Self-testing is a method to certify quantum states and measurements in a device-independent way. The device-independent certification of quantum properties is purely based on input-output measurement statistics of the involved devices with minimal knowledge about their internal workings. Bipartite pure entangled states can be self-tested, but, in the case of multipartite pure entangled states, the answer is not so straightforward. Nevertheless, \v{S}upi\'{c} et al. recently introduced a novel self-testing method for any pure entangled quantum state, which leverages network assistance and relies on bipartite entangled measurements. Hence, their scheme loses the true device-independent flavor of self-testing. In this regard, we provide a self-testing scheme for genuine multipartite pure entangle states in the true sense by employing a generalized Hardy-type non-local argument. It is important to note that our approach involves only local operations and classical communications and it does not depend on bipartite entangled measurements and is free from any network assistance. In addition, we provide the device-independent bound of the maximum probability of success of the generalized Hardy-type nonlocality test.
相關內容
Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會議。
Publisher：IFIP。
SIT：
In many jurisdictions, forensic evidence is presented in the form of categorical statements by forensic experts. Several large-scale performance studies have been performed that report error rates to elucidate the uncertainty associated with such categorical statements. There is growing scientific consensus that the likelihood ratio (LR) framework is the logically correct form of presentation for forensic evidence evaluation. Yet, results from the large-scale performance studies have not been cast in this framework. Here, I show how to straightforwardly calculate an LR for any given categorical statement using data from the performance studies. This number quantifies how much more we should believe the hypothesis of same source vs different source, when provided a particular expert witness statement. LRs are reported for categorical statements resulting from the analysis of latent fingerprints, bloodstain patterns, handwriting, footwear and firearms. The highest LR found for statements of identification was 376 (fingerprints), the lowest found for statements of exclusion was 1/28 (handwriting). The LRs found may be more insightful for those used to this framework than the various error rates reported previously. An additional advantage of using the LR in this way is the relative simplicity; there are no decisions necessary on what error rate to focus on or how to handle inconclusive statements. The values found are closer to 1 than many would have expected. One possible explanation for this mismatch is that we undervalue numerical LRs. Finally, a note of caution: the LR values reported here come from a simple calculation that does not do justice to the nuances of the large-scale studies and their differences to casework, and should be treated as ball-park figures rather than definitive statements on the evidential value of whole forensic scientific fields.
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded rectangular table in multiple dimensions. To derive a second-order scheme, we combine a MUSCL type spatial reconstruction with strong stability preserving Runge-Kutta time stepping method. The resulting scheme is ensured to be well-balanced through a modified limiting approach that allows the scheme to reduce to well-balanced first-order scheme near the steady state while maintaining the second-order accuracy away from it. The well-balanced property of the scheme is proven analytically in one dimension and demonstrated numerically in two dimensions. Additionally, numerical experiments reveal that the second-order scheme reduces finite time oscillations, takes fewer time iterations for achieving the steady state and gives sharper resolutions of the physical structure of the sandpile, as compared to the existing first-order schemes of the literature.
A joint mix is a random vector with a constant component-wise sum. The dependence structure of a joint mix minimizes some common objectives such as the variance of the component-wise sum, and it is regarded as a concept of extremal negative dependence. In this paper, we explore the connection between the joint mix structure and popular notions of negative dependence in statistics, such as negative correlation dependence, negative orthant dependence and negative association. A joint mix is not always negatively dependent in any of the above senses, but some natural classes of joint mixes are. We derive various necessary and sufficient conditions for a joint mix to be negatively dependent, and study the compatibility of these notions. For identical marginal distributions, we show that a negatively dependent joint mix solves a multi-marginal optimal transport problem for quadratic cost under a novel setting of uncertainty. Analysis of this optimal transport problem with heterogeneous marginals reveals a trade-off between negative dependence and the joint mix structure.
The increasing availability of temporal data poses a challenge to time-series and signal-processing domains due to its high numerosity and complexity. Symbolic representation outperforms raw data in a variety of engineering applications due to its storage efficiency, reduced numerosity, and noise reduction. The most recent symbolic aggregate approximation technique called ABBA demonstrates outstanding performance in preserving essential shape information of time series and enhancing the downstream applications. However, ABBA cannot handle multiple time series with consistent symbols, i.e., the same symbols from distinct time series are not identical. Also, working with appropriate ABBA digitization involves the tedious task of tuning the hyperparameters, such as the number of symbols or tolerance. Therefore, we present a joint symbolic aggregate approximation that has symbolic consistency, and show how the hyperparameter of digitization can itself be optimized alongside the compression tolerance ahead of time. Besides, we propose a novel computing paradigm that enables parallel computing of symbolic approximation. The extensive experiments demonstrate its superb performance and outstanding speed regarding symbolic approximation and reconstruction.
It is well-known that mood and pain interact with each other, however individual-level variability in this relationship has been less well quantified than overall associations between low mood and pain. Here, we leverage the possibilities presented by mobile health data, in particular the "Cloudy with a Chance of Pain" study, which collected longitudinal data from the residents of the UK with chronic pain conditions. Participants used an App to record self-reported measures of factors including mood, pain and sleep quality. The richness of these data allows us to perform model-based clustering of the data as a mixture of Markov processes. Through this analysis we discover four endotypes with distinct patterns of co-evolution of mood and pain over time. The differences between endotypes are sufficiently large to play a role in clinical hypothesis generation for personalised treatments of comorbid pain and low mood.
By abstracting over well-known properties of De Bruijn's representation with nameless dummies, we design a new theory of syntax with variable binding and capture-avoiding substitution. We propose it as a simpler alternative to Fiore, Plotkin, and Turi's approach, with which we establish a strong formal link. We also show that our theory easily incorporates simple types and equations between terms.
In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are typically used to study biological structures like tissues, organs, cartilage and bones, which are known for a nonlinear dependence of their permeability/hydraulic conductivity on solid dilation. We formulate (extend to the present situation) one of the most popular splitting schemes, namely the fixed-stress split method for the iterative solution of the coupled problem. The method is proven to converge linearly for sufficiently small time steps under standard assumptions. The error contraction factor then is strictly less than one, independent of the Lam\'{e} parameters, Biot and storage coefficients if the hydraulic conductivity is a strictly positive, bounded and Lipschitz-continuous function.
Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions produced by this so-called \emph{predict-then-optimize} procedure can be highly sensitive to uncertain parameters. In this work, we contribute to recent efforts in producing \emph{decision-focused} predictions, i.e., to build predictive models that are constructed with the goal of minimizing a \emph{regret} measure on the decisions taken with them. We formulate the exact expected regret minimization as a pessimistic bilevel optimization model. Then, using duality arguments, we reformulate it as a non-convex quadratic optimization problem. Finally, we show various computational techniques to achieve tractability. We report extensive computational results on shortest-path instances with uncertain cost vectors. Our results indicate that our approach can improve training performance over the approach of Elmachtoub and Grigas (2022), a state-of-the-art method for decision-focused learning.
The conditional backward sampling particle filter (CBPF) is a powerful Markov chain Monte Carlo algorithm for general state space hidden Markov model smoothing. We show that, under a general (strong mixing) condition, its mixing time is upper bounded by $O(\log T)$ where $T$ is the time horizon. The result holds for a fixed number of particles $N$ which is sufficiently large (depending on the strong mixing constants), and therefore guarantees an overall computational complexity of $O(T\log T)$ f or general hidden Markov model smoothing. We provide an example which shows that the mixing time $O(\log T)$ is optimal. Our proof relies on analysis of a novel coupling of two CBPFs, which involves a maximal coupling of two particle systems at each time instant. The coupling is implementable, and can be used to construct unbiased, finite variance estimates of functionals which have arbitrary dependence on the latent state path, with expected $O(T \log T)$ cost. We also investigate related couplings, some of which have improved empirical behaviour.
Word embedding methods (WEMs) are extensively used for representing text data. The dimensionality of these embeddings varies across various tasks and implementations. The effect of dimensionality change on the accuracy of the downstream task is a well-explored question. However, how the dimensionality change affects the bias of word embeddings needs to be investigated. Using the English Wikipedia corpus, we study this effect for two static (Word2Vec and fastText) and two context-sensitive (ElMo and BERT) WEMs. We have two observations. First, there is a significant variation in the bias of word embeddings with the dimensionality change. Second, there is no uniformity in how the dimensionality change affects the bias of word embeddings. These factors should be considered while selecting the dimensionality of word embeddings.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191