于各类图像复原任务。另外,非局部图像块之间存在依赖关系,能够辅助提升复原性能。而传...目的 图像复原是计算机视觉领域的经典研究问题。选择性状态空间模型(selective state space model,selective SSM)因其高效的序列建模能力,广泛应用于各类图像复原任务。另外,非局部图像块之间存在依赖关系,能够辅助提升复原性能。而传统SSM采用确定性的令牌(token)扫描方式,仅能提取令牌序列的单向依赖关系。此时,令牌间的关系建模因在序列中的先后顺序受到因果性制约,这与图像块之间的非因果相互关系形成冲突,限制了复原性能的进一步提升。针对此问题,提出一种面向图像复原的非因果选择性状态空间模型,旨在赋予SSM建模令牌之间非因果依赖关系的能力。方法 为解决SSM在因果性建模与图像内容非因果关系之间的矛盾,提出随机扫描策略,突破了传统扫描方式在因果性和空间限制上的局限,实现了令牌序列之间的非因果建模。具体而言,构建了随机重排和逆重排函数,实现了非固定次序下的令牌扫描,有效建模了不同令牌之间的非因果依赖关系。此外,针对图像退化干扰存在空间尺度变化和形态结构复杂的特点,融合多尺度先验构建了具有局部与全局信息互补性的非因果Mamba模型(non-causal Mamba,NCMamba),实现了对于各类图像复原任务的有效适配。结果 实验分别在图像去噪、去模糊和去阴影任务上进行,验证了所提非因果建模和局部—全局互补策略的有效性。与现有方法相比,所提模型在图像去阴影数据集SRD(shadow removal dataset)上的峰值信噪比提升0.86 dB。结论 面向图像复原任务,构建了非因果选择性状态空间模型,建模了令牌之间的非因果依赖关系,实现了局部与全局信息的有效互补,显著提升了复原性能。所提方法在主客观评价指标上均取得优异性能,为图像复原领域提供了新的解决方案。展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11271059)
文摘We discuss the properties of causal LTI operators on weighted ？2 spaces for different choices of the weighting sequence {w（t）}t∈Z. Problems of closability of unstable causal LTI convolution operators are also discussed. We shall provide a new type of argument concerning causal LTI operators and robust design that can be applied to a large class of weighted ？2 spaces on Z.
文摘Analysis of a four-dimensional displacement vector on the fabric of space-time in the special or general case into two Four-dimensional vectors, according to specific conditions leads to the splitting of the total fabric of space-time into a positive subspace-time that represents the space of causality and a negative subspace-time which represents a space without causality, thus, in the special case, we have new transformations for the coordinates of space and time modified from Lorentz transformations specific to each subspace, where the contraction of length disappears and the speed of light is no longer a universal constant. In the general case, we have new types of matric tensor, one for positive subspace-time and the other for negative subspace-time. We also find that the speed of the photon decreases in positive subspace-time until it reaches zero and increases in negative subspace-time until it reaches the speed of light when the photon reaches the Schwarzschild radius.
文摘A causal-directed graphical space-time model has been suggested in which the recurrence phenomena that happen in history and science can be naturally explained. In this Ramsey theorem inspired model, the regular and repeated patterns are interpreted as identical or semi-identical space-time causal chains. The “same colored paths and subgraphs” in the classical Ramsey theorem are interpreted as identical or semi-identical causal chains. In the framework of the model, Poincare recurrence and the cosmological recurrence arise naturally. We use Ramsey theorem to prove that there’s always a possibility of predictability no matter how chaotic the system is.
文摘The distinctions between locality and non-locality as well as causality and excess correlation may be related to coupling between increments of space-time or to the total space-time within the universe as a unit. The most likely candidates for the latter are the proton and the electron when related by Minkowski’s space-time. When two velocities: light in a vacuum for locality and the “entanglement” velocity based upon parameters that define the universe for non-locality, are considered the two times required to produce identities for the -v<sup>2</sup>t<sup>2</sup> components are frequencies whose energies approximate the neutral hydrogen line (primarily associated with shifts in electron spin direction) and the mass equivalence of a proton. The values for the additional three spatial dimensions required to produce a solution whose square root is not imaginary and greater than zero are within the domains of the surface areas of the human cerebrum. Detailed calculations converge to show that the proportions of energy that represent the electron’s Compton energy and the proton’s mass equivalent may be central to the condition of excess correlation within the cerebral volume. Proton channels within the neuronal cell plasma membranes whose pH-dependent specific currents produce the required magnetic field strengths could be the physical substrates by which excess correlations between brain activities of human subjects separated by non-local distances might occur. If protons are considered as the basic Eddington (number) units of the universe then Mach’s principle that any component of the universe is determined by all of its components may be testable empirically.
文摘The proposed work handles the concept of fuzzy space as a set of real numbers with a set finite membership function. Extending standard arithmetic operations through a fuzzy space, the fuzzy Green’s function is created here with an analysis of its behavior inside and outside the light cone. The fuzzy causality principle is generalized to field models. Also, this work demonstrates the ability to use fuzzy space to regularize divergences in quantum field theory. The passage to the limit to a system of interacting particles enables the obtaining of the dissipative projection operator, represented earlier. The Liouville equation is solved here by successive approximations in the range of times much larger than the typical scale of fuzziness, by assuming the interaction as a small parameter. As well, here was applied the standard diagram technique.
