Recursive Properties Research Articles

Exploring recursive properties and dynamical complexity in scalar time-series using threshold-free recursive analysis approach

Exploring recursive properties and dynamical complexity in scalar time-series using threshold-free recursive analysis approach

Toward multiloop local renormalization within causal loop-tree duality

Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on dimensional regularization, these become manifest as ε poles, allowing one to define counterterms with useful recursive properties. However, this procedure requires one to work at “integral level” and poses difficulties to achieve a smooth combination with seminumerical approaches. This article is devoted to the development of an integrand-level renormalization formalism, better suited for semi- or fully numerical calculations. Starting from the loop-tree duality, we keep the causal representations of the integrands of multiloop Feynman diagrams and explore their UV behavior. Then, we propose a strategy that allows one to build local counterterms, capable of rendering the expressions integrable in the high-energy limit and in four space-time dimensions. Our procedure was tested on diagrams up to three loops, and we found a remarkably smooth cancellation of divergences. The results of this work constitute a powerful step toward a fully local renormalization framework in quantum field theory. Published by the American Physical Society 2024

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.

\(q\)-Analogue of the Generalized Fibonacci and Lucas Polynomials

In this article, we define \(q\)-generalized Fibonacci polynomials and \(q\)-generalized Lucas polynomials using \(q\)-binomial coefficient and obtain their recursive properties. In addition, we introduce generalized \(q\)-Fibonacci matrix and generalized \(q\)-Lucas matrix, then we derive their basic identities. We define \((k,q,t)\)-symmetric generalized Fibonacci matrix and \((k,q,t)\)-symmetric generalized Lucas matrix, then we give the Cholesky factorization of these matrices. Finally, we give determinantal and permanental representations of these new polynomial sequences.

Efficient implementation of the linear layer of block ciphers with large MDS matrices based on a new lookup table technique.

Block cipher is a cryptographic field that is now widely applied in various domains. Besides its security, deployment issues, implementation costs, and flexibility across different platforms are also crucial in practice. From an efficiency perspective, the linear layer is often the slowest transformation and requires significant implementation costs in block ciphers. Many current works employ lookup table techniques for linear layers, but they are quite costly and do not save memory storage space for the lookup tables. In this paper, we propose a novel lookup table technique to reduce memory storage when executing software. This technique is applied to the linear layer of block ciphers with recursive Maximum Distance Separable (MDS) matrices, Hadamard MDS matrices, and circulant MDS matrices of considerable sizes (e.g. sizes of 16, 32, 64, and so on). The proposed lookup table technique leverages the recursive property of linear matrices and the similarity in elements of Hadamard or circulant MDS matrices, allowing the construction of a lookup table for a submatrix instead of the entire linear matrix. The proposed lookup table technique enables the execution of the diffusion layer with unchanged computational complexity (number of XOR operations and memory accesses) compared to conventional lookup table implementations but allows a substantial reduction in memory storage for the pre-computed tables, potentially reducing the storage needed by 4 or 8 times or more. The memory storage will be reduced even more as the size of the MDS matrix increases. For instance, analysis shows that when the matrix size is 64, the memory storage ratio with the proposed lookup table technique decreases by 87.5% compared to the conventional lookup table technique. This method also allows for more flexible software implementations of large-sized linear layers across different environments.

Set-point tracking MPC with avoidance features

This work proposes a finite-horizon optimal control strategy to solve the tracking problem while providing avoidance features to the closed-loop system. Inspired by the set-point tracking model predictive control (MPC) framework, the central idea of including artificial variables into the optimal control problem is considered. This approach allows us to add avoidance features into the set-point tracking MPC strategy without losing the properties of an enlarged domain of attraction and feasibility insurances in the face of any changing reference. Besides, the artificial variables are considered together with an avoidance cost functional to establish the basis of the strategy, maintaining the recursive feasibility property in the presence of a previously unknown number of regions to be avoided. It is shown that the closed-loop system is recursively feasible and input-to-state-stable under the mild assumption that the avoidance cost is uniformly bounded over time. Finally, two numerical examples illustrate the controller behavior.

Three Distributions in the Extended Occupancy Problem

The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and deriving the spectral decomposition of the transition probability matrix. We look at three distributions of interest that arise from the problem, all involving the noncentral Stirling numbers of the second kind. These distributions give a useful generalisation to the binomial and negative-binomial distributions. We examine how these distributions relate to one another, and we derive recursive properties and mixture properties that characterise the distributions.

Research on Microteaching Mode of College English Courses Based on Regression Network Models

Abstract This paper determines the solution vector of ELT proficiency constraint covariates using the correlation fusion approach, the proficiency prediction control objective function is constructed, and the education process’ quantitative recursive properties are discovered. The K-means algorithm is employed to obtain the predicted values of the resource limitation vector for ELT competence assessment, obtain the similarity of the distribution of teaching resources, combine linear regression grouping and integrate the ranking parameters for ELT competence assessment, obtain the characteristics of the data probability density, and finish evaluating the teaching model. The results show that the maximum utilization value reaches 99.03% by assessing English teaching ability through the K-means algorithm and linear regression, which indicates that the reasonable use of mobile Internet can enhance students’ English teaching level and ensure the efficiency of teaching resources utilization.

Holonomic representation of biadjoint scalar amplitudes

We study tree-level biadjoint scalar amplitudes in the language of D-modules. We construct left ideals in the Weyl algebra D that allow a holonomic representation of n-point amplitudes in terms of the linear partial differential equations they satisfy. The resulting representation encodes the simple pole and recursive properties of the amplitude.

A bigger problem for ideography: The pervasiveness of linguistic structure.

Writing systems display ubiquitous linguistic structure, from the recursive syntactic properties of their glyphs to the morphology/phonology of their combinatorics. This extends to Ancient Egyptian, Chinese, and Sumerian ideograms. Pure ideography requires switching this influence off. The pervasive linguistic tinge to the fabric of writing systems suggests that the chances of breaking what Morin terms language's lock-in effect are slim.

Replica higher-order topology of Hofstadter butterflies in twisted bilayer graphene

The Hofstadter energy spectrum of twisted bilayer graphene (TBG) is found to have recursive higher-order topological properties. We demonstrate that higher-order topological insulator (HOTI) phases, characterized by localized corner states, occur as replicas of the original HOTIs to fulfill the self-similarity of the Hofstadter spectrum. We show the existence of exact flux translational symmetry in TBG at all commensurate angles. Based on this result, we identify that the original HOTI phase at zero flux is re-entrant at a half-flux periodicity, where the effective twofold rotation is preserved. In addition, numerous replicas of the original HOTIs are found for fluxes without protecting symmetries. Like the original HOTIs, replica HOTIs feature both localized corner states and edge-localized real-space topological markers. The replica HOTIs originate from the different interaction scales, namely, intralayer and interlayer couplings, in TBG. The topological aspect of Hofstadter butterflies revealed in our results highlights symmetry-protected topology in quantum fractals.

Epistemic Disjunctive Datalog for Querying Knowledge Bases

The Datalog query language can express several powerful recursive properties, often crucial in real-world scenarios. While answering such queries is feasible over relational databases, the picture changes dramatically when data is enriched with intensional knowledge. It is indeed well-known that answering Datalog queries is undecidable already over lightweight knowledge bases (KBs) of the DL-Lite family. To overcome this issue, we propose a new query language based on Disjunctive Datalog rules combined with a modal epistemic operator. Rules in this language interact with the queried KB exclusively via the epistemic operator, thus extracting only the information true in every model of the KB. This form of interaction is crucial for not falling into undecidability. The contribution provided by this paper is threefold. First, we illustrate the syntax and the semantics of the novel query language. Second, we study the expressive power of different fragments of our new language and compare it with Disjunctive Datalog and its variants. Third, we outline the precise data complexity of answering queries in our new language over KBs expressed in various well-known formalisms.

Machine Learning-based Time Series Modelling for Large-Scale Regional Wind Power Forecasting: a Case Study in Ontario, Canada

Recently, time series forecasting has acquired considerable academic and industrial interests in various areas for different applications. Machine learning (ML) algorithms are known for their ability to capture the chaotic temporal non-linear relations in time series data. In this paper, various ML-based algorithms are employed and analyzed for time series forecasting of “regional wind power” in Ontario, Canada. To this end, the meteorological and spatial parameters with seasonal and temporal features are filtered and selected by a proposed deep feature selection approach. Then, multiple ML algorithms, including artificial neural network (ANN), deep neural network (DNN), long short-term memory (LSTM), bagging tree (BT), and support vector machine/regression (SVM/SVR), are used for training one-step ahead forecasting models. Finally, a comprehensive assessment of the constructed models is conducted based on different error criteria metrics. By evaluating and analyzing the performance of the models using testing data, it is observed that SVR/SVM is one of the most promising robust ML-based forecasting models. This technique results in reliable generic models that perform well with new data, where the testing MAPE % reaches a value of 13 %. Almost a similar MAPE is obtained from the ensemble modeling approach, which means combining process of the generated ML-based models does not significantly improve the predictions, in comparison with the developed SVR/SVM model. On the other hand, when constructing the multi-step ahead forecasting models, the predictions obtained from the multi-input multi-output (MIMO) LSTM approach are more reliable with higher accuracies. In other words, it is shown that the performance of the MIMO multi-step strategy is superior to the direct multi-step forecasting method, while employing algorithms with recursive properties.

An O(log(N)) Algorithm View: Reliability Evaluation of Folded-crossed Hypercube in Terms of h-extra Edge-connectivity

An interconnection network can be modelled as a connected graph [Formula: see text]. The reliability of interconnection networks is critical for multiprocessor systems. Several conditional edge-connectivities have been introduced in the past for accurately reflecting various realistic network situations, with the [Formula: see text]-extra edge-connectivity being one such conditional edge-connectivity. The [Formula: see text]-extra edge-connectivity of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of faulty edges whose deletion disconnects the graph [Formula: see text] with each resulting component containing at least [Formula: see text] processors. In general, for a connected graph [Formula: see text], determining whether the graph exists an [Formula: see text]-extra edge-cut is [Formula: see text]-hard. The folded-crossed hypercube [Formula: see text] is a variation of the crossed hypercube [Formula: see text] with [Formula: see text] processors. In this paper, after excavating the layer structure of folded-crossed hypercube, we investigate some recursive properties of [Formula: see text], based on some recursive properties, an effective [Formula: see text] algorithm of [Formula: see text]-extra edge-connectivity of folded-crossed hypercube is designed, which can determine the exact value and the [Formula: see text]-optimality of [Formula: see text] for each positive integer [Formula: see text]. Our results solve this problem thoroughly.

LANDAU SUB-BAND FIELDS IN CH3NH3PBI3 CRYSTALS WITHIN WIGNER–SEITZ PRIMITIVE CELL

The titling of orientations is believed to influence electrostatic and steric interactions on sub-band touching levels, positions and density of states in a CH3NH3PbI3 perovskite crystal. Sub-band touching exhibit recursive properties that sometimes result in forming new material properties like an adjusted band gap, a modified sub band energy level, a modified ground level excitation state, a modified density of state or a lattice frustration when exposed to an external magnetic field in the Bravais lattice. A geometrical structural model with a tight-bound sub band structure was developed in this study. It was analyzed with an aim of describing how its tight-bound electrons are influenced by a rational magnetic field to distort tilting and rotation in CH3NH3PbI3 lattice. The model had a rotating and tilting orientation angle, (ψ) with a precision angle, Φ. It was analyzed. The findings showed that, out of all the sum of angles in all the orientations, it is only the precession angle that was to influence electrostatic and steric interactions and only two angles were found to influence the lead–iodine-bond lengths, density of states modify sub bands level tilting. The finding also showed that a magnetic field has a significant influence on sub band touching of immediate neighbouring sub bands since it since a frustration in the lattice was exhibited as a recursive property. It was then concluded that a sum of density of states below an energy gap in a CH3NH3PbI3 lattice under an irrational magnetic field had a significant influence on sub band touching the magnitudes and thus influencing its density of states.

Recursive Estimation in the Moving Window: Efficient Detection of the Distortions in the Grids with Desired Accuracy

The development of fast convergent and computationally efficient algorithms for monitoring waveform distortions and harmonic emissions will be an important problem in future electrical networks due to the high penetration level of renewable energy systems, smart loads, new types of power electronics, and many others. Estimating the signal quantities in the moving window is the most accurate way of monitoring these distortions. Such estimation is usually associated with significant computational loads, which can be reduced by utilizing the recursion and information matrix properties. Rank two update representation of the information matrix allows the derivation of a new computationally efficient recursive form of the inverse of this matrix and recursive parameter update law. Newton-Schulz and Richardson correction algorithms are introduced in this paper to prevent error propagation and for accuracy maintenance. Extensive comparative analysis is performed on real data for proposed recursive algorithms and the Richardson algorithm with an optimally chosen preconditioner. Recursive algorithms show the best results in estimation with ill-conditioned information matrices.

On the hyperbolic Horadam matrix functions

In this study, we introduce a new class of the hyperbolic matrix functions which are called symmetrical hyperbolic Horadam sine and cosine matrix functions and we present some hyperbolic and recursive properties of these new matrix functions. In addition, we introduce quasi-sine Horadam matrix function and also define the matrix form of the metallic shofars that related to the hyperbolic Horadam sine and hyperbolic Horadam cosine matrix functions.

Double Hurwitz numbers: polynomiality, topological recursion and intersection theory

Double Hurwitz numbers enumerate branched covers of {{{mathbb {C}}}}{{{mathbb {P}}}}^1 with prescribed ramification over two points and simple ramification elsewhere. In contrast to the single case, their underlying geometry is not well understood. In previous work by the second- and third-named authors, the double Hurwitz numbers were conjectured to satisfy a polynomiality structure and to be governed by the topological recursion, analogous to existing results concerning single Hurwitz numbers. In this paper, we resolve these conjectures by a careful analysis of the semi-infinite wedge representation for double Hurwitz numbers. We prove an ELSV-like formula for double Hurwitz numbers, by deforming the Johnson–Pandharipande–Tseng formula for orbifold Hurwitz numbers and using properties of the topological recursion under variation of spectral curves. In the course of this analysis, we unveil certain vanishing properties of Omega -classes.

High-speed recursive-separable image processing filters

The development of modern technologies in the field of image formation leads to an increase in the size of the generated images, as a result the question of reducing the processing computational costs arises, and this is an important factor in the creation of real-time systems. The study provides a description of high-speed recursive-separable filters for improving the quality of images, which, due to the peculiarities of their implementation, can reduce the number of computational operations required for the image processing process. This type of filters is obtained from two-dimensional linear digital filters, which are modified by applying recursive and separable properties to them. The MATLAB environment computing method for implementation of these filters is described. An extensive performance research of the developed filters has been carried out at various sizes of the test image and on various experimental installations. The comparison with the classical two-dimensional convolution method of the developed filters is demonstrated, and it shows the time gain required for the image processing. The results obtained can be applied in biomedical image processing systems or in vision systems working in heavy weather conditions.

Modifikasi Algoritma Vigenere Cipher dengan Pembangkit Kunci Random Number Generator Dalam Pengamanan Citra Digital

Digital image is an image that can be processed by a computer. Digital images that are not allowed to be known by others or are said to be private and are not allowed to be manipulated by other irresponsible parties. The act of manipulating, hijacking or tapping the image will cause harm to the owner of the image. The technique to reduce these actions is to use cryptographic techniques. Cryptographic techniques are very well known for securing information with a password that only the owner of the image understands. To strengthen the results of the encryption carried out by the Vigenere Cipher Algorithm, modifications are made to the Random Number Generator. The Random Number Generator used is Linear Congruent Generator which has linear recursive properties combined with modulus. So the combination of vigenere cipher with random number generator Linear Congruent Generator is very difficult for other parties to abuse the image