亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of homoscedasticity is often supposed in existing studies. However, this assumption is restrictive and often unrealistic in practice. Therefore, in this paper, we consider the allometric extension model, that is, the directions of the first eigenvectors of two covariance matrices and the direction of the difference of two mean vectors coincide, and we provide a non-asymptotic bound of the error probability of the spectral clustering algorithm for the allometric extension model. As a byproduct of the result, we obtain the consistency of the clustering method in high-dimensional settings.

We analyse a numerical scheme for a system arising from a novel description of the standard elastic--perfectly plastic response. The elastic--perfectly plastic response is described via rate-type equations that do not make use of the standard elastic-plastic decomposition, and the model does not require the use of variational inequalities. Furthermore, the model naturally includes the evolution equation for temperature. We present a low order discretisation based on the finite element method. Under certain restrictions on the mesh we subsequently prove the existence of discrete solutions, and we discuss the stability properties of the numerical scheme. The analysis is supplemented with computational examples.

We explore a link between complexity and physics for circuits of given functionality. Taking advantage of the connection between circuit counting problems and the derivation of ensembles in statistical mechanics, we tie the entropy of circuits of a given functionality and fixed number of gates to circuit complexity. We use thermodynamic relations to connect the quantity analogous to the equilibrium temperature to the exponent describing the exponential growth of the number of distinct functionalities as a function of complexity. This connection is intimately related to the finite compressibility of typical circuits. Finally, we use the thermodynamic approach to formulate a framework for the obfuscation of programs of arbitrary length -- an important problem in cryptography -- as thermalization through recursive mixing of neighboring sections of a circuit, which can viewed as the mixing of two containers with ``gases of gates''. This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits with same size and functionality that cannot be connected via local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide, a statement that implies the collapse of the polynomial hierarchy of complexity theory to its first level.

We develop a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. In order to numerically reproduce the blow-up phenomena, we propose a rule of scaling transformation, which is a variant of what was successfully used in the case of nonlinear parabolic equations. A careful study of the convergence of the proposed scheme is carried out and several numerical examples are performed in illustration.

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.

Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A quadratization reveals new variables and structures of a model, which may be easier to analyze, simulate, control, and provides a convenient parametrization for learning. This paper presents novel theory, algorithms and software capabilities for quadratization of non-autonomous ODEs. We provide existence results, depending on the regularity of the input function, for cases when a quadratic-bilinear system can be obtained through quadratization. We further develop existence results and an algorithm that generalizes the process of quadratization for systems with arbitrary dimension that retain the nonlinear structure when the dimension grows. For such systems, we provide dimension-agnostic quadratization. An example is semi-discretized PDEs, where the nonlinear terms remain symbolically identical when the discretization size increases. As an important aspect for practical adoption of this research, we extended the capabilities of the QBee software towards both non-autonomous systems of ODEs and ODEs with arbitrary dimension. We present several examples of ODEs that were previously reported in the literature, and where our new algorithms find quadratized ODE systems with lower dimension than the previously reported lifting transformations. We further highlight an important area of quadratization: reduced-order model learning. This area can benefit significantly from working in the optimal lifting variables, where quadratic models provide a direct parametrization of the model that also avoids additional hyperreduction for the nonlinear terms. A solar wind example highlights these advantages.

It is disproved the Tokareva's conjecture that any balanced boolean function of appropriate degree is a derivative of some bent function. This result is based on new upper bounds for the numbers of bent and plateaued functions.

For a singular integral equation on an interval of the real line, we study the behavior of the error of a delta-delta discretization. We show that the convergence is non-uniform, between order $O(h^{2})$ in the interior of the interval and a boundary layer where the consistency error does not tend to zero.

In settings where interference between units is possible, we define the prevelance of peer effects to be the number of units who are affected by the treatment of others. This quantity does not fully identify a peer effect, but may be used to show whether peer effects are widely prevalent. Given a randomized experiment with binary-valued outcomes, methods are presented for conservative point estimation and one-sided interval estimation. To show asymptotic coverage of our intervals in settings not previously covered, we provide a central limit theorem that combines local dependence and sampling without replacement. Consistency and minimax properties of the point estimator are shown as well. The approach is demonstrated on an experiment in which students were treated for a highly transmissible parasitic infection, for which we find that a significant fraction of students were affected by the treatment of schools other than their own.

Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.