General Topology Research Articles

A pragmatic ensemble learning approach for rainfall prediction

Heavy rainfall and precipitation play a massive role in shaping the socio-agricultural landscape of a country. Being one of the key indicators of climate change, natural disasters, and of the general topology of a region, rainfall prediction is a gift of estimation that can be used for multiple beneficial causes. Machine learning has an impressive repertoire in aiding prediction and estimation of rainfall. This paper aims to find the effect of ensemble learning, a subset of machine learning, on a rainfall prediction dataset, to increase the predictability of the models used. The classification models used in this paper were tested once individually, and then with applied ensemble techniques like bagging and boosting, on a rainfall dataset based in Australia. The objective of this paper is to demonstrate a reduction in bias and variance via ensemble learning techniques while also analyzing the increase or decrease in the aforementioned metrics. The study shows an overall reduction in bias by an average of 6% using boosting, and an average reduction in variance by 13.6%. Model performance was observed to become more generalized by lowering the false negative rate by an average of more than 20%. The techniques explored in this paper can be further utilized to improve model performance even further via hyper-parameter tuning.

New algorithm for the analysis of nucleotide and amino acid evolutionary relationships based on Klein four-group

Phylogenetics is the study of ancestral relationships among biological species. Such sequence analyses are often represented as phylogenetic trees. The branching pattern of each tree and its topology reflect the evolutionary relatedness between analyzed sequences. We present a Klein four-group algorithm (K4A) for the evolutionary analysis of nucleotide and amino acid sequences. Klein four-group set of operators consists of: identity e (U), and three elements—a = transition (C), b = transversion (G) and c = transition-transversion or complementarity (A). We generated Klein four-group based distance matrices of: 1. Cayley table (CK4), 2. Table rows (K4R), 3. Table columns (K4C), and 4. Euclidean 2D distance (K4E). The performance of the matrices was tested on a dataset of RecA proteins in bacteria, eukaryotes (Rad51 homolog) and archaea (RadA homolog). RecA and its functional homologs are found in all species, and are essential for the repair and maintenance of DNA. Consequently, they represent a good model for the study of evolutionary relationship of protein and nucleotide sequences. The ancestral relationship between the sequences was correctly classified by all K4A matrices concerning general topology. All distance matrices exhibited small variations among species, and overall results of tree classification were in agreement with the general patterns obtained by standard BLOSUM and PAM substitution matrices. During the evolution of a code there is a phase of optimization of system rules, the ambiguity of a code is eliminated, and the system starts producing specific components. Klein four-group algorithm is consistent with the concept of ambiguity reduction. It also enables the use of different genetic code table variants optimized for particular transitions in evolution based on biological specificity.

McKinsey-Tarski algebras: An alternative pointfree approach to topology

McKinsey and Tarski initiated the study of interior algebras. We propose complete interior algebras as an alternative pointfree approach to topology. We term these algebras McKinsey-Tarski algebras or simply MT-algebras. Associating with each MT-algebra the lattice of its open elements defines a functor from the category of MT-algebras to the category of frames, which we study in depth. We also study the dual adjunction between the categories of MT-algebras and topological spaces, and show that MT-algebras provide a faithful generalization of topological spaces. Our main emphasis is on developing a unified approach to separation axioms in the language of MT-algebras, which generalizes separation axioms for both topological spaces and frames.

Optimization Effect of the Improved Power System Integrating Composite Motors on the Energy Consumption of Electric Vehicles

The multi-power source coupled transmission system is a high-performance and energy-saving potential power transmission system, and most of the commonly used pure electric vehicles in the market that use multi-power source coupled drive adopt the motor dual-axis distributed independent drive scheme. The configuration design method for multi-power source fusion hybrid systems mainly focuses on the search and selection of power split hybrid systems based on planetary gear mechanisms. But it has not yet covered the configuration design of transmission systems, resulting in a lack of universal expression and generation methods for the configuration of multi-power source fusion hybrid systems in pure electric vehicles. Therefore, to solve the configuration optimization design problem of a dual-motor single-planetary-array power system, an improved general matrix topology design method is proposed to generate all feasible topology structures. And energy consumption, economy, and the dynamic performance of alternative configurations are optimized and simulated through the control strategy based on a dynamic programming algorithm. Under comprehensive testing conditions, 25 alternative options that met the screening criteria were selected, and, ultimately, five optimized configuration options were obtained. Configuration 1 has the best economy, reducing energy consumption by about 6.3%and increasing driving range by about 6.7%. Its 0–100 km/h acceleration time is about 31.4% faster than the reference configuration. In addition, the energy consumption economy during actual driving is almost the same as the theoretical optimal energy consumption economy, with a difference of only 0.3%. The success of this study not only provides an innovative method for optimizing the configuration of dual-motor single-row star train power systems, but also has a positive impact on improving energy utilization efficiency, reducing energy consumption, and improving the overall performance of electric vehicles.

Graph based routing algorithm for torus topology and its evaluation for the Angara interconnect

Several approaches and techniques exist to resolve load balancing problem in general and torus topology networks. Graph methods are natural ways to perform balancing of routing paths. A routing balancing algorithm must operate within the constraints of the underlying network architecture that limits several parameters, such as the number of logical paths in the network. In this paper, we consider a torus topology that is one of the common topologies that are used in high performance computing systems. We introduce a routing graph that corresponds to a interconnect topology, abstracts interconnect routing rules, providing one-to-one correspondence of network routes and graph paths. We propose a deadlock-free routing algorithm based on a fast single-source shortest path algorithm in a routing graph for the deterministic routing of a torus topology interconnect with a single virtual channel. The proposed algorithm is a tradeoff between two existing routing algorithms, also the algorithm is optimized for multidimensional torus topology and can be applied to any torus topology HPC system. We present a complete description of a routing graph that abstracts the Angara interconnect with 4D torus topology. We evaluated the proposed routing algorithm and benchmarked the maximum performance improvement of 71% for the Alltoall pattern for torus topology systems up to 432 nodes on the Angara interconnect simulator. The performance improvement of more than 5% was obtained for the NPB FT and IS application kernels on a 32-node supercomputer.

A Distributed Privacy-Preserving Learning Dynamics in General Social Networks

In this paper, we study a distributed privacy-preserving learning problem in social networks with general topology. The agents can communicate with each other over the network, which may result in privacy disclosure, since the trustworthiness of the agents cannot be guaranteed. Given a set of options which yield unknown stochastic rewards, each agent is required to learn the best one, aiming at maximizing the resulting expected average cumulative reward. To serve the above goal, we propose a four-staged distributed algorithm which efficiently exploits the collaboration among the agents while preserving the local privacy for each of them. In particular, our algorithm proceeds iteratively, and in every round, each agent i) randomly perturbs its adoption for the privacy-preserving purpose, ii) disseminates the perturbed adoption over the social network in a nearly uniform manner through random walking, iii) selects an option by referring to the perturbed suggestions received from its peers, and iv) decides whether or not to adopt the selected option as preference according to its latest reward feedback. Through solid theoretical analysis, we quantify the trade-off among the number of agents (or communication overhead), privacy preserving and learning utility. We also perform extensive simulations to verify the efficacy of our proposed social learning algorithm.

Flows past cylinders confined within ducts. Effects of the duct width

We present direct numerical simulations (DNS) of the flow past a circular cylinder confined in a rectangular duct at a Reynolds number of Re=630, based on the bulk velocity and the cylinder diameter. The blockage ratio, defined as the ratio of the cylinder diameter to the duct height, is set at β=0.6. We find the topology of the wake is highly sensitive to the duct width, and suggest that care needs to be taken comparing results with experimental data sets. This is unlike the flow past an unconfined or lowly confined cylinder where the general topology remains relatively similar with duct width. Ducts of width 4.44, 10, and 20 times the cylinder diameter have been considered along with an infinite channel. For the smallest duct of 4.44 cylinder diameters, the effects of the side walls of the duct, or the end walls from the perspective of the cylinder, extend into the core region, where there are strong interactions between the influence from opposing sides. The wake formed is much more chaotic, with Kelvin–Helmholtz vortices observed to form in the shear layers off the cylinder. Hence leading to a shorter wake. With increases in the duct width to 10 cylinder diameters, the separation of the side walls lessens the interactions within the centre of the duct. The shear layers off the cylinder are less destabilised as a result, leading to the formation of a more classical Kármán vortex street. The wake was also found to be longer as a result. However, the blockage effect was still evident at such a duct width. It was only for widths of 20 cylinder diameters or greater, a flow structurally similar to that in an infinite channel could be obtained, with asymmetric structures modulated along the span. Furthermore, the increases in the duct width beyond 10 cylinder diameters lead to decreases in the wake length.

A numerical method for the funicular analysis of masonry vaults accounting for stereotomy, finite strength and finite friction

The funicular analysis of curved masonry structures is addressed, considering the stereotomy of the voussoirs, a limited compressive strength, and a limited friction coefficient. The force density method is used to handle the equilibrium of the loaded nodes of the network, whose vertices lie along vertical lines passing through the centroids of the blocks. For the resulting grid with fixed plan projection, the minimization of the horizontal thrusts is formulated in terms of the height of the restrained nodes and of any set of independent force densities. Anti-funicular networks are sought by enforcing compression-only branches of the network. Local constraints are stated at each joint addressing the hypothesis of a limited compressive strength and a finite value of the friction coefficient between two adjacent voussoirs. To enforce no-tension blocks, lower and upper bounds for the vertical coordinates of the unrestrained vertices of the network are prescribed, as well. Sequential convex programming is used to solve the arising multi-constrained minimization problem. The algorithm, which can handle networks with general topology, is assessed by comparisons with results achieved with the Durand–Claye method, a semi-analytical method for the equilibrium analysis of symmetric masonry arches and domes that accounts for the limited compressive strength of masonry, the friction coefficient and the stereotomy of the voussoirs. Numerical examples concern arches, domes and a cloister vault, considering varying mechanical parameters.

Spacetime topology from holographic entanglement

An asymptotically AdS geometry connecting two or more boundaries is given by a entangled state, that can be expanded in the product basis of the Hilbert spaces of each CFT living on the boundaries. We derive a prescription to compute this expansion for states describing spacetimes with general spatial topology in arbitrary dimension. To large N, the expansion coincides with the Schmidt decomposition and the coefficients are given by n-point correlation functions on a particular Euclidean geometry.We show that this applies to all spacetime that admits a Hartle-Hawking type of wave functional, which via a standard hypothesis on the spatial topology, can be (one to one) mapped to CFT states defined on the asymptotic boundary. It is also observed that these states are endowed with quantum coherence properties.Applying this as holographic engineering, one can to construct an emergent space geometry with certain predetermined topology by preparing an entangled state of the dual quantum system. As an example, we apply the method to calculate the expansion and characterize a spacetime whose initial spatial topology is a (genus one) handlebody.

Fluid Cohomology

The vorticity-streamfunction formulation for incompressible inviscid fluids is the basis for many fluid simulation methods in computer graphics, including vortex methods, streamfunction solvers, spectral methods, and Monte Carlo methods. We point out that current setups in the vorticity-streamfunction formulation are insufficient at simulating fluids on general non-simply-connected domains. This issue is critical in practice, as obstacles, periodic boundaries, and nonzero genus can all make the fluid domain multiply connected. These scenarios introduce nontrivial cohomology components to the flow in the form of harmonic fields. The dynamics of these harmonic fields have been previously overlooked. In this paper, we derive the missing equations of motion for the fluid cohomology components. We elucidate the physical laws associated with the new equations, and show their importance in reproducing physically correct behaviors of fluid flows on domains with general topology.

Black Lenses in Kaluza-Klein Matter.

We present the first examples of formally asymptotically flat black hole solutions with horizons of general lens space topology L(p,q). These five-dimensional static or stationary spacetimes are regular on and outside the event horizon for any choice of relatively prime integers 1≤q<p; in particular, conical singularities are absent. They are supported by Kaluza-Klein matter fields arising from higher dimensional vacuum solutions through reduction on tori. The technique is sufficiently robust that it leads to the explicit construction of regular solutions, in any dimension, realizing the full range of possible topologies for the horizon as well as the domain of outer communication, that are allowable with multi-axisymmetry. Lastly, as a by-product, we obtain new examples of regular gravitational instantons in higher dimensions.

Detecting the complexity of a functional time series

ABSTRACT Consider a time series that takes values in a general topological space, and suppose that its Small-ball probability is factorised into two terms that play the role of a surrogate density and a volume term. The latter allows us to study the complexity of the underlying process. In some cases, the volume term can be analytically specified in a parametric form as a function of a complexity index. This work presents the study of an estimator for such an index whenever the volume term is monomial. Weak consistency and asymptotic Gaussianity are shown under an appropriate dependence structure, providing theoretical support for the construction of confidence intervals. A Monte Carlo simulation is performed to evaluate the performance of the approach under various conditions. Finally, the method is applied to identify the complexity of two real data sets.

R-Compatible Ideals of topological spaces

Abstract. This paper's goal is to present the idea of regular-compatibility of ideals by replaced the open set is Regular-open set and with respect to topology, which is abbreviated as (τ ∼ R I ), Using a brand-new local function termed the regular-local function A(*R) (I, T), it is also possible to examine the connection between this idea and the idea of the R-compatibility of an ideal with I. A few comparable circumstances are established. By employing the new operator is Regular -psi set short (ΨR(A)), we further analyze the characterizations of Regular -compatibility with the aid of this local function. And the relationship between them. Several notions of compatibility between a partially ordered set and a topology on its underlying set are comparable to separation axioms and other well-known ideas from general topology.

Efficient Distributed Inference of Deep Neural Networks via Restructuring and Pruning

In this paper, we consider the parallel implementation of an already-trained deep model on multiple processing nodes (a.k.a. workers). Specifically, we investigate as to how a deep model should be divided into several parallel sub-models, each of which is executed efficiently by a worker. Since latency due to synchronization and data transfer among workers negatively impacts the performance of the parallel implementation, it is desirable to have minimum interdependency among parallel sub-models. To achieve this goal, we propose to rearrange the neurons in the neural network, partition them (without changing the general topology of the neural network), and modify the weights such that the interdependency among sub-models is minimized under the computations and communications constraints of the workers while minimizing its impact on the performance of the model. We propose RePurpose, a layer-wise model restructuring and pruning technique that guarantees the performance of the overall parallelized model. To efficiently apply RePurpose, we propose an approach based on L0 optimization and the Munkres assignment algorithm. We show that, compared to the existing methods, RePurpose significantly improves the efficiency of the distributed inference via parallel implementation, both in terms of communication and computational complexity.

Privacy-preserving Resilient Consensus for Multi-agent Systems in a General Topology Structure

Recent advances of consensus control have made it significant in multi-agent systems such as in distributed machine learning, distributed multi-vehicle cooperative systems. However, during its application it is crucial to achieve resilience and privacy; specifically, when there are adversary/faulty nodes in a general topology structure, normal agents can also reach consensus while keeping their actual states unobserved. In this article, we modify the state-of-the-art Q-consensus algorithm by introducing predefined noise or well-designed cryptography to guarantee the privacy of each agent state. In the former case, we add specified noise on agent state before it is transmitted to the neighbors and then gradually decrease the value of noise so the exact agent state cannot be evaluated. In the latter one, the Paillier cryptosystem is applied for reconstructing reward function in two consecutive interactions between each pair of neighboring agents. Therefore, multi-agent privacy-preserving resilient consensus (MAPPRC) can be achieved in a general topology structure. Moreover, in the modified version, we reconstruct reward function and credibility function so both convergence rate and stability of the system are improved. The simulation results indicate the algorithms’ tolerance for constant and/or persistent faulty agents as well as their protection of privacy. Compared with the previous studies that consider both resilience and privacy-preserving requirements, the proposed algorithms in this article greatly relax the topological conditions. At the end of the article, to verify the effectiveness of the proposed algorithms, we conduct two sets of experiments, i.e., a smart-car hardware platform consisting of four vehicles and a distributed machine learning platform containing 10 workers and a server.

Advances in General Topology and Its Application

In recent years, mathematical and, in particular, topological models and methods have been used extensively in real-world problems related to economics, engineering, biology, computer science, medical science, social science, etc [...]

Un enfoque realmente topológico de algunos aspectos de la teoría de los extremos primos de Carathéodory

A homeomorphism approximation technique is applied to give (1) proofs of some theorems of C. Carathéodory, and (2) a proof of a theorem of N. Rutt. The proofs use only tools from general topology (and are new in that respect), and a generalization of a theorem of Carathéodory is obtained.

Cohomology of the discrete de Rham complex on domains of general topology

In this work we prove that, for a general polyhedral domain of mathbb {R}^3, the cohomology spaces of the discrete de Rham complex of Di Pietro and Droniou (Found Comput Math 23:85–164, 2023, https://doi.org/10.1007/s10208-021-09542-8) are isomorphic to those of the continuous de Rham complex. This is, to the best of our knowledge, the first result of this kind for a fully computable arbitrary-order complex built from a general polyhedral mesh.

Geometric T-Duality: Buscher Rules in General Topology

The classical Buscher rules d escribe T-duality for metrics and B-fields in a topologically trivial setting. On the other hand, topological T-duality addresses aspects of non-trivial topology while neglecting metrics and B-fields. In this article, we develop a new unifying framework for both aspects.

Periodic event‐triggered consensus based on triggered communication states for multi‐agent systems with packet losses

AbstractIn this paper, periodic event‐triggered leaderless and leader‐following consensus problems are studied for linear multi‐agent systems with deterministic packet losses under the generic directed communication topology. Specially, an event‐triggered mechanism is proposed, which only needs to communicate the event‐triggered states of the agent and verify the event‐triggered condition at the periodic sampling instants. A switched system with stable and unstable subsystems is used to describe packet dropouts in a deterministic way. The incidence matrix of a directed spanning tree in the directed communication topology is utilized to construct a linear transformation so that the consensus problems are equivalently transformed into the asymptotic stability problems of reduced‐order systems. Then, some sufficient consensus conditions are derived and the consensus protocol gains are designed. Finally, simulation examples are given to show the effectiveness of the proposed results.