Academic literature on the topic 'Variation graph'
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Journal articles on the topic "Variation graph"
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Arifin, Samsul, Indra Bayu Muktyas, and Jeremy Matthew Mandei. "Graph coloring program for variation of exam scheduling modeling at Binus University based on Welsh and Powell algorithm." Journal of Physics: Conference Series 2279, no. 1 (May 1, 2022): 012005. http://dx.doi.org/10.1088/1742-6596/2279/1/012005.
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Abstract In this article, we will design a computer program to solve graph colouring and to visualize the variation of exam scheduling modelling at Binus University in graphs based on the Welch and Powell Algorithm. A vertex colouring of graph G = (V, E) is an F: V → N mapping where the adjacent vertex are different colours in N, i.e. if the edge (u, v) are in E, then F (u) is not equal to F (v). The formulation of problems regarding computer programs based on a small experiment and variations in modelling exams is carried out in graph form using the Visual Basic Application.
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Firmansah, Fery. "Pelabelan Harmonis Ganjil pada Graf Bunga Double Quadrilateral." JURNAL ILMIAH SAINS 20, no. 1 (March 10, 2020): 12. http://dx.doi.org/10.35799/jis.20.1.2020.27278.
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Graf harmonis ganjil adalah graf yang memenuhi sifat-sifat pelabelan harmonis ganjil. Tujuan dari penelitian ini adalah mendapatkan kelas graf baru yang merupakan graf harmonis ganjil. Metode penelitian yang digunakan terdiri dari beberapa tahapan yaitu konstruksi definisi, formulasi fungsi pelabelan dan pembuktian teorema. Hasil dari penelitian ini adalah konstruksi graf bunga double quadrilateral dengan dan graf bunga variasi double quadrilateral dengan yang merupakan pengembangan dari graf double quadrilateral dan graf variasi double quadrilateral . Lebih lanjut telah dibuktikan bahwa graf dan adalah graf harmonis ganjil.Kata Kunci: graf double quadrilateral, graf bunga, graf harmonis ganjil, pelabelan graf Odd Harmonious Labelling on The Flower Double Quadrilateral Graphs ABSTRACTOdd harmonious graphs are graphs that have odd harmonious labeling properties. The purpose of this study is to get a new class of graphs which are odd harmonious graphs. The research method used consists of several stages, namely construction of definitions, formulation of labeling functions and proof of theorems. The results of this study is to get a graph construction will be given, namely the flower quadrilateral graphs with and the flower variation of quadrilateral graphs with , which are the development of double quadrilateral graphs and variation double quadrilateral graphs . It has further been proven that and are odd harmonious graphs.Keywords: double quadrilateral graph, flower graph, labeling graph, odd harmonious graph
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Prabhakaran, Rahul, Giovanni Bertotti, Janos Urai, and David Smeulders. "Investigating spatial heterogeneity within fracture networks using hierarchical clustering and graph distance metrics." Solid Earth 12, no. 10 (September 30, 2021): 2159–209. http://dx.doi.org/10.5194/se-12-2159-2021.
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Abstract. Rock fractures organize as networks, exhibiting natural variation in their spatial arrangements. Therefore, identifying, quantifying, and comparing variations in spatial arrangements within network geometries are of interest when explicit fracture representations or discrete fracture network models are chosen to capture the influence of fractures on bulk rock behaviour. Treating fracture networks as spatial graphs, we introduce a novel approach to quantify spatial variation. The method combines graph similarity measures with hierarchical clustering and is applied to investigate the spatial variation within large-scale 2-D fracture networks digitized from the well-known Lilstock limestone pavements, Bristol Channel, UK. We consider three large, fractured regions, comprising nearly 300 000 fractures spread over 14 200 m2 from the Lilstock pavements. Using a moving-window sampling approach, we first subsample the large networks into subgraphs. Four graph similarity measures – fingerprint distance, D-measure, Network Laplacian spectral descriptor (NetLSD), and portrait divergence – that encapsulate topological relationships and geometry of fracture networks are then used to compute pair-wise subgraph distances serving as input for the statistical hierarchical clustering technique. In the form of hierarchical dendrograms and derived spatial variation maps, the results indicate spatial autocorrelation with localized spatial clusters that gradually vary over distances of tens of metres with visually discernable and quantifiable boundaries. Fractures within the identified clusters exhibit differences in fracture orientations and topology. The comparison of graph similarity-derived clusters with fracture persistence measures indicates an intra-network spatial variation that is not immediately obvious from the ubiquitous fracture intensity and density maps. The proposed method provides a quantitative way to identify spatial variations in fracture networks, guiding stochastic and geostatistical approaches to fracture network modelling.
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Rautiainen, Mikko, Veli Mäkinen, and Tobias Marschall. "Bit-parallel sequence-to-graph alignment." Bioinformatics 35, no. 19 (March 9, 2019): 3599–607. http://dx.doi.org/10.1093/bioinformatics/btz162.
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Abstract Motivation Graphs are commonly used to represent sets of sequences. Either edges or nodes can be labeled by sequences, so that each path in the graph spells a concatenated sequence. Examples include graphs to represent genome assemblies, such as string graphs and de Bruijn graphs, and graphs to represent a pan-genome and hence the genetic variation present in a population. Being able to align sequencing reads to such graphs is a key step for many analyses and its applications include genome assembly, read error correction and variant calling with respect to a variation graph. Results We generalize two linear sequence-to-sequence algorithms to graphs: the Shift-And algorithm for exact matching and Myers’ bitvector algorithm for semi-global alignment. These linear algorithms are both based on processing w sequence characters with a constant number of operations, where w is the word size of the machine (commonly 64), and achieve a speedup of up to w over naive algorithms. For a graph with |V| nodes and |E| edges and a sequence of length m, our bitvector-based graph alignment algorithm reaches a worst case runtime of O(|V|+⌈mw⌉|E| log w) for acyclic graphs and O(|V|+m|E| log w) for arbitrary cyclic graphs. We apply it to five different types of graphs and observe a speedup between 3-fold and 20-fold compared with a previous (asymptotically optimal) alignment algorithm. Availability and implementation https://github.com/maickrau/GraphAligner Supplementary information Supplementary data are available at Bioinformatics online.
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Bhat, Farooq Ahmad, and M. Arif Wani. "Elastic Bunch Graph Matching Based Face Recognition Under Varying Lighting, Pose, and Expression Conditions." IAES International Journal of Artificial Intelligence (IJ-AI) 3, no. 4 (August 20, 2016): 177. http://dx.doi.org/10.11591/ijai.v3.i4.pp177-182.
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In this paper performance of elastic bunch graph matching (EBGM) for face recognition under variation in facial expression, variation in lighting condition and variation in poses are given. In this approach faces are represented by labelled graphs. Experimental results of EBGM on ORL, Yale B and FERET datasets are provided. Strong and weak features of EBGM algorithm are discussed.
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Qiu, Yutong, and Carl Kingsford. "Constructing small genome graphs via string compression." Bioinformatics 37, Supplement_1 (July 1, 2021): i205—i213. http://dx.doi.org/10.1093/bioinformatics/btab281.
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Abstract Motivation The size of a genome graph—the space required to store the nodes, node labels and edges—affects the efficiency of operations performed on it. For example, the time complexity to align a sequence to a graph without a graph index depends on the total number of characters in the node labels and the number of edges in the graph. This raises the need for approaches to construct space-efficient genome graphs. Results We point out similarities in the string encoding mechanisms of genome graphs and the external pointer macro (EPM) compression model. We present a pair of linear-time algorithms that transform between genome graphs and EPM-compressed forms. The algorithms result in an upper bound on the size of the genome graph constructed in terms of an optimal EPM compression. To further reduce the size of the genome graph, we propose the source assignment problem that optimizes over the equivalent choices during compression and introduce an ILP formulation that solves that problem optimally. As a proof-of-concept, we introduce RLZ-Graph, a genome graph constructed based on the relative Lempel–Ziv algorithm. Using RLZ-Graph, across all human chromosomes, we are able to reduce the disk space to store a genome graph on average by 40.7% compared to colored compacted de Bruijn graphs constructed by Bifrost under the default settings. The RLZ-Graph scales well in terms of running time and graph sizes with an increasing number of human genome sequences compared to Bifrost and variation graphs produced by VGtoolkit. Availability The RLZ-Graph software is available at: https://github.com/Kingsford-Group/rlzgraph. Supplementary information Supplementary data are available at Bioinformatics online.
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Angadi, Shanmukhappa A., and Sanjeevakumar M. Hatture. "Face Recognition Through Symbolic Modeling of Face Graphs and Texture." International Journal of Pattern Recognition and Artificial Intelligence 33, no. 12 (November 2019): 1956008. http://dx.doi.org/10.1142/s0218001419560081.
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Face recognition helps in authentication of the user using remotely acquired facial information. The dynamic nature of face images like pose, illumination, expression, occlusion, aging, etc. degrades the performance of the face recognition system. In this paper, a new face recognition system using facial images with illumination variation, pose variation and partial occlusion is presented. The facial image is described as a collection of three complete connected graphs and these graphs are represented as symbolic objects. The structural characteristics, i.e. graph spectral properties, energy of graph, are extracted and embedded in a symbolic object. The texture features from the cheeks portions are extracted using center symmetric local binary pattern (CS-LBP) descriptor. The global features of the face image, i.e. length and width, are also extracted. Further symbolic data structure is constructed using the above features, namely, the graph spectral properties, energy of graph, global features and texture features. User authentication is performed using a new symbolic similarity metric. The performance is investigated by conducting the experiments with AR face database and VTU-BEC-DB multimodal database. The experimental results demonstrate an identification rate of 95.97% and 97.20% for the two databases.
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Youssef, Maged Zakaria, and Zainab Saad Almoreed. "On odd prime labeling of graphs." Open Journal of Discrete Applied Mathematics 3, no. 3 (October 20, 2020): 33–40. http://dx.doi.org/10.30538/psrp-odam2020.0041.
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In this paper we give a new variation of the prime labeling. We call a graph \(G\) with vertex set \(V(G)\) has an odd prime labeling if its vertices can be labeled distinctly from the set \(\big\{1, 3, 5, ...,2\big|V(G)\big| -1\big\}\) such that for every edge \(xy\) of \(E(G)\) the labels assigned to the vertices of \(x\) and \(y\) are relatively prime. A graph that admits an odd prime labeling is called an <i>odd prime graph</i>. We give some families of odd prime graphs and give some necessary conditions for a graph to be odd prime. Finally, we conjecture that every prime graph is odd prime graph.
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Kuhlmann, Marco, and Stephan Oepen. "Towards a Catalogue of Linguistic Graph Banks." Computational Linguistics 42, no. 4 (December 2016): 819–27. http://dx.doi.org/10.1162/coli_a_00268.
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Graphs exceeding the formal complexity of rooted trees are of growing relevance to much NLP research. Although formally well understood in graph theory, there is substantial variation in the types of linguistic graphs, as well as in the interpretation of various structural properties. To provide a common terminology and transparent statistics across different collections of graphs in NLP, we propose to establish a shared community resource with an open-source reference implementation for common statistics.
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Da Silva, Kévin, Nicolas Pons, Magali Berland, Florian Plaza Oñate, Mathieu Almeida, and Pierre Peterlongo. "StrainFLAIR: strain-level profiling of metagenomic samples using variation graphs." PeerJ 9 (August 23, 2021): e11884. http://dx.doi.org/10.7717/peerj.11884.
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Current studies are shifting from the use of single linear references to representation of multiple genomes organised in pangenome graphs or variation graphs. Meanwhile, in metagenomic samples, resolving strain-level abundances is a major step in microbiome studies, as associations between strain variants and phenotype are of great interest for diagnostic and therapeutic purposes. We developed StrainFLAIR with the aim of showing the feasibility of using variation graphs for indexing highly similar genomic sequences up to the strain level, and for characterizing a set of unknown sequenced genomes by querying this graph. On simulated data composed of mixtures of strains from the same bacterial species Escherichia coli, results show that StrainFLAIR was able to distinguish and estimate the abundances of close strains, as well as to highlight the presence of a new strain close to a referenced one and to estimate its abundance. On a real dataset composed of a mix of several bacterial species and several strains for the same species, results show that in a more complex configuration StrainFLAIR correctly estimates the abundance of each strain. Hence, results demonstrated how graph representation of multiple close genomes can be used as a reference to characterize a sample at the strain level.
Dissertations / Theses on the topic "Variation graph"
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Kural, Deniz. "Methods for Inter- and Intra-Species Genomics for the Detection of Variation and Function." Thesis, Boston College, 2014. http://hdl.handle.net/2345/bc-ir:104053.
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Thesis advisor: Gabor T. MarthThis thesis concerns itself with the development of methods for comparing genomes. Chapter 2 is a comparative genomics investigation of coding regions across multiple species. Regions of the genome coding for proteins show higher conservation than non-coding regions. Furthermore, we show that a portion of coding regions are conserved beyond the requirements of protein conservation, supporting functions such as microRNA binding and splicing enhancement, providing the non-coding functional impetus to conservation. In Chapter 3, we focus on the detection and characterization of a particular type of structural variation - mobile element insertions (MEIs). While there are many types of mobile elements in the human genome, three of these are active and cause most of the MEI variation observed in humans: ALU, L1 and SVA elements. We detect variation across 1000 Genomes Pilot populations caused by these elements, assemble ALU elements to single nucleotide resolution, and determine actively copying species of this element. We've developed a variety of algorithmic approaches to MEI detection, and present these. Chapter 4 outlines an approach to remedy reference bias via the incorporation of variation data into the reference. In particular, we construct a pan-genome reference, demonstrated concretely via resolving ALU regions, and develop new alignment software to align against this enriched reference structure
Thesis (PhD) — Boston College, 2014
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Biology
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Romain, Sandra. "Identification, génotypage et représentation des variants de structure dans les pangénomes." Electronic Thesis or Diss., Université de Rennes (2023-....), 2024. https://ged.univ-rennes1.fr/nuxeo/site/esupversions/71b8c90f-bac9-4948-9bb1-a4b6d953f322.
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Les variants structuraux (SVs), des variations génomiques de plus de 50 pb, contribuent de manière significative à la diversité génétique et à l'évolution des espèces. La détection et le génotypage précis des SVs est crucial pour comprendre leur rôle dans la variation phénotypique et l'adaptation. Les graphes de variation (VGs) et graphes de pangénomes (PGs), qui représentent les variations génomiques comme des chemins alternatifs dans un graphe, offrent une approche prometteuse pour l'analyse des SVs. Cette thèse explore l'utilisation des VGs et PGs pour la détection et le génotypage des SVs, en se concentrant sur un complexe de quatre espèces de papillons Coenonympha alpins. Deux outils bio-informatiques ont été développés au cours de cette thèse : (1) SVJedi-graph, le premier génotypeur de SVs à partir de lectures longues utilisant un VG pour représenter les SVs, fournissant une précision de génotypage supérieure aux outils de l’état de l’art, en particulier pour les SVs proches et chevauchants, et (2) INVPG-annot, un outil d’identification des inversions dans les PGs, qui a permi de démontrer que les inversions sont représentées par différentes topologies dans les PGs selon l’outil de construction utilisé. L'analyse comparative des génomes des papillons Coenonympha a permis d'identifier douze grandes inversions (≥ 100 kbp) entre les quatre espèces, dont certaines pourraient jouer un rôle dans l'isolement reproductif et l'adaptation locale de deux de ces espèces. Bien que l'approche basée sur les PGs présente des avantages pour la comparaison de génomes, des défis restent à relever pour l'analyse des grands variants comme les inversionsStructural variants (SVs), genomic variations of more than 50 bp, contribute significantly to genetic diversity and species evolution. Accurate detection and genotyping SVs is crucial to understanding their role in phenotypic variation and adaptation. Variation graphs (VGs) and pangenome graphs (PGs), which represent genomic variations as alternative paths in a graph, offer a promising approach for the analysis of SVs. This thesis explores the use of VGs and PGs for the detection and genotyping of SVs, focusing on a complex of four species of alpine Coenonympha butterflies. Two bioinformatics tools were developed during this thesis: (1) SVJedi-graph, the first long-read SV genotyper using a VG to represent SVs, providing a genotyping accuracy superior to state-of-the-art tools, particularly for close and overlapping SVs, and (2) INVPG-annot, a tool for identifying inversions in PGs, which demonstrated that inversions are represented by different topologies in PGs depending on the construction tool used. Comparative analysis of the Coenonympha butterfly genomes identified twelve large inversions (≥ 100 kbp) between the four species, some of which could play a role in the reproductive isolation and local adaptation of two of these species. While the PG-based approach offers advantages for genome comparison, challenges remain for the analysis of large variants such as inversions
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Jaillard, Dancette Magali. "Vers une cartographie fine des polymorphismes liés à la résistance aux antimicrobiens." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1282/document.
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Mieux comprendre les mécanismes de la résistance aux antibiotique est un enjeu important dans la lutte contre les maladies infectieuses, qui fait face à la propagation de bactéries multi-résistantes. Les études d'association à l'échelle des génomes sont des outils puissants pour explorer les polymorphismes liés aux variations phénotypiques dans une population. Leur cadre méthodologique est très documenté pour les eucaryotes, mais leur application aux bactéries est très récente. Durant cette thèse, j'ai cherché à rendre ces outils mieux adaptés aux génomes plastiques des bactéries, principalement en travaillant sur la représentation des variations génétiques. En effet, parce que les bactéries ont la capacité à échanger du matériel génétique avec leur environnement, leurs génomes peuvent être trop différents au sein d'une espèce pour être alignés contre une référence. La description des variations par des fragments de séquence de longueur k, les k-mers, offre la flexibilité nécessaire mais ne permet pas une interprétation directe des résultats obtenus. La méthode mise au point teste l'association de ces k-mers avec le phénotype, et s'appuie sur un graphe de De Bruijn pour permettre la visualisation du contexte génomique des k-mers identifiés par le test, sous forme de graphes. Cette vue synthétique renseigne sur la nature de la séquence identifiée: il peut par exemple s'agir de polymorphisme local dans un gène ou de l'acquisition d'un gène dans un plasmide. Le type de variant représenté dans un graphe peut être prédit avec une bonne performance à partir de descripteurs du graphe, rendant plus opérationnelles les approches par k-mers pour l'étude des génomes bactériensThe emergence and spread of multi-drug resistance has become a major worldwide public health concern, calling for better understanding of the underlying resistance mechanisms. Genome-wide association studies are powerful tools to finely map the genetic polymorphism linked to the phenotypic variability observed in a population. However well documented for eukaryotic genome analysis, these studies were only recently applied to prokaryota.Through this PhD project, I searched how to better adapt these tools to the highly plastic bacterial genomes, mainly by working on the representation of the genetic variations in these genomes. Indeed, because the bacteria have the faculty to acquire genetic material by a means other than direct inheritance from a parent cell, their genomes can differ too much within a species to be aligned against a reference. A representation using sequence fragments of length k - the so-called k-mers - offers the required flexibility but generates redundancy and does not allow for a direct interpretation of the identified associations. The method we set up tests the association of these k-mers with the phenotype, and takes advantage of a De Bruijn graph (DBG) built over all genomes to remove the local redundancy of k-mers, and offer a visualisation of the genomic context of the k-mers identified by the test. This synthetic view as DBG subgraphs informs on the nature of the identified sequence: e.g. local polymorphism in a gene or gene acquired through a plasmid. The type of variant can be predicted correctly in 96% of the cases from descriptors of the subgraphs, providing a tractable framework for k-mer-based association studies
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Yeo, Ronald A., Sephira G. Ryman, den Heuvel Martijn P. van, Reus Marcel A. de, Rex E. Jung, Jessica Pommy, Andrew R. Mayer, et al. "Graph Metrics of Structural Brain Networks in Individuals with Schizophrenia and Healthy Controls: Group Differences, Relationships with Intelligence, and Genetics." Cambridge University Press, 2016. https://tud.qucosa.de/id/qucosa%3A70691.
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Objectives: One of the most prominent features of schizophrenia is relatively lower general cognitive ability (GCA). An emerging approach to understanding the roots of variation in GCA relies on network properties of the brain. In this multi-center study, we determined global characteristics of brain networks using graph theory and related these to GCA in healthy controls and individuals with schizophrenia.
Methods: Participants (N = 116 controls, 80 patients with schizophrenia) were recruited from four sites. GCA was represented by the first principal component of a large battery of neurocognitive tests. Graph metrics were derived from diffusion-weighted imaging.
Results: The global metrics of longer characteristic path length and reduced overall connectivity predicted lower GCA across groups, and group differences were noted for both variables. Measures of clustering, efficiency, and modularity did not differ across groups or predict GCA. Follow-up analyses investigated three topological types of connectivity—connections among high degree “rich club” nodes, “feeder” connections to these rich club nodes, and “local” connections not involving the rich club. Rich club and local connectivity predicted performance across groups. In a subsample (N = 101 controls, 56 patients), a genetic measure reflecting mutation load, based on rare copy number deletions, was associated with longer characteristic path length.
Conclusions: Results highlight the importance of characteristic path lengths and rich club connectivity for GCA and provide no evidence for group differences in the relationships between graph metrics and GCA.
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Meinhardt, Llopis Enric. "Morphological and statistical techniques for the analysis of 3D images." Doctoral thesis, Universitat Pompeu Fabra, 2011. http://hdl.handle.net/10803/22719.
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Aquesta tesi proposa una estructura de dades per
emmagatzemar imatges tridimensionals. L'estructura da dades té
forma d'arbre i codifica les components connexes dels conjunts de
nivell de la imatge. Aquesta estructura és la eina bàsica per
moltes aplicacions proposades: operadors morfològics
tridimensionals, visualització d'imatges mèdiques, anàlisi
d'histogrames de color, seguiment d'objectes en vídeo i detecció
de vores. Motivada pel problema de la completació de vores, la
tesi conté un estudi de com l'eliminació de soroll mitjançant variació
total anisòtropa es pot fer servir per calcular conjunts de
Cheeger en mètriques anisòtropes. Aquests conjunts de Cheeger
anisòtrops es poden utilitzar per trobar òptims globals d'alguns
funcionals per completar vores. També estan relacionats amb
certs invariants afins que s'utilitzen en reconeixement
d'objectes, i en la tesi s'explicita aquesta relació.This thesis proposes a tree data structure to encode the connected components of level sets of 3D images. This data structure is applied as a main tool in several proposed applications: 3D morphological operators, medical image visualization, analysis of color histograms, object tracking in videos and edge detection. Motivated by the problem of edge linking, the thesis contains also an study of anisotropic total variation denoising as a tool for computing anisotropic Cheeger sets. These anisotropic Cheeger sets can be used to find global optima of a class of edge linking functionals. They are also related to some affine invariant descriptors which are used in object recognition, and this relationship is laid out explicitly.
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Jacob, Jobby. "Variations on graph products and vertex partitions." Connect to this title online, 2009.
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Sonnerat, Nicolas. "Galaxy cutsets and graph connectivity: variations on a theme." Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=97002.
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In this thesis we consider cutsets in graphs which can be expressed as unionsof sets each of which is spanned by a tree of diameter at most d-1 for someinteger d ≥ 1; we call these sets galaxy cutsets. These galaxycutsets generalise both star-cutsets and vertex-cuts, and serve as simple models for virus-like attacks on or cascading failures in networks,the crucial property being that neighbours of affected vertices may alsofail and cease to function. We approach our subject from four different pointsof view. We begin by exploring the connection between galaxiesand a suitable type of flow, proving a min-max result for planargraphs. Then, after tackling the fundamental issue of recognising whethera given graph is susceptible to virus-like attacks, i.e. whether it contains a galaxy cutset, we consider a weighted version of the flows that are dualto the galaxies, and prove Θ(log n) lower and upper approximability boundsfor the problem of finding a maximum such flow. We then investigate the problem of network design, that is tosay, the problem of constructing low cost spanning subgraphs of a given graph which are not vulnerable to cascading failures. Finally, weembark on a detailed analysis of the structure of star-cutsets in planar graphs and useour results to derive a polynomial time algorithm for the problem ofneutralising every star-cutset by protecting edges.Dans cette thèse, nous considerons des séparateurs dans les graphes qui peuvent être éxprimés sous forme d'une union d'ensembles de sommets dans laquelle chaque ensemble est couvert par un arbre de diamètre d-1 pour un nombre entier d ≥ 1; nous appellons ces séparateurs des galaxies séparatrices. Les galaxies séparatrices genéralisent les étoiles séparatrices et les séparateurs formés par un ensemble de sommets, et elles servent comme simple modèle pour des attaques de virus sur ou des cascades de défaillances dans un réseau, la proprieté distinguante étant que les voisins des sommets qui sont affectés peuvent eux aussi faillir. Nous approchons le sujet depuis quatre points de vue différents. Nous commençons par explorer le lien entre les galaxies et un type de flot approprié, et nous prouvons un résultat de type min max pour les graphes planaires. Ensuite, après avoir résolu la question fondamentale de reconnaitre si un graphe donné est sensible aux attaques de virus, c'est-à-dire s'il contient une galaxie séparatrice, nous introduisons des capacités dans les flots correspondants aux galaxies, et demontrons une borne d'approximabilité inférieure et supérieure de Θ(log n)pour le problème de trouver un flot maximum. Ensuite, nous enquêtons sur le problème de dessein de réseau, c'est-à-dire le problème de construire des sous-graphes couvrants peu coûteux qui ne sont pas sensibles aux cascades de défaillances. Finalement, nous nous lançons dans une analyse détaillée de la structure des étoiles séparatrices dans les graphes planaires, et nous utilisons nos résultats pour développer un algorithme polynomial qui résout le problème de neutraliser toutes les étoiles séparatrices en protégeant des arêtes.
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Pandey, Arti. "Algorithmic aspects of domination and its variations." Thesis, IIT Delhi, 2016. http://localhost:8080/xmlui/handle/12345678/7038.
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Trillos, Nicolás Garcia. "Variational Limits of Graph Cuts on Point Clouds." Research Showcase @ CMU, 2015. http://repository.cmu.edu/dissertations/518.
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The main goal of this thesis is to develop tools that enable us to study the convergence of minimizers of functionals defined on point clouds towards minimizers of equivalent functionals in the continuum; the point clouds we consider are samples of a ground-truth distribution. In particular, we investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based on graph cuts like the Cheeger and ratio cuts. We show that minimizers of these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut (which partitions the ground-truth distribution). Moreover, we obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for the consistency to hold. We provide results for two-way and for multi-way cuts. The results are obtained by using the notion of Γ-convergence and an appropriate choice of metric which allows us to compare functions defined on point clouds with functions defined on continuous domains.
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Couprie, Camille. "Graph-based variational optimization and applications in computer vision." Phd thesis, Université Paris-Est, 2011. http://tel.archives-ouvertes.fr/tel-00666878.
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Many computer vision applications such as image filtering, segmentation and stereovision can be formulated as optimization problems. Recently discrete, convex, globally optimal methods have received a lot of attention. Many graph-based methods suffer from metrication artefacts, segmented contours are blocky in areas where contour information is lacking. In the first part of this work, we develop a discrete yet isotropic energy minimization formulation for the continuous maximum flow problem that prevents metrication errors. This new convex formulation leads us to a provably globally optimal solution. The employed interior point method can optimize the problem faster than the existing continuous methods. The energy formulation is then adapted and extended to multi-label problems, and shows improvements over existing methods. Fast parallel proximal optimization tools have been tested and adapted for the optimization of this problem. In the second part of this work, we introduce a framework that generalizes several state-of-the-art graph-based segmentation algorithms, namely graph cuts, random walker, shortest paths, and watershed. This generalization allowed us to exhibit a new case, for which we developed a globally optimal optimization method, named "Power watershed''. Our proposed power watershed algorithm computes a unique global solution to multi labeling problems, and is very fast. We further generalize and extend the framework to applications beyond image segmentation, for example image filtering optimizing an L0 norm energy, stereovision and fast and smooth surface reconstruction from a noisy cloud of 3D points
Books on the topic "Variation graph"
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Science, Lawrence Hall of, ed. Equals investigations, remote rulers: A middle-school mathematics unit focusing on the relationship between algebraic graphs and graphs from real data involving direct and inverse variation. Berkeley, CA: University of California at Berkeley, 1994.
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de, Werra D., and Hertz A, eds. Graph colouring and variations. Amsterdam: North-Holland, 1989.
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Krishnamoorthy, Raju. Dynamics, Graph Theory, and Barsotti-Tate Groups: Variations on a Theme of Mochizuki. [New York, N.Y.?]: [publisher not identified], 2016.
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Salavessa, Isabel Maria da Costa. Graphs with parallel mean curvature and a variational problem in conformal geometry. [s.l.]: typescript, 1987.
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E, Gaines Steven, Hipskind R. Stephen, United States. National Aeronautics and Space Administration., and San Jose State University. Meteorology Dept., eds. An atlas of objectively analyzed atmospheric cross sections 1973-1980. [Washington, D.C: National Aeronautics and Space Administration, 1985.
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Barg, Alexander, and O. R. Musin. Discrete geometry and algebraic combinatorics. Providence, Rhode Island: American Mathematical Society, 2014.
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Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.
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Lyman, R. Lee. Graphing Culture Change in North American Archaeology. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198871156.001.0001.
Full textAbstract:
Documentation, analysis, and explanation of culture change have long been goals of archaeology. The earliest archaeological spindle graphs appeared in the 1880s and 1890s, but had no influence on subsequent archaeologists. Line graphs showing change in frequencies of specimens in each of several artifact types were used in the 1910s and 1920s. Seriograms or straight-sided spindles diagraming interpretations of culture change were published in the 1930s, but were seldom subsequently mimicked. Spindle graphs of centered and stacked columns of bars, each column representing a distinct artifact type, each bar the empirically documented relative frequency of specimens in an assemblage, were developed in the 1940s, became popular in the 1950s and 1960s, and are often used to illustrate culture change in textbooks published during the twentieth century. Graphs facilitate visual thinking, different graph types suggest different ontologies and theories of change, and particular techniques of parsing temporally continuous morphological variation of artifacts into types influence graph form. Line graphs, bar graphs, spindle diagrams, and phylogenetic trees of artifacts and cultures indicate archaeologists often mixed elements of Darwinian variational evolutionary change with elements of Midas-touch-like transformational change. Today there is minimal discussion of graph theory or graph grammar in both introductory archaeology textbooks and advanced texts, and elements of the two theories of evolution are often mixed. Culture has changed, and despite archaeology’s unique access to the totality of humankind’s cultural past, there is minimal discussion on graph theory, construction, and decipherment in the archaeological literature.
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Werra, D. de, and A. Hertz. Graph Colouring and Variations. Elsevier Science & Technology Books, 1989.
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Graph Colouring and Variations. Elsevier, 1989. http://dx.doi.org/10.1016/s0167-5060(08)x7011-6.
Full textBook chapters on the topic "Variation graph"
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Mitra, Susanta, and Aditya Bagchi. "Modeling Temporal Variation in Social Network: An Evolutionary Web Graph Approach." In Handbook of Social Network Technologies and Applications, 169–84. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-7142-5_8.
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Salim, Asif, S. S. Shiju, and S. Sumitra. "Effectiveness of Representation and Length Variation of Shortest Paths in Graph Classification." In Lecture Notes in Computer Science, 509–16. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-69900-4_65.
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Subercaseaux, Bernardo, and Marijn J. H. Heule. "The Packing Chromatic Number of the Infinite Square Grid is 15." In Tools and Algorithms for the Construction and Analysis of Systems, 389–406. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30823-9_20.
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AbstractA packing k-coloring is a natural variation on the standard notion of graph k-coloring, where vertices are assigned numbers from $$\{1, \ldots , k\}$$ { 1 , … , k } , and any two vertices assigned a common color $$c \in \{1, \ldots , k\}$$ c ∈ { 1 , … , k } need to be at a distance greater than c (as opposed to 1, in standard graph colorings). Despite a sequence of incremental work, determining the packing chromatic number of the infinite square grid has remained an open problem since its introduction in 2002. We culminate the search by proving this number to be 15. We achieve this result by improving the best-known method for this problem by roughly two orders of magnitude. The most important technique to boost performance is a novel, surprisingly effective propositional encoding for packing colorings. Additionally, we developed an alternative symmetry breaking method. Since both new techniques are more complex than existing techniques for this problem, a verified approach is required to trust them. We include both techniques in a proof of unsatisfiability, reducing the trusted core to the correctness of the direct encoding.
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Alivanistos, Dimitrios, Seth van der Bijl, Michael Cochez, and Frank van Harmelen. "The Effect of Knowledge Graph Schema on Classifying Future Research Suggestions." In Lecture Notes in Computer Science, 149–70. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-65794-8_10.
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AbstractThe output of research doubles at least every 20 years and in most research fields the number of research papers has become overwhelming. A critical task for researchers is to find promising future directions and interesting scientific challenges in the literature. To tackle this problem, we hypothesize that structured representations of information in the literature can be used to identify these elements. Specifically, we look at structured representations in the form of Knowledge Graphs (KGs) and we investigate how using different input schemas for extraction impacts the performance on the tasks of classifying sentences as future directions. Our results show that the MECHANIC-Granular schema yields the best performance across different settings and achieves state of the art performance when combined with pretrained embeddings. Overall, we observe that schemas with limited variation in the resulting node degrees and significant interconnectedness lead to the best downstream classification performance.
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Lodhi, Aminah Bilal, Muhammad Abdullah Bilal, Hafiz Syed Muhammad Bilal, Kifayat Ullah Khan, Fahad Ahmed Satti, Shah Khalid, and Sungyoung Lee. "PNRG: Knowledge Graph-Driven Methodology for Personalized Nutritional Recommendation Generation." In Digital Health Transformation, Smart Ageing, and Managing Disability, 230–38. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43950-6_20.
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AbstractChronic Diseases are a prevalent problem that affects millions of people worldwide. It is a prevalent health condition that requires careful diet and medication management and preventing chronic diseases. Traditional approaches to nutritional recommendation generation often rely on generic guidelines and population-based data, which may not account for individual dietary needs and preferences variations. In this paper, we propose a knowledge graph driven methodology for generating highly personalized nutritional recommendations that leverage the power of knowledge graphs to integrate and analyze complex data about an individual's health, lifestyle, and dietary habits. Our methodology employs a multi-step process that includes data collection and curation, knowledge graph construction, and personalized recommendation generation. We illustrate the effectiveness of our approach through a case study in which we generate personalized nutritional recommendations for a sample individual based on their specific health and dietary goals.
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Müller-Olm, Markus. "5. Parallel Flow Graphs." In Variations on Constants, 81–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11871743_5.
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Ayabe, Hiroaki, Emmanuel Manalo, Mari Fukuda, and Norihiro Sadato. "What Diagrams Are Considered Useful for Solving Mathematical Word Problems in Japan?" In Diagrammatic Representation and Inference, 79–83. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86062-2_8.
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AbstractPrevious studies have shown that diagram use is effective in mathematical word problem solving. However, they have also revealed that students manifest many problems in using diagrams for such purposes. A possible reason is an inadequacy in students’ understanding of variations in types of problems and the corresponding kinds of diagrams appropriate to use. In the present study, a preliminary investigation was undertaken of how such correspondences between problem types and kinds of diagrams are represented in textbooks. One government-approved textbook series for elementary school level in Japan was examined for the types of mathematical word problems, and the kinds of diagrams presented with those problems. The analyses revealed significant differences in association between kinds of diagrams and types of problems. More concrete diagrams were included with problems involving change, combination, variation, and visualization of quantities; while number lines were more often used with comparison and variation problems. Tables and graphs corresponded to problems requiring organization of quantities; and more concrete diagrams and graphs to problems involving quantity visualization. These findings are considered in relation to the crucial role of textbooks and other teaching materials in facilitating strategy knowledge acquisition in students.
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Mahdavi, Sedigheh, Shima Khoshraftar, and Aijun An. "Dynamic Joint Variational Graph Autoencoders." In Machine Learning and Knowledge Discovery in Databases, 385–401. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43823-4_32.
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Dontchev, Asen L. "Mappings with Convex Graphs." In Lectures on Variational Analysis, 53–59. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79911-3_6.
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Finn, Robert. "The inclination of an H-graph." In Calculus of Variations and Partial Differential Equations, 40–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0082884.
Full textConference papers on the topic "Variation graph"
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Crowley, Daniel, Marco Dalla, Barry O'Sullivan, and Andrea Visentin. "SAT Instances Generation Using Graph Variational Autoencoders." In ESANN 2024, 369–74. Louvain-la-Neuve (Belgium): Ciaco - i6doc.com, 2024. http://dx.doi.org/10.14428/esann/2024.es2024-223.
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Shahid, Nauman, Nathanael Perraudin, Vassilis Kalofolias, Benjamin Ricaud, and Pierre Vandergheynst. "PCA using graph total variation." In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472562.
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Ono, Shunsuke, Isao Yamada, and Itsuo Kumazawa. "Total generalized variation for graph signals." In ICASSP 2015 - 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2015. http://dx.doi.org/10.1109/icassp.2015.7179014.
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Ahmed, H. Bay, D. Dare, and A. O. Boudraa. "Graph signals classification using total variation and graph energy informations." In 2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2017. http://dx.doi.org/10.1109/globalsip.2017.8309043.
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Berger, Peter, Manfred Buchacher, Gabor Hannak, and Gerald Matz. "Graph Learning Based on Total Variation Minimization." In ICASSP 2018 - 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018. http://dx.doi.org/10.1109/icassp.2018.8461603.
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Bin Wu, Xin Yang, Yi Huang, and Jianbin Tan. "Analyzing temporal variation of telecom graph structure." In China-Ireland International Conference on Information and Communications Technologies (CIICT 2008). IEE, 2008. http://dx.doi.org/10.1049/cp:20080791.
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Li, Ying, Jing Qin, Stanley Osher, and Wentai Liu. "Graph fractional-order total variation EEG source reconstruction." In 2016 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE, 2016. http://dx.doi.org/10.1109/embc.2016.7590650.
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Bai, Yuanchao, Gene Cheung, Xianming Liu, and Wen Gao. "Blind Image Deblurring Via Reweighted Graph Total Variation." In ICASSP 2018 - 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018. http://dx.doi.org/10.1109/icassp.2018.8462255.
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Shi, Min, Yu Huang, Xingquan Zhu, Yufei Tang, Yuan Zhuang, and Jianxun Liu. "GAEN: Graph Attention Evolving Networks." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/213.
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Real-world networked systems often show dynamic properties with continuously evolving network nodes and topology over time. When learning from dynamic networks, it is beneficial to correlate all temporal networks to fully capture the similarity/relevance between nodes. Recent work for dynamic network representation learning typically trains each single network independently and imposes relevance regularization on the network learning at different time steps. Such a snapshot scheme fails to leverage topology similarity between temporal networks for progressive training. In addition to the static node relationships within each network, nodes could show similar variation patterns (e.g., change of local structures) within the temporal network sequence. Both static node structures and temporal variation patterns can be combined to better characterize node affinities for unified embedding learning. In this paper, we propose Graph Attention Evolving Networks (GAEN) for dynamic network embedding with preserved similarities between nodes derived from their temporal variation patterns. Instead of training graph attention weights for each network independently, we allow model weights to share and evolve across all temporal networks based on their respective topology discrepancies. Experiments and validations, on four real-world dynamic graphs, demonstrate that GAEN outperforms the state-of-the-art in both link prediction and node classification tasks.
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Vu, Huy, Gene Cheung, and Yonina C. Eldar. "Unrolling of Deep Graph Total Variation for Image Denoising." In ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2021. http://dx.doi.org/10.1109/icassp39728.2021.9414453.
Full textReports on the topic "Variation graph"
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Panas, R., J. Cuadra, K. Mohan, and R. Morales. Model and Standard Operating Procedures Supporting Signal Variation Flow Graph Analysis. Office of Scientific and Technical Information (OSTI), September 2020. http://dx.doi.org/10.2172/1668519.
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Kriegel, Francesco. Efficient Axiomatization of OWL 2 EL Ontologies from Data by means of Formal Concept Analysis. Technische Universität Dresden, 2023. http://dx.doi.org/10.25368/2023.214.
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We present an FCA-based axiomatization method that produces a complete EL TBox (the terminological part of an OWL 2 EL ontology) from a graph dataset in at most exponential time. We describe technical details that allow for efficient implementation as well as variations that dispense with the computation of extremely large axioms, thereby rendering the approach applicable albeit some completeness is lost. Moreover, we evaluate the prototype on real-world datasets.
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Heitman, Joshua L., Alon Ben-Gal, Thomas J. Sauer, Nurit Agam, and John Havlin. Separating Components of Evapotranspiration to Improve Efficiency in Vineyard Water Management. United States Department of Agriculture, March 2014. http://dx.doi.org/10.32747/2014.7594386.bard.
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Vineyards are found on six of seven continents, producing a crop of high economic value with much historic and cultural significance. Because of the wide range of conditions under which grapes are grown, management approaches are highly varied and must be adapted to local climatic constraints. Research has been conducted in the traditionally prominent grape growing regions of Europe, Australia, and the western USA, but far less information is available to guide production under more extreme growing conditions. The overarching goal of this project was to improve understanding of vineyard water management related to the critical inter-row zone. Experiments were conducted in moist temperate (North Carolina, USA) and arid (Negev, Israel) regions in order to address inter-row water use under high and low water availability conditions. Specific objectives were to: i) calibrate and verify a modeling technique to identify components of evapotranspiration (ET) in temperate and semiarid vineyard systems, ii) evaluate and refine strategies for excess water removal in vineyards for moist temperate regions of the Southeastern USA, and iii) evaluate and refine strategies for water conservation in vineyards for semi-arid regions of Israel. Several new measurement and modeling techniques were adapted and assessed in order to partition ET between favorable transpiration by the grapes and potentially detrimental water use within the vineyard inter-row. A micro Bowen ratio measurement system was developed to quantify ET from inter-rows. The approach was successful at the NC site, providing strong correlation with standard measurement approaches and adding capability for continuous, non-destructive measurement within a relatively small footprint. The environmental conditions in the Negev site were found to limit the applicability of the technique. Technical issues are yet to be solved to make this technique sufficiently robust. The HYDRUS 2D/3D modeling package was also adapted using data obtained in a series of intense field campaigns at the Negev site. The adapted model was able to account for spatial variation in surface boundary conditions, created by diurnal canopy shading, in order to accurately calculate the contribution of interrow evaporation (E) as a component of system ET. Experiments evaluated common practices in the southeastern USA: inter-row cover crops purported to reduce water availability and thereby favorably reduce grapevine vegetative growth; and southern Israel: drip irrigation applied to produce a high value crop with maximum water use efficiency. Results from the NC site indicated that water use by the cover crop contributed a significant portion of vineyard ET (up to 93% in May), but that with ample rainfall typical to the region, cover crop water use did little to limit water availability for the grape vines. A potential consequence, however, was elevated below canopy humidity owing to the increased inter-row evapotranspiration associated with the cover crops. This creates increased potential for fungal disease occurrence, which is a common problem in the region. Analysis from the Negev site reveals that, on average, E accounts for about10% of the total vineyard ET in an isolated dripirrigated vineyard. The proportion of ET contributed by E increased from May until just before harvest in July, which could be explained primarily by changes in weather conditions. While non-productive water loss as E is relatively small, experiments indicate that further improvements in irrigation efficiency may be possible by considering diurnal shading effects on below canopy potential ET. Overall, research provided both scientific and practical outcomes including new measurement and modeling techniques, and new insights for humid and arid vineyard systems. Research techniques developed through the project will be useful for other agricultural systems, and the successful synergistic cooperation amongst the research team offers opportunity for future collaboration.
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Monetary Policy Report, July 2023. Banco de la República, September 2023. http://dx.doi.org/10.32468/inf-pol-mont-eng.tr3-2023.
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In the second quarter of 2023, total annual infation fell to 12.1% and the rise of core infation halted and stood at 10.5%; both measures were lower than those forecasted in the April Report but remained well above the 3.0% target. The aggregate effects of monetary policy actions and the unwinding of certain shocks that affected prices will contribute towards bringing infation closer to the target in 2024. By component, the annual variations in the CPI for food and the CPI excluding food and regulated items have lessened more markedly than anticipated by the Central Bank’s technical staff, underlying the decline in annual infation. However, prices of regulated items and services continued to rise, nonetheless at a slower pace than expected, particularly in the case of services. For these two groups, price indexation mechanisms have resulted in the transmission of some transitory increases in certain CPI sub-components (e.g., food) to other items (e.g., rents, utilities, etc.), thus generating a greater persistence of already high infation. This is acerbated by the gasoline price increases required to correct the defcit of the Fuel Price Stabilization Fund (Fondo de Estabilización de los Precios de los Combustibles, FEPC). Consequently, the CPI for regulated items forecast increased going forward relative to the April Report given the higher gasoline price adjustments announced by the Government. For the remaining items (food, goods, and services), the forecasted trajectory declined due partly to the lower-than-estimated infation, a more notable reduction in the international prices of some food items and freight costs, lower exchange rate and cost pressures on prices, and a faster than anticipated decrease in excess demand. This occurs in a contractionary monetary policy environment that aims to reduce infation towards rates close to the 3.0% target by the end of 2024. Against this background, headline infation for yearend 2023 is forecast at 9.0% (formerly 9.5%) and 3.5% for yearend 2024 (previously 3.4%) (Graph 1.1). In the same timeframes, the core infation forecast has been revised downward from 8.9% to 7.9%, and from 3.9% to 3.7%, respectively (Graph 1.2). These projections are subject to high uncertainty, especially surrounding future behavior of international fnancing conditions and the exchange rate, fuctuations in domestic demand, the possible occurrence of the El Niño natural climate phenomenon, and future decisions regarding domestic fuel and electricity prices.
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Monetary Policy Report - January 2023. Banco de la República, June 2023. http://dx.doi.org/10.32468/inf-pol-mont-eng.tr1-2023.
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1. Macroeconomic Summary In December, headline inflation (13.1%) and the average of the core inflation measures (10.3%) continued to trend upward, posting higher rates than those estimated by the Central Bank's technical staff and surpassing the market average. Inflation expectations for all terms exceeded the 3.0% target. In that month, every major group in the Consumer Price Index (CPI) registered higher-than-estimated increases, and the diffusion indicators continued to show generalized price hikes. Accumulated exchange rate pressures on prices, indexation to high inflation rates, and several food supply shocks would explain, in part, the acceleration in inflation. All of this is in a context of significant surplus demand, a tight labor market, and inflation expectations at different terms that exceed the 3.0% target. Compared to the October edition of the Monetary Policy Report, the forecast path for headline and core inflation (excluding food and regulated items: EFR) increased (Graphs 1.1 and 1.2), reflecting heightened accumulated exchange rate pressures, price indexation to a higher inflation rate (CPI and the producer price index: PPI), and the rise in labor costs attributed to a larger-than-estimated adjustment in the minimum wage. Nevertheless, headline inflation is expected to begin to ease by early 2023, although from a higher level than had been estimated in October. This would be supported initially by the slowdown forecast for the food CPI due to a high base of comparison, the end anticipated for the shocks that have affected the prices of these products, and the estimated improvement in external and domestic supply in this sector. In turn, the deterioration in real household income because of high inflation and the end of the effects of pent-up demand, plus tighter external and domestic financial conditions would contribute to diluting surplus demand in 2023 and reducing inflation. By the end of 2023, both headline and core (EFR) inflation would reach 8.7% and would be 3.5% and 3.8%, respectively, by December 2024. These forecasts are subject to a great deal of uncertainty, especially concerning the future behavior of international financial conditions, the evolution of the exchange rate, the pace of adjustment in domestic demand, the extent of indexation of nominal contracts, and the decisions taken regarding the domestic price of fuel and electricity. In the third quarter, economic activity surprised again on the upside and the growth projection for 2022 rose to 8.0% (previously 7.9%). However, it declined to 0.2% for 2023 (previously 0.5%). With this, surplus demand continues to be significant and is still expected to weaken during the current year. Annual economic growth in the third quarter (7.1 % SCA)1 was higher than estimated in October (6.4 % SCA), given stronger domestic demand specifically because of higher-than-expected investment. Private consumption fell from the high level witnessed a quarter earlier and net exports registered a more negative contribution than anticipated. For the fourth quarter, economic activity indicators suggest that gross domestic product (GDP) would have remained high and at a level similar to that observed in the third quarter, with an annual variation of 4.1%. Domestic demand would have slowed in annual terms, although at levels that would have remained above those for output, mainly because of considerable private consumption. Investment would have declined slightly to a value like the average observed in 2019. The real trade deficit would have decreased due to a drop in imports that was more pronounced than the estimated decline in exports. On the forecast horizon, consumption is expected to decline from current elevated levels, partly because of tighter domestic financial conditions and a deterioration in real income due to high inflation. Investment would also weaken and return to levels below those seen before the pandemic. In real terms, the trade deficit would narrow due to a lower momentum projection for domestic demand and higher cumulative real depreciation. In sum, economic growth for all of 2022, 2023, and 2024 would stand at 8.0%, 0.2% and 1.0%, respectively (Graph 1.3). Surplus demand remains high (as measured by the output gap) and is expected to decline in 2023 and could turn negative in 2024 (Graph 1.4). Although the macroeconomic forecast includes a marked slowdown in the economy, an even greater adjustment in domestic absorption cannot be ruled out due to the cumulative effects of tighter external and domestic financial conditions, among other reasons. These estimates continue to be subject to a high degree of uncertainty, which is associated with factors such as global political tensions, changes in international interest rates and their effects on external demand, global risk aversion, the effects of the approved tax reform, the possible impact of reforms announced for this year (pension, health, and labor reforms, among others), and future measures regarding hydrocarbon production. In 2022, the current account deficit would have been high (6.3 % of GDP), but it would be corrected significantly in 2023 (to 3.9 % of GDP) given the expected slowdown in domestic demand. Despite favorable terms of trade, the high external imbalance that would occur during 2022 would be largely due to domestic demand growth, cost pressures associated with high freight rates, higher external debt service payments, and good performance in terms of the profits of foreign companies.2 By 2023, the adjustment in domestic demand would be reflected in a smaller current account deficit especially due to fewer imports, a global moderation in prices and cost pressures, and a reduction in profits remitted abroad by companies with foreign direct investment (FDI) focused on the local market. Despite this anticipated correction in the external imbalance, its level as a percentage of GDP would remain high in the context of tight financial conditions. In the world's main economies, inflation forecasts and expectations point to a reduction by 2023, but at levels that still exceed their central banks' targets. The path anticipated for the Federal Reserve (Fed) interest rate increased and the forecast for global growth continues to be moderate. In the fourth quarter of 2022, logistics costs and international prices for some foods, oil and energy declined from elevated levels, bringing downward pressure to bear on global inflation. Meanwhile, the higher cost of financing, the loss of real income due to high levels of global inflation, and the persistence of the war in Ukraine, among other factors, have contributed to the reduction in global economic growth forecasts. In the United States, inflation turned out to be lower than estimated and the members of the Federal Open Market Committee (FOMC) reduced the growth forecast for 2023. Nevertheless, the actual level of inflation in that country, its forecasts, and expectations exceed the target. Also, the labor market remains tight, and fiscal policy is still expansionary. In this environment, the Fed raised the expected path for policy interest rates and, with this, the market average estimates higher levels for 2023 than those forecast in October. In the region's emerging economies, country risk premia declined during the quarter and the currencies of those countries appreciated against the US dollar. Considering all the above, for the current year, the Central Bank's technical staff increased the path estimated for the Fed's interest rate, reduced the forecast for growth in the country's external demand, lowered the expected path of oil prices, and kept the country’s risk premium assumption high, but at somewhat lower levels than those anticipated in the previous Monetary Policy Report. Moreover, accumulated inflationary pressures originating from the behavior of the exchange rate would continue to be important. External financial conditions facing the economy have improved recently and could be associated with a more favorable international context for the Colombian economy. So far this year, there has been a reduction in long-term bond interest rates in the markets of developed countries and an increase in the prices of risky assets, such as stocks. This would be associated with a faster-than-expected reduction in inflation in the United States and Europe, which would allow for a less restrictive course for monetary policy in those regions. In this context, the risks of a global recession have been reduced and the global appetite for risk has increased. Consequently, the risk premium continues to decline, the Colombian peso has appreciated significantly, and TES interest rates have decreased. Should this trend consolidate, exchange rate inflationary pressures could be less than what was incorporated into the macroeconomic forecast. Uncertainty about external forecasts and their impact on the country remains high, given the unpredictable course of the war in Ukraine, geopolitical tensions, local uncertainty, and the extensive financing needs of the Colombian government and the economy. High inflation with forecasts and expectations above 3.0%, coupled with surplus demand and a tight labor market are compatible with a contractionary stance on monetary policy that is conducive to the macroeconomic adjustment needed to mitigate the risk of de-anchoring inflation expectations and to ensure that inflation converges to the target. Compared to the forecasts in the October edition of the Monetary Policy Report, domestic demand has been more dynamic, with a higher observed level of output exceeding the productive capacity of the economy. In this context of surplus demand, headline and core inflation continued to trend upward and posted surprising increases. Observed and expected international interest rates increased, the country’s risk premia lessened (but remains at high levels), and accumulated exchange rate pressures are still significant. The technical staff's inflation forecast for 2023 increased and inflation expectations remain well above 3.0%. All in all, the risk of inflation expectations becoming unanchored persists, which would accentuate the generalized indexation process and push inflation even further away from the target. This macroeconomic context requires consolidating a contractionary monetary policy stance that aims to meet the inflation target within the forecast horizon and bring the economy's output to levels closer to its potential. 1.2 Monetary Policy Decision At its meetings in December 2022 and January 2023, Banco de la República’s Board of Directors (BDBR) agreed to continue the process of normalizing monetary policy. In December, the BDBR decided by a majority vote to increase the monetary policy interest rate by 100 basis points (bps) and in its January meeting by 75 bps, bringing it to 12.75% (Graph 1.5). 1/ Seasonally and calendar adjusted. 2/ In the current account aggregate, the pressures for a higher external deficit come from those companies with FDI that are focused on the domestic market. In contrast, profits in the mining and energy sectors are more than offset by the external revenue they generate through exports. Box 1 - Electricity Rates: Recent Developments and Indexation. Author: Édgar Caicedo García, Pablo Montealegre Moreno and Álex Fernando Pérez Libreros Box 2 - Indicators of Household Indebtedness. Author: Camilo Gómez y Juan Sebastián Mariño