In this paper, we obtain sufficient and necessary conditions for quasi-cyclic codes with index even to be symplectic self-orthogonal. Then, we propose a method for constructing symplectic self-orthogonal quasi-cyclic codes, which allows arbitrary polynomials that coprime $x^{n}-1$ to construct symplectic self-orthogonal codes. Moreover, by decomposing the space of quasi-cyclic codes, we provide lower and upper bounds on the minimum symplectic distances of a class of 1-generator quasi-cyclic codes and their symplectic dual codes. Finally, we construct many binary symplectic self-orthogonal codes with excellent parameters, corresponding to 117 record-breaking quantum codes, improving Grassl's table (Bounds on the Minimum Distance of Quantum Codes. //www.codetables.de).
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Binaural multichannel blind speaker separation with a causal low-latency and low-complexity approach
In this paper, we introduce a causal low-latency low-complexity approach for binaural multichannel blind speaker separation in noisy reverberant conditions. The model, referred to as Group Communication Binaural Filter and Sum Network (GCBFSnet) predicts complex filters for filter-and-sum beamforming in the time-frequency domain. We apply Group Communication (GC), i.e., latent model variables are split into groups and processed with a shared sequence model with the aim of reducing the complexity of a simple model only containing one convolutional and one recurrent module. With GC we are able to reduce the size of the model by up to 83 % and the complexity up to 73 % compared to the model without GC, while mostly retaining performance. Even for the smallest model configuration, GCBFSnet matches the performance of a low-complexity TasNet baseline in most metrics despite the larger size and higher number of required operations of the baseline.
In this paper we explore the concept of sequential inductive prediction intervals using theory from sequential testing. We furthermore introduce a 3-parameter PAC definition of prediction intervals that allows us via simulation to achieve almost sharp bounds with high probability.
In this paper, we propose a new method for the augmentation of numeric and mixed datasets. The method generates additional data points by utilizing cross-validation resampling and latent variable modeling. It is particularly efficient for datasets with moderate to high degrees of collinearity, as it directly utilizes this property for generation. The method is simple, fast, and has very few parameters, which, as shown in the paper, do not require specific tuning. It has been tested on several real datasets; here, we report detailed results for two cases, prediction of protein in minced meat based on near infrared spectra (fully numeric data with high degree of collinearity) and discrimination of patients referred for coronary angiography (mixed data, with both numeric and categorical variables, and moderate collinearity). In both cases, artificial neural networks were employed for developing the regression and the discrimination models. The results show a clear improvement in the performance of the models; thus for the prediction of meat protein, fitting the model to the augmented data resulted in a reduction in the root mean squared error computed for the independent test set by 1.5 to 3 times.
This paper considers the problem of robust iterative Bayesian smoothing in nonlinear state-space models with additive noise using Gaussian approximations. Iterative methods are known to improve smoothed estimates but are not guaranteed to converge, motivating the development of more robust versions of the algorithms. The aim of this article is to present Levenberg-Marquardt (LM) and line-search extensions of the classical iterated extended Kalman smoother (IEKS) as well as the iterated posterior linearisation smoother (IPLS). The IEKS has previously been shown to be equivalent to the Gauss-Newton (GN) method. We derive a similar GN interpretation for the IPLS. Furthermore, we show that an LM extension for both iterative methods can be achieved with a simple modification of the smoothing iterations, enabling algorithms with efficient implementations. Our numerical experiments show the importance of robust methods, in particular for the IEKS-based smoothers. The computationally expensive IPLS-based smoothers are naturally robust but can still benefit from further regularisation.
In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural generalizations of classical information-theoretic divergences, such as the $f$-divergences and the R\'enyi divergence between probability measures, to the context of finite Markov chains. We begin by detailing and deriving fundamental properties of these divergences and notably gives a Markov chain version of the Pinsker's inequality and Chernoff information. We then utilize these notions in a few applications. First, we investigate the binary hypothesis testing problem of Markov chains, where the newly defined R\'enyi divergence between Markov chains and its geometric interpretation play an important role in the analysis. Second, we propose and analyze information-theoretic (Ces\`aro) mixing times and ergodicity coefficients, along with spectral bounds of these notions in the reversible setting. Examples of the random walk on the hypercube, as well as the connections between the critical height of the low-temperature Metropolis-Hastings chain and these proposed ergodicity coefficients, are highlighted.
We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, obtaining multimode extensions of the cat codes that can outperform previous constructions while requiring a similar type of overhead. Our polytope-based cat codes consist of sets of points with large separation that at the same time form averaging sets known as spherical designs. We also recast concatenations of CSS codes with cat codes as quantum spherical codes, revealing a new way to autonomously protect against dephasing noise.
A linear code is said to be self-orthogonal if it is contained in its dual. Self-orthogonal codes are of interest because of their important applications, such as for constructing linear complementary dual (LCD) codes and quantum codes. In this paper, we construct several new families of ternary self-orthogonal codes by employing weakly regular plateaued functions. Their parameters and weight distributions are completely determined. Then we apply these self-orthogonal codes to construct several new families of ternary LCD codes. As a consequence, we obtain many (almost) optimal ternary self-orthogonal codes and LCD codes.
We introduce the new setting of open-vocabulary object 6D pose estimation, in which a textual prompt is used to specify the object of interest. In contrast to existing approaches, in our setting (i) the object of interest is specified solely through the textual prompt, (ii) no object model (e.g. CAD or video sequence) is required at inference, (iii) the object is imaged from two different viewpoints of two different scenes, and (iv) the object was not observed during the training phase. To operate in this setting, we introduce a novel approach that leverages a Vision-Language Model to segment the object of interest from two distinct scenes and to estimate its relative 6D pose. The key of our approach is a carefully devised strategy to fuse object-level information provided by the prompt with local image features, resulting in a feature space that can generalize to novel concepts. We validate our approach on a new benchmark based on two popular datasets, REAL275 and Toyota-Light, which collectively encompass 39 object instances appearing in four thousand image pairs. The results demonstrate that our approach outperforms both a well-established hand-crafted method and a recent deep learning-based baseline in estimating the relative 6D pose of objects in different scenes. Project page: //jcorsetti.github.io/oryon/.
Finite volume method (FVM) is a widely used mesh-based technique, renowned for its computational efficiency and accuracy but it bears significant drawbacks, particularly in mesh generation and handling complex boundary interfaces or conditions. On the other hand, smoothed particle hydrodynamics (SPH) method, a popular meshless alternative, inherently circumvents the mesh generation and yields smoother numerical outcomes but at the expense of computational efficiency. Therefore, numerous researchers have strategically amalgamated the strengths of both methods to investigate complex flow phenomena and this synergy has yielded precise and computationally efficient outcomes. However, algorithms involving the weak coupling of these two methods tend to be intricate, which has issues pertaining to versatility, implementation, and mutual adaptation to hardware and coding structures. Thus, achieving a robust and strong coupling of FVM and SPH in a unified framework is imperative. Due to differing boundary algorithms between these methods in Wang's work, the crucial step for establishing a strong coupling of both methods within a unified SPH framework lies in incorporating the FVM boundary algorithm into the Eulerian SPH method. In this paper, we propose a straightforward algorithm in the Eulerian SPH method, algorithmically equivalent to that in FVM, grounded in the principle of zero-order consistency. Moreover, several numerical examples, including fully and weakly compressible flows with various boundary conditions in the Eulerian SPH method, validate the stability and accuracy of the proposed algorithm.
In this paper we argue that topic plays a fundamental role in conversations, and that the concept is needed in addition to that of genre to define interactions. In particular, the concepts of genre and topic need to be separated and orthogonally defined. This would enable modular, reliable and controllable flexible-domain dialogue systems.
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