A (k, g)-graph Γ, k ≥ 2, g ≥ 3, is k-regular of girth g. We refer to the complete set of possible orders of connected (k, g)-graphs for each pair of parameters (k, g) as the spectrum of orders of (k, g)-graphs;or t...
详细信息
One of the most influential factors in space development is cosmic radiation and its detrimental effects on microelectronics and life outside of the protection of Earth's atmosphere. While most primary cosmic rays...
详细信息
We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any ...
We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called teaching dimension. A recent paper (Ferri et al., 2024) conjectured that a worst case for this model, as a function of the size of the concept class, occurs when the consistency matrix contains the binary representations of numbers from zero and up. In this paper we prove their conjecture. The result can be seen as a generalization of a theorem resolving the edge isoperimetry problem for hypercubes (Hart, 1976). Our proof is based on a generalization of a lemma of (Graham, 1970). Copyright 2024 by the author(s)
We have found long-living periodic solutions of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) perturbed with intrapulse Raman scattering. To achieve this we have applied a model system of ordinary differ...
详细信息
We have found long-living periodic solutions of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) perturbed with intrapulse Raman scattering. To achieve this we have applied a model system of ordinary differential equations (SODE). A set of the fixed points of the system has been described. A complete phase portrait as well as phase portraits near the fixed points have been built for a proper choice of parameters. The behavior of the model system near the fixed points has been determined. We have presented a detailed description of the subcritical Poincaré-Andronov-Hopf bifurcation due to the intrapulse Raman scattering that appears at one of the fixed points. We have established that there appears an unstable limit cycle in the SODE. To check the validity of the obtained results from the model system we have compared them with the results of the numerical solution of the CCQGLE perturbed with intrapulse Raman scattering. There has been found a remarkable correspondence between the obtained numerical results for the amplitude and frequency of the soliton pulses and the results for these parameters of the bifurcation theory. We have observed that the numerical characteristics of the propagating solitonlike pulses—amplitude, frequency, width, and position—periodically change if we change the distance with a period determined by the bifurcation analysis.
We propose to create the global network of small, cheap and simple school Extensive Air Shower mini-arrays. The data registered in each school will be sent to a local database of the city/region supervised by the near...
详细信息
Given a finite group G, the hypergraphical regular representation problem asks about the existence of a hypergraph whose full automorphism group is equal to G acting regularly on the set of its vertices. In our paper,...
详细信息
The progenitors of gamma-ray bursts (GRBs) are massive stars still immersed in dense stellar clusters. We consider a scenario in which protons accelerated within the jet of GRB can escape to dense regions. Protons int...
详细信息
Federated learning is a machine learning method that allows models to be trained on decentralised data without participants sharing it with a central server. Federated learning can be modelled using Petri nets, mathem...
详细信息
We propose a new technique for creating a space-efficient index for large repetitive text collections, such as pangenomic databases containing sequences of many individuals from the same species. We combine two recent...
详细信息
ISBN:
(纸本)9783959772433
We propose a new technique for creating a space-efficient index for large repetitive text collections, such as pangenomic databases containing sequences of many individuals from the same species. We combine two recent techniques from this area: Wheeler graphs (Gagie et al., 2017) and prefix-free parsing (PFP, Boucher et al., 2019). Wheeler graphs are a general framework encompassing several indexes based on the Burrows-Wheeler transform (BWT), such as the FM-index. Wheeler graphs admit a succinct representation which can be further compacted by employing the idea of tunnelling, which exploits redundancies in the form of parallel, equally-labelled paths called blocks that can be merged into a single path. The problem of finding the optimal set of blocks for tunnelling, i.e. the one that minimizes the size of the resulting Wheeler graph, is known to be NP-complete and remains the most computationally challenging part of the tunnelling process. To find an adequate set of blocks in less time, we propose a new method based on the prefix-free parsing (PFP). The idea of PFP is to divide the input text into phrases of roughly equal sizes that overlap by a fixed number of characters. The phrases are then sorted lexicographically. The original text is represented by a sequence of phrase ranks (the parse) and a list of all used phrases (the dictionary). In repetitive texts, the PFP representation of the text is generally much shorter than the original since individual phrases are used many times in the parse, thus reducing the size of the dictionary. To speed up the block selection for tunnelling, we apply the PFP to obtain the parse and the dictionary of the original text, tunnel the Wheeler graph of the parse using existing heuristics and subsequently use this tunnelled parse to construct a compact Wheeler graph of the original text. Compared with constructing a Wheeler graph from the original text without PFP, our method is much faster and uses less memory on collections of
We use educational VR and AR solutions in hybrid learning and authoring and present several approaches for teachers enabling them to better engage their students in the educational process. We propose ideas for workin...
详细信息
暂无评论