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

We propose (k,k') stabilizing codes, which is a type of delayless error correction codes that are useful for control over networks with erasures. For each input symbol, k output symbols are generated by the stabilizing code. Receiving any k' of these outputs guarantees stability. Thus, the system to be stabilized is taken into account in the design of the erasure codes. Our focus is on LTI systems, and we construct codes based on independent encodings and multiple descriptions. The theoretical efficiency and performance of the codes are assessed, and their practical performances are demonstrated in a simulation study. There is a significant gain over other delayless codes such as repetition codes.

In this paper, we study the \emph{type graph}, namely a bipartite graph induced by a joint type. We investigate the maximum edge density of induced bipartite subgraphs of this graph having a number of vertices on each side on an exponential scale in the length $n$ of the type. This can be seen as an isoperimetric problem. We provide asymptotically sharp bounds for the exponent of the maximum edge density as the length of the type goes to infinity. We also study the biclique rate region of the type graph, which is defined as the set of $\left(R_{1},R_{2}\right)$ such that there exists a biclique of the type graph which has respectively $e^{nR_{1}}$ and $e^{nR_{2}}$ vertices on the two sides. We provide asymptotically sharp bounds for the biclique rate region as well. We then apply our results and proof ideas to noninteractive simulation problems. We completely characterize the exponents of maximum and minimum joint probabilities when the marginal probabilities vanish exponentially fast with given exponents. These results can be seen as strong small-set expansion theorems. We extend the noninteractive simulation problem by replacing Boolean functions with arbitrary nonnegative functions, and obtain new hypercontractivity inequalities which are stronger than the common hypercontractivity inequalities. Furthermore, as an application of our results, a new outer bound for the zero-error capacity region of the binary adder channel is provided, which improves the previously best known bound, due to Austrin, Kaski, Koivisto, and Nederlof. Our proofs in this paper are based on the method of types, linear algebra, and coupling techniques.

Petri nets, equivalently presentable as vector addition systems with states, are an established model of concurrency with widespread applications. The reachability problem, where we ask whether from a given initial configuration there exists a sequence of valid execution steps reaching a given final configuration, is the central algorithmic problem for this model. The complexity of the problem has remained, until recently, one of the hardest open questions in verification of concurrent systems. A first upper bound has been provided only in 2015 by Leroux and Schmitz, then refined by the same authors to non-primitive recursive Ackermannian upper bound in 2019. The exponential space lower bound, shown by Lipton already in 1976, remained the only known for over 40 years until a breakthrough non-elementary lower bound by Czerwi{\'n}ski, Lasota, Lazic, Leroux and Mazowiecki in 2019. Finally, a matching Ackermannian lower bound announced this year by Czerwi{\'n}ski and Orlikowski, and independently by Leroux, established the complexity of the problem. Our primary contribution is an improvement of the former construction, making it conceptually simpler and more direct. On the way we improve the lower bound for vector addition systems with states in fixed dimension (or, equivalently, Petri nets with fixed number of places): while Czerwi{\'n}ski and Orlikowski prove $F_k$-hardness (hardness for $k$th level in Grzegorczyk Hierarchy) in dimension $6k$, our simplified construction yields $F_k$-hardness already in dimension $3k+2$.

We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposal recovers the Hamming distance for the vectors of the canonical basis, and more generally the classical Wasserstein distance for quantum states diagonal in the canonical basis. The proposed distance is invariant with respect to permutations of the qudits and unitary operations acting on one qudit and is additive with respect to the tensor product. Our main result is a continuity bound for the von Neumann entropy with respect to the proposed distance, which significantly strengthens the best continuity bound with respect to the trace distance. We also propose a generalization of the Lipschitz constant to quantum observables. The notion of quantum Lipschitz constant allows us to compute the proposed distance with a semidefinite program. We prove a quantum version of Marton's transportation inequality and a quantum Gaussian concentration inequality for the spectrum of quantum Lipschitz observables. Moreover, we derive bounds on the contraction coefficients of shallow quantum circuits and of the tensor product of one-qudit quantum channels with respect to the proposed distance. We discuss other possible applications in quantum machine learning, quantum Shannon theory, and quantum many-body systems.

This paper is concerned with the asymptotic distribution of the largest eigenvalues for some nonlinear random matrix ensemble stemming from the study of neural networks. More precisely we consider $M= \frac{1}{m} YY^\top$ with $Y=f(WX)$ where $W$ and $X$ are random rectangular matrices with i.i.d. centered entries. This models the data covariance matrix or the Conjugate Kernel of a single layered random Feed-Forward Neural Network. The function $f$ is applied entrywise and can be seen as the activation function of the neural network. We show that the largest eigenvalue has the same limit (in probability) as that of some well-known linear random matrix ensembles. In particular, we relate the asymptotic limit of the largest eigenvalue for the nonlinear model to that of an information-plus-noise random matrix, establishing a possible phase transition depending on the function $f$ and the distribution of $W$ and $X$. This may be of interest for applications to machine learning.

In this study, we analyze the efficiency of a protocol with discrete modulation of continuous variable non-Gaussian states, the coherent states having one photon added and then one photon subtracted (PASCS). We calculate the secure key generation rate against collective attacks using the fact that Eve's information can be bounded based on the protocol with Gaussian modulation, which in turn is unconditionally secure. Our results for a four-state protocol show that the PASCS always outperforms the equivalent coherent states protocol under the same environmental conditions. Interestingly, we find that for the protocol using discrete-modulated PASCS, the noisier the line, the better will be its performance compared to the protocol using coherent states. Thus, our proposal proves to be advantageous for performing quantum key distribution in non-ideal situations.

Interactive recommendation that models the explicit interactions between users and the recommender system has attracted a lot of research attentions in recent years. Most previous interactive recommendation systems only focus on optimizing recommendation accuracy while overlooking other important aspects of recommendation quality, such as the diversity of recommendation results. In this paper, we propose a novel recommendation model, named \underline{D}iversity-promoting \underline{D}eep \underline{R}einforcement \underline{L}earning (D$^2$RL), which encourages the diversity of recommendation results in interaction recommendations. More specifically, we adopt a Determinantal Point Process (DPP) model to generate diverse, while relevant item recommendations. A personalized DPP kernel matrix is maintained for each user, which is constructed from two parts: a fixed similarity matrix capturing item-item similarity, and the relevance of items dynamically learnt through an actor-critic reinforcement learning framework. We performed extensive offline experiments as well as simulated online experiments with real world datasets to demonstrate the effectiveness of the proposed model.

Matter evolved under influence of gravity from minuscule density fluctuations. Non-perturbative structure formed hierarchically over all scales, and developed non-Gaussian features in the Universe, known as the Cosmic Web. To fully understand the structure formation of the Universe is one of the holy grails of modern astrophysics. Astrophysicists survey large volumes of the Universe and employ a large ensemble of computer simulations to compare with the observed data in order to extract the full information of our own Universe. However, to evolve trillions of galaxies over billions of years even with the simplest physics is a daunting task. We build a deep neural network, the Deep Density Displacement Model (hereafter D$^3$M), to predict the non-linear structure formation of the Universe from simple linear perturbation theory. Our extensive analysis, demonstrates that D$^3$M outperforms the second order perturbation theory (hereafter 2LPT), the commonly used fast approximate simulation method, in point-wise comparison, 2-point correlation, and 3-point correlation. We also show that D$^3$M is able to accurately extrapolate far beyond its training data, and predict structure formation for significantly different cosmological parameters. Our study proves, for the first time, that deep learning is a practical and accurate alternative to approximate simulations of the gravitational structure formation of the Universe.

This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm adversarial perturbations, for example). Most previous work on this topic was limited in its applicability by the size of the network, network architecture and the complexity of properties to be verified. In contrast, our framework applies to a general class of activation functions and specifications on neural network inputs and outputs. We formulate verification as an optimization problem (seeking to find the largest violation of the specification) and solve a Lagrangian relaxation of the optimization problem to obtain an upper bound on the worst case violation of the specification being verified. Our approach is anytime i.e. it can be stopped at any time and a valid bound on the maximum violation can be obtained. We develop specialized verification algorithms with provable tightness guarantees under special assumptions and demonstrate the practical significance of our general verification approach on a variety of verification tasks.