Shape Partitioning via $${L}_{p}$$ Compressed Modes

The eigenfunctions of the Laplace–Beltrami operator (manifold harmonics) define a function basis that can be used in spectral analysis on manifolds. In Ozoli et al. (Proc Nat Acad Sci 110(46):18368–18373, 2013) the authors recast the problem as an orthogonality constrained optimization problem and pioneer the use of an \(L_1\) penalty term to obtain sparse (localized) solutions. In this context, the notion corresponding to sparsity is compact support which entails spatially localized solutions. We propose to enforce such a compact support structure by a variational optimization formulation with an \(L_p\) penalization term, with \(0<p<1\). The challenging solution of the orthogonality constrained non-convex minimization problem is obtained by applying splitting strategies and an ADMM-based iterative algorithm. The effectiveness of the novel compact support basis is demonstrated in the solution of the 2-manifold decomposition problem which plays an important role in shape geometry processing where the boundary of a 3D object is well represented by a polygonal mesh. We propose an algorithm for mesh segmentation and patch-based partitioning (where a genus-0 surface patching is required). Experiments on shape partitioning are conducted to validate the performance of the proposed compact support basis.     

In Between the $$LQG/H_{2}$$ - and $$H_{infty } $$ -Control Theories

Automation and Remote Control - In this survey, we discuss various approaches to control theory that have arisen in the recent decades and reflect the desire to reach a trade-off between the $$LQG...     

Adaptive $$H_{infty }$$ -Optimal Control

Automation and Remote Control - For linear dynamic plants, we consider a new class of controllers with adjustable parameters synthesized so as to reduce the integral indicators of the influence of...     

Square roots of $${3\times 3}$$ matrices

We find square roots of a complex-valued matrix \(A_{3 \times 3}\) using equation \(B^{2}=A\). The proposed method is faster than Higham’s method and provides up to 8 square roots with less relative residual and error.     

Experimental estimation of discord in an antiferromagnetic Heisenberg compound $$\hbox {Cu}(\hbox {NO}_{3})_{2}\cdot 2.5\,\hbox {H}_{2}\hbox {O}$$

Temperature-dependent static magnetic susceptibility and heat capacity data were employed to quantify quantum discord in copper nitrate \((\hbox {CN, Cu}(\hbox {NO}_{3})_{2}\cdot 2.5\, \hbox {H}_{2}\hbox {O})\) which is a spin 1/2 antiferromagnetic Heisenberg system. With the help of existing theoretical formulations, quantum discord, mutual information, and purely classical correlation were estimated as a function of temperature using the experimental data. The experimentally quantified correlations estimated from susceptibility and heat capacity data are consistent with each other, and they exhibit a good match with theoretical predictions. Violation of Bell’s inequality was also checked using the static magnetic susceptibility as well as heat capacity data. Quantum discord estimated from magnetic susceptibility as well as heat capacity data is found to be present in the thermal states of the system even when the system is in a separable state.     

Singular $$\mathcal{H}$$ 2-optimization problems for discrete-time systems

Singular ₂-optimization problems are considered for the standard discrete-time control system. Two types of singularity (type I and type II) are distinguished. A detailed treatment of problems with singularity of type II, which leads to nonuniqueness of solution, is presented. New algorithms for design of optimal controllers are presented both in frequency domain and state space, which generalize standard procedures onto the case of singular ₂-problems. A parameterization of the set of optimal controllers is given.Translated from Avtomatika i Telemekhanika, No. 3, 2005, pp. 20–33.Original Russian Text Copyright © 2005 by Polyakov.This paper was recommended for publication by B.T. Polyak, a member of the Editorial Board     

New asymmetric quantum codes over $$F_{q}$$

Two families of new asymmetric quantum codes are constructed in this paper. The first family is the asymmetric quantum codes with length \(n=q^{m}-1\) over \(F_{q}\), where \(q\ge 5\) is a prime power. The second one is the asymmetric quantum codes with length \(n=3^{m}-1\). These asymmetric quantum codes are derived from the CSS construction and pairs of nested BCH codes. Moreover, let the defining set \(T_{1}=T_{2}^{-q}\), then the real Z-distance of our asymmetric quantum codes are much larger than \(\delta _\mathrm{max}+1\), where \(\delta _\mathrm{max}\) is the maximal designed distance of dual-containing narrow-sense BCH code, and the parameters presented here have better than the ones available in the literature.     

Quaternary Codes and Biphase Sequences from $$\mathbb{Z}_8 $$ -Codes

Composing the Carlet map with the inverse Gray map, a new family of cyclic quaternary codes is constructed from 5-cyclic -codes. This new family of codes is inspired by the quaternary Shanbag–Kumar–Helleseth family, a recent improvement on the Delsarte–Goethals family. We conjecture that these -codes are not linear. As applications, we construct families of low-correlation quadriphase and biphase sequences.     

Forecasting hourly $${\hbox {NO}_{2}}$$ concentrations by ensembling neural networks and mesoscale models

In the framework of extreme pollution concentrations being more and more frequent in many cities nowadays, air quality forecasting is crucial to protect public health through the anticipation of unpopular measures like traffic restrictions. In this work, we develop the core of a 48 h ahead forecasting system which is being deployed for the city of Madrid. To this end, we investigate the predictive power of a set of neural network models, including several families of deep networks, applied to the task of predicting nitrogen dioxide concentrations in an urban environment. Careful feature engineering on a set of related magnitudes as meteorology and traffic has proven useful, and we have coupled these neural models with mesoscale numerical pollution forecasts, which improve precision by up to 10%. The experiments show that some neural networks and ensembles consistently outperform the reference models, particularly improving the Naive model’s results from around (20%) up to (57%) for longer forecasting horizons. However, results also reveal that deeper networks are not particularly better than shallow ones in this setting.

     

Sufficient conditions for robustness of $$\mathcal{K}\mathcal{L}$$ -stability for difference inclusions

Difference inclusions arise naturally in the study of discrete-time or sampled-data systems. We develop two novel sufficient conditions for robustness of a stability property referred to as -stability with respect to an arbitrary measure; i.e., where a continuous positive definite function of the solutions satisfies a class- estimate of time and the continuous positive definite function of the initial condition. Christopher M. Kellett was supported by the Australian Research Council under Discovery Project Grant DP0771131. Andrew R. Teel was supported by NSF grants ECS-0324679, ECS-0622253, and AFOSR grants F49620-03-1-0203 and FA9550-06-1-0134.     

Unextendible maximally entangled bases in $${\mathbb {C}}^{pd}\otimes {\mathbb {C}}^{qd}$$

The construction of unextendible maximally entangled bases is tightly related to quantum information processing like local state discrimination. We put forward two constructions of UMEBs in \({\mathbb {C}}^{pd}\otimes {\mathbb {C}}^{qd}\)(\(p\le q\)) based on the constructions of UMEBs in \({\mathbb {C}}^{d}\otimes {\mathbb {C}}^{d}\) and in \({\mathbb {C}}^{p}\otimes {\mathbb {C}}^{q}\), which generalizes the results in Guo (Phys Rev A 94:052302, 2016) by two approaches. Two different 48-member UMEBs in \({\mathbb {C}}^{6}\otimes {\mathbb {C}}^{9}\) have been constructed in detail.     

Interval type-2 fuzzy neural network based constrained GPC for NH $$_{3}$$ flow in SCR de-NO $$_{x}$$ process

Neural Computing and Applications - To overcome the difficulty of controlling ammonia (NH $$_{3}$$ ) flow in the selective catalytic reduction (SCR) nitrogen oxides (NO $$_{x}$$ ) decomposition...     

High granular and short term time series forecasting of $$\hbox {PM}_{2.5}$$ PM 2.5 air pollutant - a comparative review

Forecasting time series has acquired immense research importance and has vast applications in the area of air pollution monitoring. This work attempts to investigate the abilities of various existing techniques when applied for short term, high granular time series forecasting of PM_2.5. More specifically, a comparative study has been provided, taking into account both popularly used models and lesser-used models in this area. The study has been carried out considering ten well defined models that are ARIMA (auto-regressive integrated moving average), SARIMA (seasonal ARIMA), SES (single exponential smoothing), DES (double exponential smoothing), TES (triple exponential smoothing), ANN (artificial neural network), DT (decision tree), kNN (k-nearest neighbor), LSTM (long short-term memory) and MCFO (markov chain first order). A framework has been built that categories the models, implements them under identical execution environment and forecasts succeeding values. Implementation has been carried out over five data sets of real-world air pollution time series, that are collected from five differently located government setup monitoring stations over a period of 1 year (July 2018-June 2019). Rigorous statistical analysis has been performed that yields an insight to the nature and variability of these time series data. Forecasting has been carried out on short term basis, focusing on high granularity whereas, three different lengths of forecast horizon (1 day, 1 week, and 1 month) have been tested. Eventually, the models have been compared in terms of their associated performance measuring units namely, RMSE (root mean of squared error), MAE (mean absolute error) and MAPE (mean absolute percentage error). The comparative results verified with multiple datasets show that all the models posses less error for a shorter forecast horizon, where LSTM providing the best performance. Superiority of machine learning and deep learning models are found in case of longer length of forecast horizon with kNN achieving best accuracy whereas, significant performance degradation of ARIMA is found for longer forecast horizon. Moreover, TES, DT, kNN, LSTM, MCFO are found to be well adopted in relation with shape and variability of the data. Note that the performance on various length of high granular forecast horizon have been studied over multiple datasets that give an added value to this work.

     

Subspace Learning by $$\ell ^{0}$$-Induced Sparsity

Subspace clustering methods partition the data that lie in or close to a union of subspaces in accordance with the subspace structure. Such methods with sparsity prior, such as sparse subspace clustering (SSC) (Elhamifar and Vidal in IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781, 2013) with the sparsity induced by the \(\ell ^{1}\)-norm, are demonstrated to be effective in subspace clustering. Most of those methods require certain assumptions, e.g. independence or disjointness, on the subspaces. However, these assumptions are not guaranteed to hold in practice and they limit the application of existing sparse subspace clustering methods. In this paper, we propose \(\ell ^{0}\)-induced sparse subspace clustering (\(\ell ^{0}\)-SSC). In contrast to the required assumptions, such as independence or disjointness, on subspaces for most existing sparse subspace clustering methods, we prove that \(\ell ^{0}\)-SSC guarantees the subspace-sparse representation, a key element in subspace clustering, for arbitrary distinct underlying subspaces almost surely under the mild i.i.d. assumption on the data generation. We also present the “no free lunch” theorem which shows that obtaining the subspace representation under our general assumptions can not be much computationally cheaper than solving the corresponding \(\ell ^{0}\) sparse representation problem of \(\ell ^{0}\)-SSC. A novel approximate algorithm named Approximate \(\ell ^{0}\)-SSC (A\(\ell ^{0}\)-SSC) is developed which employs proximal gradient descent to obtain a sub-optimal solution to the optimization problem of \(\ell ^{0}\)-SSC with theoretical guarantee. The sub-optimal solution is used to build a sparse similarity matrix upon which spectral clustering is performed for the final clustering results. Extensive experimental results on various data sets demonstrate the superiority of A\(\ell ^{0}\)-SSC compared to other competing clustering methods. Furthermore, we extend \(\ell ^{0}\)-SSC to semi-supervised learning by performing label propagation on the sparse similarity matrix learnt by A\(\ell ^{0}\)-SSC and demonstrate the effectiveness of the resultant semi-supervised learning method termed \(\ell ^{0}\)-sparse subspace label propagation (\(\ell ^{0}\)-SSLP).     

A semantically complete extension sequence of the system $$\mathcal{L}^* $$

In this paper, the method of well-combined semantics and syntax proposed by Pavelka is applied to the research of the propositional calculus formal system . The partial constant values are taken as formulas, formulas are fuzzified in two manners of semantics and syntax, and inferring processes are fuzzified. A sequence of new extensions { } of the system is proposed, and the completeness of is proved.     

Mutually unbiased maximally entangled bases in $$\mathbb {C}^d\otimes \mathbb {C}^d$$

We study mutually unbiased maximally entangled bases (MUMEB’s) in bipartite system \(\mathbb {C}^d\otimes \mathbb {C}^d (d \ge 3)\). We generalize the method to construct MUMEB’s given in Tao et al. (Quantum Inf Process 14:2291–2300, 2015), by using any commutative ring R with d elements and generic character of \((R,+)\) instead of \(\mathbb {Z}_d=\mathbb {Z}/d\mathbb {Z}\). Particularly, if \(d=p_1^{a_1}p_2^{a_2}\ldots p_s^{a_s}\) where \(p_1, \ldots , p_s\) are distinct primes and \(3\le p_1^{a_1}\le \cdots \le p_s^{a_s}\), we present \(p_1^{a_1}-1\) MUMEB’s in \(\mathbb {C}^d\otimes \mathbb {C}^d\) by taking \(R=\mathbb {F}_{p_1^{a_1}}\oplus \cdots \oplus \mathbb {F}_{p_s^{a_s}}\), direct sum of finite fields (Theorem 3.3).     

The preparation of organic light-emitting diode encapsulation barrier layer by low-temperature plasma-enhanced chemical vapor deposition: a study on the $$\hbox {SiO}_\mathrm{x}\hbox {N}_\mathrm{y}$$ film parameter optimization

This study prepared \(\hbox {SiO}_\mathrm{x}\hbox {N}_\mathrm{y}\) film by using plasma-enhanced chemical vapor deposition in organic light-emitting diode (OLED) encapsulation to prevent the invasion of moisture and oxygen for longer light-emitting lifetime of OLED components. It applied high density inductively coupled plasma for the coating of film on polyethersulfone, silicon and glass substrate, and discussed the relevance between process parameters and quality characteristics including coating uniformity, coating thickness and moisture permeation. This study used Taguchi method to plan the experiment and calculated the optimal parameters of each quality, used technique for order preference by similarity to ideal solution and grey relational analysis to determine the optimal parameter of all qualities. The back-propagation neural network was combined with Levenberg–Marquardt algorithm to construct the simulation and prediction system. Based on the quality optimization design, the single layer film’s moisture permeation rate was 0.02 g/m\(^{2}\)/day, the maximum coating thickness reached 420 nm, and the fastest rate was 21 nm/min, which was higher than the industrial standard specification (10 nm/min) by 110 %.