We quantify the usefulness of a bipartite quantum state in the ancilla-assisted channel discrimination of arbitrary quantum channels, formally defining a worst-case-scenario channel discrimination power for bipartite quantum states. We show that such a quantifier is deeply connected with the operator Schmidt decomposition of the state. We compute the channel discrimination power exactly for pure states, and provide upper and lower bounds for general mixed states. We show that highly entangled states can outperform any state that passes the realignment criterion for separability. Furthermore, while also unentangled states can be used in ancilla-assisted channel discrimination, we show that the channel discrimination power of a state is bounded by its quantum discord.
I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological role of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability theory. The theory is preceded by a general chapter on counting methods. Then, the theory of probabilities is presented in a discrete framework. Two objectives are sought. The first is to give the reader the ability to solve a large number of problems related to probability theory, including application problems in a variety of disciplines. The second was to prepare the reader before he approached the manual on the mathematical foundations of probability theory. In this book, the reader will concentrate more on mathematical concepts, while in the present text, experimental frameworks are mostly found. If both objectives are met, the reader will have already acquired a definitive experience in problem-solving ability with the tools of probability theory and at the same time he is ready to move on to a theoretical course on probability theory based on the theory of measurement and integration. The book ends with a chapter that allows the reader to begin an intermediate course in mathematical statistics.
This paper presents real-time vibration based identification technique using measured frequency response functions(FRFs) under random vibration loading. Artificial Neural Networks (ANNs) are trained to map damage fingerprints to damage characteristic parameters. Principal component statistical analysis(PCA) technique was used to tackle the problem of high dimensionality and high noise of data, which is common for industrial structures. The present study considers Crack, Rivet hole expansion and redundant uniform mass as damages on the structure. Frequency response function data after being reduced in size using PCA is fed to individual neural networks to localize and predict the severity of damage on the structure. The system of ANNs trained with both numerical and experimental model data to make the system reliable and robust. The methodology is applied to a numerical model of stiffened panel structure, where damages are confined close to the stiffener. The results showed that, in all the cases considered, it is possible to localize and predict severity of the damage occurrence with very good accuracy and reliability.
In visual exploration and analysis of data, determining how to select and transform the data for visualization is a challenge for data-unfamiliar or inexperienced users. Our main hypothesis is that for many data sets and common analysis tasks, there are relatively few "data slices" that result in effective visualizations. By focusing human users on appropriate and suitably transformed parts of the underlying data sets, these data slices can help the users carry their task to correct completion. To verify this hypothesis, we develop a framework that permits us to capture exemplary data slices for a user task, and to explore and parse visual-exploration sequences into a format that makes them distinct and easy to compare. We develop a recommendation system, DataSlicer, that matches a "currently viewed" data slice with the most promising "next effective" data slices for the given exploration task. We report the results of controlled experiments with an implementation of the DataSlicer system, using four common analytical task types. The experiments demonstrate statistically significant improvements in accuracy and exploration speed versus users without access to our system.
We study a variant of the source identification game with training data in which part of the training data is corrupted by an attacker. In the addressed scenario, the defender aims at deciding whether a test sequence has been drawn according to a discrete memoryless source $X \sim P_X$, whose statistics are known to him through the observation of a training sequence generated by $X$. In order to undermine the correct decision under the alternative hypothesis that the test sequence has not been drawn from $X$, the attacker can modify a sequence produced by a source $Y \sim P_Y$ up to a certain distortion, and corrupt the training sequence either by adding some fake samples or by replacing some samples with fake ones. We derive the unique rationalizable equilibrium of the two versions of the game in the asymptotic regime and by assuming that the defender bases its decision by relying only on the first order statistics of the test and the training sequences. By mimicking Stein's lemma, we derive the best achievable performance for the defender when the first type error probability is required to tend to zero exponentially fast with an arbitrarily small, yet positive, error exponent. We then use such a result to analyze the ultimate distinguishability of any two sources as a function of the allowed distortion and the fraction of corrupted samples injected into the training sequence.
Recently, several discriminative learning approaches have been proposed for effective image restoration, achieving convincing trade-off between image quality and computational efficiency. However, these methods require separate training for each restoration task (e.g., denoising, deblurring, demosaicing) and problem condition (e.g., noise level of input images). This makes it time-consuming and difficult to encompass all tasks and conditions during training. In this paper, we propose a discriminative transfer learning method that incorporates formal proximal optimization and discriminative learning for general image restoration. The method requires a single-pass training and allows for reuse across various problems and conditions while achieving an efficiency comparable to previous discriminative approaches. Furthermore, after being trained, our model can be easily transferred to new likelihood terms to solve untrained tasks, or be combined with existing priors to further improve image restoration quality.
Real-world robots are becoming increasingly complex and commonly act in poorly understood environments where it is extremely challenging to model or learn their true dynamics. Therefore, it might be desirable to take a task-specific approach, wherein the focus is on explicitly learning the dynamics model which achieves the best control performance for the task at hand, rather than learning the true dynamics. In this work, we use Bayesian optimization in an active learning framework where a locally linear dynamics model is learned with the intent of maximizing the control performance, and used in conjunction with optimal control schemes to efficiently design a controller for a given task. This model is updated directly based on the performance observed in experiments on the physical system in an iterative manner until a desired performance is achieved. We demonstrate the efficacy of the proposed approach through simulations and real experiments on a quadrotor testbed.
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar  by taking a different perspective, leading to an algorithm which is conceptually more natural, has notably improved convergence rates, and for which the analysis is surprisingly simple. At each iteration, the algorithm takes a subgradient step and then performs a line search to move radially towards (or away from) the known feasible point. Our convergence results have striking similarities to those of traditional methods that require Lipschitz continuity. Costly orthogonal projections typical of subgradient methods are entirely avoided.
In this study we present a Deep Mixture of Experts (DMoE) neural-network architecture for single microphone speech enhancement. By contrast to most speech enhancement algorithms that overlook the speech variability mainly caused by phoneme structure, our framework comprises a set of deep neural networks (DNNs), each one of which is an 'expert' in enhancing a given speech type corresponding to a phoneme. A gating DNN determines which expert is assigned to a given speech segment. A speech presence probability (SPP) is then obtained as a weighted average of the expert SPP decisions, with the weights determined by the gating DNN. A soft spectral attenuation, based on the SPP, is then applied to enhance the noisy speech signal. The experts and the gating components of the DMoE network are trained jointly. As part of the training, speech clustering into different subsets is performed in an unsupervised manner. Therefore, unlike previous methods, a phoneme-labeled database is not required for the training procedure. A series of experiments with different noise types verified the applicability of the new algorithm to the task of speech enhancement. The proposed scheme outperforms other schemes that either do not consider phoneme structure or use a simpler training methodology.