Academic literature on the topic 'Ordinal information'

In this paper an ordinal Information Retrieval model is proposed, which is formalised within fuzzy set theory and is based on the notion of linguistic granules of information. Linguistic expressions are defined to represent and manage the importance of both the index terms as descriptors of the information items and the query terms (content selectors) as descriptors of users' needs. The advantage of this approach with respect to the (numeric) fuzzy IR models is that the query evaluation mechanism and the definition of the importance semantics are simplified.

At the beginning of this work, recent studies had evidenced a tight link between serial order in verbal working memory and space processing. In a first study, we investigated the nature of this link. By discarding the possibility that it results from conceptual associations, our results favoured the idea that the representation of serial order is intrinsically of a spatial nature. This led us to hypothesize that a deficit of space processing should be accompanied by a deficit of serial order. To test this hypothesis, we investigated verbal working memory abilities in a group of brain-damaged patients with hemispatial neglect, a syndrome characterized by a deficit of spatial attention. We showed that these patients have a specific deficit for serial order, as they showed difficulties when judging the ordinal relations between memorized items, whereas they were able to judge the identity of these items. This deficit of serial order was related to hemispatial neglect severity and to posterior parietal lesions. We formulated the hypothesis that the link between serial order and space results from the overlap of brain networks subtending these cognitive processes, at the level of the posterior parietal cortex. To test this hypothesis, we used transcranial magnetic stimulation (TMS) to temporarily disrupt this area in healthy participants, with the prediction that TMS would induce a similar bias when judging the position of a landmark on horizontal lines (spatial task), and when judging the position of an item in memorized sequences (ordinal task). In line with previous studies, TMS induced a bias in the spatial task. However, contrary to our prediction, TMS over the same area in the same participants did not induce a similar bias in the ordinal task.
Doctorat en Sciences psychologiques et de l'éducation
info:eu-repo/semantics/nonPublished

The great interest on the origin of space-number associations has motivated recent investigation on spatial compatibility effects (e.g., the SNARC effect) induced by over-learned non-numerical sequences (e.g., letters, months). The work included in the present thesis aims to contribute to our understanding of the determinants of the spatial mapping of ordinal information, including both numbers and other general series. Firstly, the increasing evidence of the link between finger counting and number processing has been considered, in particular the specific role of handedness on this interaction and the influence of finger counting direction on number mapping in the representational space. Results showed that handedness fully predicts finger counting direction and that the directional asymmetries of finger counting are not relevant for shaping the mental representation of numbers. Secondly, the peculiarity of numbers evoking a spatially organized mental representation has been argued, showing that the oriented spatial representation is the privileged way of mentally organizing serial information, even newly acquired arbitrary sequences. Finally, a potential explanation for ordinal spatial associations has been evaluated, analyzing the role of working memory in determining the spatial compatibility effects of serial information observed with numerical and non-numerical sequences as stimuli.

This Thesis is devoted to the construction of global climate networks (CNs) built from time series -surface air temperature anomalies (SAT)- using nonlinear analysis. Several information theory measures have been used including mutual information (MI) and conditional mutual information (CMI). The ultimate goal of the study is to improve the present understanding of climatic variability by means of networks, focusing on the different spatial and time-scales of climate phenomena. An introduction to the main components of this interdisciplinary work are offered in the first three chapters. Climate variability and patterns are introduced Chapter 1, network theory in Chapter 2, and nonlinear time series analysis -especially information theoretic methodology- in Chapter 3. In Chapter 4, the statistical similarity of SAT anomalies in different regions of the world is assessed using MI. These climate networks are constructed from time series of monthly averaged SAT anomalies, and from their symbolic ordinal representation, which allows an analysis of these interdependencies on different time scales. This analysis allows identifying topological changes in the networks when using ordinal patterns (OPs) of different time intervals. Intra-seasonal (of a few months), inter-seasonal (covering a year) and inter-annual (several years) timescales are considered. The nature of the interdependencies is then explored in Chapter 5 by using SAT data from an ensemble of atmospheric general circulation model (AGCM) runs, all of them forced by the same historical sea surface temperature (SST). It is possible to separate atmospheric variability into a forced component, and another one intrinsic to the atmosphere. In this way, it is possible to obtain climate networks for both types of variability and characterize them. Furthermore, an analysis using OP allows to construct CNs for several time scales, and evaluate the connectivity of each different network. This selecting both time scale and variability type allows to obtain a further insight into the study of SAT anomalies. The connectivity of the constructed CNs allows to assess the influence of two main climate phenomena: ENSO and the North Atlantic Oscillation (NAO). In Chapter 6, a natural extension of the network construction methodology is implemented in order to infer the direction of the links. A directionality index (DI) is used. DI can be defined as the difference of the CMI between two time series x(t) and y(t), calculated in two ways: i) considering the information about x(t) contained in t time units in the past of y(t), and ii) considering the information about y(t) contained in t time units in the past of x(t). DI is used to quantify the direction of information flow among the series, indicating the direction of the links of the network. Two SAT datasets -one monthly-averaged and another daily-averaged- are used. The links of the obtained networks are interpreted in terms of known atmospheric tropical and extra-tropical variability phenomena. Specific and relevant geographical regions are selected, the net direction of propagation of the atmospheric patterns is analyzed, and the direction of the inferred links is tested using surrogate data. These patterns are also found to be acting on various time scales, such as synoptic atmospheric waves in the extra-tropics or longer time scale events in the tropics. The final Chapter 7 presents the main conclusions, and a discussion of future work.
El objetivo de esta tesis es la creación de redes climáticas (CN por las siglas en inglés) a partir de un conjunto global de series temporales de temperatura del aire superficial (SAT), utilizando técnicas de análisis no lineal de series temporales. Varias metodologías son aplicadas al estudio de la variabilidad climática, incluyendo la Información mutua (MI) y la información mutual condicional (CMI). El objetivo principal de esta tesis es estudiar la variabilidad climática a través del análisis de redes haciendo énfasis en los diferentes patrones espaciales y temporales del sistema climático. Una introducción a los componentes principales de este trabajo interdisciplinario se presenta en los primeros tres capítulos. La variabilidad climática y los patrones atmosféricos se introducen en el Capítulo 1, la teoría de redes en el Capítulo 2, y el análisis no lineal de series temporales, especialmente metodos en teorá de la información, en el Capítulo 3. En el Capítulo 4, la similitud estadística de las anomalías de SAT en diferentes regiones del mundo es evaluada utilizando MI. Estas redes climáticas globales son construidas a partir de series temporales de SAT promediadas a escalas de tiempo mensuales, y a partir de su representación simbólica, permitiendo un análisis de estas interdependencias en varias escalas temporales. Se identifican cambios topológicos entre las redes, como resultado de variaciones en el intervalo de construcción de losOP. Escalas intra-estacionales (unos meses), inter-estacionales (cubriendo un año) e inter-anuales (varios años), son consideradas. Se encuentra que un incremento en el espaciado de los patrones ordinales (por lo tanto, en la escala de tiempo del análisis ordinal), resulta en redes climáticas con un incremento en la conectividad en el Pacífico ecuatorial. Al contrario, el número de conexiones significativas decrece al realizar el análisis ordinal en una escala de tiempo más corta (es decir, comparando meses consecutivos). Este efecto es interpretado como una consecuencia del efecto de El Niño-Oscilación Sud (ENSO) actuando en escalas de tiempo más largas y de una mayor estocasticidad en las series temporales en escalas de tiempo más cortas. La naturaleza de las interdependencias es explorada en el Capítulo 5, utilizando datos de SAT, resultantes de un conjunto de salidas de un modelo atmosférico de circulación global (AGCM), todas forzadas por la misma temperatura de la superficie del mar (SST). Es posible separar la variabilidad atmosférica en una componente forzada y otra intrínseca a la atmósfera. De esta forma, se obtienen redes climáticas para ambos tipos de variabilidad, lo que posibilita caracterizarlas. Un análisis utilizando OP permite crear CNs para diferentes escalas temporales, y encontrar la escala de OP para la cual las diferentes redes presentan mayor conectividad. Este doble proceso de selección permitie estudiar la variabilidad de las anomalías de SAT desde un nuevo punto de vista. La conectividad de las redes climáticas así construídas permite evaluar la influencia de dos fenómenos climáticos: ENSO y la Oscilación del Atlántico Norte (NAO). Para esto, se pueden comparar las redes originales, con redes provenientes de series temporales a las que se les quitaron linealmente estos fenómenos. Un resultado clave de este análisis es que la conectividad de la red de variabilidad forzada es muy afectada por ENSO: eliminando el índice NINO3.4 (que caracteriza ENSO), se provoca una pérdida general de la conectividad en la red. El hecho de que incluso conexiones entre áreas muy alejadas del océano Pacífico ecuatorial se hayan perdido al quitar el índice, sugiere que estas regiones no están directamente conectadas sino que ambas son influenciadas por la zona dominada por ENSO, especialmente en escalas de tiempo interanuales. Por otro lado, en la red de variabilidad interna, independiente del forzado de las SST, las conexiones delMar del Labrador con el resto del mundo resultan significantemente afectadas por NAO, con un máximo en escalas intra-anuales. Aunque las conexiones no locales más fuertes resultan las forzadas por el océano, se muestra la presencia de teleconexiones asociadas con la variabilidad interna. En el Capítulo 6, una extensión natural de la metodología de construcción de redes es implementada, permitiendo inferir la dirección de las conexiones. Un índice de direccionalidad (DI), puede ser definido como la diferencia entre la CMI entre dos series temporales x(t ) e y(t ) calculada de dos formas: i) considerando la información de x(t ) contenida en τ unidades de tiempo en el pasado de y(t ) y ii) considerando la información de y(t ) contenida en τ unidades de tiempo en el pasado de x(t ). Este índice DI, se utiliza para cuantificar la dirección del flujo de información entre las series, lo que equivale a la dirección de la conexión entre los respectivos nodos de la red. Dos conjuntos de series temporales, uno promediado mensualmente y el otro promediado diariamente, son usados. Las conexiones de las redes resultantes son interpretadas en términos de fenómenos de variabilidad tropical y extratropical conocidos. Regiones específicas y relevantes son seleccionadas, la dirección neta de propagación de los patrones atmosféricos es analizada y contrastada con un test de inferencia estadística. Se encuentra que diferentes patrones de variabilidad, actúan en varias escalas de tiempo, tales como ondas sinópticas atmosféricas en los extra-trópicos o escalas de tiempo mayores en los trópicos. La dependencia de valores de DI con τ es investigada. Para la escala sinóptica (τ Ç 10 días), DI presenta una dependencia con τ, con un mínimo en los trópicos y máximos (en forma de trenes de ondas) en los extra-trópicos. Para valores mayores de τ, los links resultan ser relativamente robustos a la elección del parámetro, mostrando una conectividad alta en los trópicos y baja en los extra trópicos. El análisis demuestra la capacidad de DI de inferir la dirección neta de las interacciones climáticas, y de mejorar la compresión actual de fenómenos climáticos y de la predictabilidad climática. La red resultante está en total acuerdo con los conocimientos actuales de fenómenos climáticos, validando esta metodología para inferir, directamente de los datos, la dirección neta de las interacciones climáticas. Finalmente, el Capítulo 7, presenta las conclusiones, y una discusión de trabajo futuro.

An important issue in human cognition concerns the origins and nature of the capacity to represent number. A great deal of research has focused on infants’ comprehension of the cardinal properties of number but another essential component of the concept of number is ordinality, which refers to the inherent “greater than” or “less than” relationships between numbers. Until recently, the development of this aspect of human numerical cognition in infancy had received little attention. while little is know. The aim of the current series of studies was to investigate whether the ability to appreciate ordinal relationships between numerical magnitudes is present in preverbal infants at an earlier age than previously reported. The current investigation thus includes a series of 6 experiments conducted with infants of 4 and 7 months of age and provides evidence for the debate about functional affordances of infants’ numerical representation, demonstrating that, under certain conditions, the ability to detect and grasp ordinal information embedded in non-numerical and numerical sequences of visual stimuli could be present early in infancy, at respectively 4 months and 7 months of age. Importantly, this study provided also evidence that account for the existence of a basic mapping of number to space the presence, showing that 7-month-old infants are able to link oriented spatial codes to representations of numerical magnitude.

Les jeux probabilistes à information incomplète, appelés jeux Bayesiens, offrent un cadre adapté au traitement de jeux à utilités cardinales sous incertitude. Ce type d'approche ne peut pas être utilisé dans des jeux ordinaux, où l'utilité capture un ordre de préférence, ni dans des situations de décision sous incertitude qualitative. Dans la première partie de cette thèse, nous proposons un modèle de jeux à information incomplète basé sur la théorie de l'utilité qualitative possibiliste: les jeux possibiliste à information incomplète, nommés PI-games. Ces jeux constituent un cadre approprié pour la représentation des jeux ordinaux sous connaissance incomplète. Nous étendons les notions fondamentales de stratégie de sécurité et d'équilibres de Nash (pur et mixte). De plus, nous montrons que tout jeu possibiliste à information incomplète peut être transformé en un jeu à information complète sous la forme normale équivalent au jeu initial, dont les stratégies de sécurité, les équilibres de Nash purs et mixtes sont en bijection dans les deux jeux. Ce résultat de représentation est une contrepartie qualitative de celui de Harsanyi sur la représentation des jeux Bayésiens par des jeux sous forme normale à information complète. Cela est plus un résultat de représentation qu'un outil de résolution. Nous montrons que décider si un équilibre de Nash pur existe dans un PI-game est un problème NP-complet et proposons un codage de programmation linéaire mixte en nombres entiers (PLNE) du problème. Nous proposons également un algorithme en temps polynomial pour trouver une stratégie de sécurité dans un PI-game et montrons qu'un équilibre mixte possibiliste peut être également calculé en temps polynomial (en fonction de la taille du jeu). Pour confirmer la faisabilité de la formulation de programmation linéaire en nombres entiers mixtes et des algorithmes en temps polynomial, nous introduisons aussi un nouveau générateur pour les PI-games basé sur le générateur de jeux sous la forme normale: GAMUT. Représenter un PI-game sous forme normale standard nécessite une expression extensive des fonctions d'utilité et de la distribution des possibilités, à savoir sur les espaces produits des actions et des types. La deuxième partie de cette thèse propose une vue moins coûteuse des PI-games, à savoir la polymatrix PI-games basée sur min, qui permet de spécifier de manière concise les PI-games avec des interactions locales, en d'autre termes, lorsque les interactions entre les joueurs sont par paires et l'utilité d'un joueur dépend de son voisinage et non de tous les autres joueurs du PI-game. Ce cadre permet, par exemple, la représentation compacte des jeux de coordination sous incertitude où la satisfaction d'un joueur est élevée si et seulement si sa stratégie est cohérente avec celles de l'ensemble de ses voisins. Dans cette thèse, nous montrons que n'importe quel PI-game à 2 joueurs peut être transformé en un jeu polymatriciel équivalent basé sur le min. Ce résultat est la contrepartie qualitative du théorème de Howson et Rosenthal reliant les jeux Bayésiens aux jeux polymatriciels. De plus, dès qu'une simple condition de cohérence des connaissances des joueurs sur le monde est satisfaite, tout polymatrix PI-game peut être transformé en temps polynomial en un jeu polymatriciel, basé sur le min, à information complète équivalent. Nous montrons que l'existence d'un équilibre de Nash pur dans un polymatrix PI-game est un problème NP-complet mais pas plus difficile que de décider si un équilibre de Nash pur existe dans un PI-game. Enfin, nous montrons que cette dernière famille de jeux peut être résolue grâce à une formulation de programmation linéaire en nombres entiers mixtes. Nous introduisons un nouveau générateur pour les polymatrix PI-games basés sur le générateur de PI-game. Les expérimentations confirment la faisabilité de cette approche
Probabilistic games with incomplete information, called Bayesian games, offer a suitable framework for games where the utility degrees are additive in essence. This approach does not apply to ordinal games where the utility degrees capture no more than a ranking, nor to situations of decision under qualitative uncertainty. In the first part of this thesis, we propose a representation framework for ordinal games under possibilistic incomplete information (PI-games). These games constitute a suitable framework for the representation of ordinal games under incomplete knowledge. We extend the fundamental notions of secure strategy, pure Nash equilibrium, and mixed Nash equilibrium to this framework. Furthermore, we show that any possibilis- tic game with incomplete information can be transformed into an equivalent normal form game with complete information. The fundamental notions such Nash equilibria (pure and mixed) and secure strategies are in bijection in both frameworks. This representation result is a qualitative counterpart of Harsanyi results about the representation of Bayesian games by normal form games under complete information. It is more of a representation result than the premise of a solving tool. We show that deciding whether a pure Nash equilibrium exists in a PI-game is a difficult task (NP-hard) and propose a Mixed Integer Linear Programming (MILP) encoding of this problem. We also propose a polynomial-time algorithm to find a secure strategy in a PI-game and show that a possibilistic mixed equilibrium can be computed in polynomial time (w.r.t., the size of the game), which contrasts with probabilistic mixed equilibrium computation in cardinal game theory. To confirm the feasibility of the MILP formulation and the polynomial-time algorithms, we introduce a novel generator for PI-games based on the well-known standard normal form game generator: GAMUT. Representing a PI-game in standard normal form requires an extensive expression of the utility functions and the possibility distribution on the product spaces of actions and types. This is the concern of the second part of this thesis where we propose a less costly view of PI-games, namely min-based polymatrix PI-games, which allows to concisely specify PI-games with local interactions, i.e., the interactions between players are pairwise and the utility of a player depends on her neighbors and not on all other players in the PI-game. This framework allows, for instance, the compact representation of coordination games under uncertainty where the satisfaction of a player is high if and only if her strategy is coherent with all of her neighbors, the game being possibly only incompletely known to the players. We show that any 2- player PI-game can be transformed into an equivalent min-based polymatrix game. This result is the qualitative counterpart of Howson and Rosenthal's theorem linking Bayesian games to polymatrix games. Furthermore, as soon as a simple condition on the coherence of the players' knowledge about the world is satisfied, any polymatrix PI-game can be transformed in polynomial time into an equivalent min-based and complete information polymatrix game. We show that the existence of a pure Nash equilibrium in a polymatrix PI-game is an NP-complete problem but no harder than deciding the existence of a pure Nash equilibrium in a PI-game. Finally, we show that the latter family of games can be solved through a MILP formulation. We introduce a novel generator for min-based polymatrix PI-games based on the PI-game generator. Experiments confirm the feasibility of this approach

Global tests are in demand whenever it is of interest to draw inferential conclusions about sets of variables as a whole. The present thesis attempts to develop such tests for the case of multivariate ordinal data in possibly high-dimensional set-ups, and has primarily been motivated by research questions that arise from data collected by means of the 'International Classification of Functioning, Disability and Health'. The thesis essentially comprises two parts. In the first part two tests are discussed, each of which addresses one specific problem in the classical two-group scenario. Since both are permutation tests, their validity relies on the condition that, under the null hypothesis, the joint distribution of the variables in the set to be tested is the same in both groups. Extensive simulation studies on the basis of the tests proposed suggest, however, that violations of this condition, from the purely practical viewpoint, do not automatically lead to invalid tests. Rather, two-sample permutation tests' failure appears to depend on numerous parameters, such as the proportion between group sizes, the number of variables in the set of interest and, importantly, the test statistic used. In the second part two further tests are developed which both can be used to test for association, if desired after adjustment for certain covariates, between a set of ordinally scaled covariates and an outcome variable within the range of generalized linear models. The first test rests upon explicit assumptions on the distances between the covariates' categories, and is shown to be a proper generalization of the traditional Cochran-Armitage test to higher dimensions, covariate-adjusted scenarios and generalized linear model-specific outcomes. The second test in turn parametrizes these distances and thus keeps them flexible. Based on the tests' power properties, practical recommendations are provided on when to favour one or the other, and connections with the permutation tests from the first part of the thesis are pointed out. For illustration of the methods developed, data from two studies based on the 'International Classification of Functioning, Disability and Health' are analyzed. The results promise vast potential of the proposed tests in this data context and beyond.

La perspective de cette etude s'inscrit dans une approche cognitive de l'apprenti lecteur. Les processus de traitement de l'information ordinale concernent la facon dont l'enfant apprehende les regles d'ordre etablies sur le materiel linguistique. La gestion de l'ordre de succession des lettres, elements constitutifs des mots, constitue, en effet, l'une des grandes difficultes rencontrees par l'enfant dans les tout debuts de l'apprentissage de la lecture. Parallelement, notre travail consiste a etudier la competence des apprentis lecteurs dans le traitement de l'information phonologique lors de la mise en place d'une strategie de lecture alphabetique. On suppose, par ailleurs, qu'en debut d'acquisition, le role joue par les unites syllabiques dans la mise en correspondance graphophonologique s'avere determinant. Dans ce sens, nous faisons l'hypothese que les jeunes lecteurs francais utilisent un traitement syllabique, en debut d'apprentissage, dans la reconnaissance des mots ecrits et que la syllabe consonne/voyelle peut etre consideree comme une unite privilegiee de recodage phonologique. La structure cv est presentee comme une structure pouvant etre a l'origine d'une lecture paranalogie. C'est une conception mettant en jeu des unites larges, superieures au phoneme qui permettent d'apprehender dans des mots nouveaux des configurations orthophonologiques deja connues. Les formes orales pregnantes telles que la syllabe consonne/voyelle se retrouvent ainsi en tant qu'unites saillantes pour l'utilisation d'analogies entre l'oral et l'ecrit. Les processus d'utilisation des analogies sont decrits comme occupant une place essentielle en debut d'apprentissage. Les enfants mettraient en place, de facon precoce, des strategies pour inferer progressivement les regles regissant la lecture. Une lecture analogique serait possible avant que l'apprenti lecteur n'ait largement developpe ses capacites de lecture alphabetique necessitant les correspondances graphemes-phonemes.

The textbook contains theoretical information in a volume of the lecture course are discussed in detail and examples of typical tasks and test tasks and tasks for independent work. Designed for students enrolled in directions of preparation 15.03.03 "Applied mechanics" 01.03.02 "mathematics" (specialization "Mathematical modeling"), major 23.05.01 "Land transport and technological means" (specialization "Dynamics and strength of transport and technological systems"). Can be used by teachers for conducting practical classes.

Possibilistic games with incomplete information (Π-games) constitute a suitable framework for the representation of ordinal games under incomplete knowledge. However, representing a Π-game in standard normal form requires an extensive expression of the utility functions and the possibility distribution, namely, on the product spaces of actions and types. In the present work, we propose a less costly view of Π-games, namely min-based polymatrix Π-games, which allows to concisely specify Π-games with local interactions. This framework allows, for instance, the compact representation of coordination games under uncertainty where the satisfaction of an agent is high if and only if her strategy is coherent with all of her neighbors, the game being possibly only incompletely known to the agents. Then, an important result of this paper is to show that a min-based polymatrix Π-game can be transformed, in polynomial time, into a (complete information) min-based polymatrix game with identical pure Nash equilibria. Finally, we show that the latter family of games can be solved through a MILP formulation. Experiments on variants of the GAMUT problems confirm the feasibility of this approach.

Zero-shot learning predicts new class even if no training data is available for that class. The solution to conventional zero-shot learning usually depends on side information such as attribute or text corpora. But these side information is not easy to obtain or use. Fortunately in many classification tasks, the class labels are ordered, and therefore closely related to each other. This paper deals with zero-shot learning for ordinal classification. The key idea is using label relevance to expand supervision information from seen labels to unseen labels. The proposed method SIDL generates a supervision intensity distribution (SID) that contains each label's supervision intensity, and then learns a mapping from instance to SID. Experiments on two typical ordinal classification problems, i.e., head pose estimation and age estimation, show that SIDL performs significantly better than the compared regression methods. Furthermore, SIDL appears much more robust against the increase of unseen labels than other compared baselines.

The article is devoted to the analysis of the digital content of publications of one issue of the daily All-Ukrainian newspaper “Den” (March 13-14, 2020). The author aims to identify the main thematic groups of digital designations, as well as to consider cases of justified and unsuccessful use of digital designations. Applying the content analysis method, the author identifies publications that contain numerical notations, determines the number of such notations and their affiliation with the main subject groups. Finds that the thematic group of digital designations “time” (58.6% of all digital designations) is much more dominant. This indicates that timing is the most important task of a newspaper text. The second largest group of digital designations is “measure” (15.8% of all digital designations). It covers dimensions and proportions, measurements of distance, weight, volume, and more. The third largest group of digital signage is money (8.2% of all digital signage), the fourth is numbering (5.2% of all digital signage), and the fifth is people (4.4% of all digital signage). The author focuses on the fact that the digits of the journalist’s text are both a source of information and a catch for the reader. Vivid indicators give the text a sense of accuracy. When referring digital data to the text, journalists must adhere to certain rules for the writing of ordinal numbers with incremental graduation; submission of dates; pointing to unique integers that are combined (or not combined) with units of physical quantities, monetary units, etc.; writing a numerator at the beginning of a sentence; unified presentation of data. This will greatly facilitate the reader’s perception of the information.

The Heisenberg uncertainty principle is one of the cornerstones of quantum mechanics. The modern version of the uncertainty principle, deals not with the precision of a measurement and the disturbance it introduces, but with the intrinsic uncertainty any quantum state must possess, regardless of what measurement is performed. Recently, the study of uncertainty relations in general has been a topic of growing interest, specifically in the setting of quantum information and quantum cryptography, where it is fundamental to the security of certain protocols. The aim of this study is to analyze the concepts and fundamental physical constants in terms of achievements of modern theoretical physics, they search for adequate and useful analogues in the socio-economic phenomena and processes, and their possible use in early warning of adverse crisis in financial markets. The instability of global financial systems depending on ordinary and natural disturbances in modern markets and highly undesirable financial crises are the evidence of methodological crisis in modelling, predicting and interpretation of current socio-economic conditions.

Climate change will increase weather induced risks to forests, and thus effective adaptation measures are needed. In Säätyö project funded by the Ministry of Agriculture and Forestry, we have summarized the data that facilitate adaptation measures, developed weather and climate services that benefit forestry, and mapped what kind of new weather and climate services are needed in forestry. In addition, we have recorded key further development needs to promote adaptation. The Säätyö project developed a service product describing the harvesting conditions of trees based on the soil moisture assessment. The output includes an analysis of the current situation and a 10-day forecast. In the project we also tested the usefulness of long forecasts beyond three months. The weather forecasting service is sidelined and supplemented by another co-operation project between the Finnish Meteorological Institute and Metsäteho called HarvesterSeasons (https://harvesterseasons.com/). The HarvesterSeasons service utilizes long-term forecasts of up to 6 months to assess terrain bearing conditions. A test version of a wind damage risk tool was developed in cooperation with the Department of Forest Sciences of the University of Eastern Finland and the Finnish Meteorological Institute. It can be used to calculate the wind speeds required in a forest area for wind damage (falling trees). It is currently only suitable for researcher use. In the Säätyö project the possibility of locating the most severe wind damage areas immediately after a storm was also tested. The method is based on the spatial interpolation of wind observations. The method was used to analyze storms that caused forest damages in the summer and fall of 2020. The produced maps were considered illustrative and useful to those responsible for compiling the situational picture. The accumulation of snow on tree branches, can be modeled using weather data such as rainfall, temperature, air humidity, and wind speed. In the Säätyö project, the snow damage risk assessment model was further developed in such a way that, in addition to the accumulated snow load amount, the characteristics of the stand and the variations in terrain height were also taken into account. According to the verification performed, the importance of abiotic factors increased under extreme snow load conditions (winter 2017-2018). In ordinary winters, the importance of biotic factors was emphasized. According to the comparison, the actual snow damage could be explained well with the tested model. In the interviews and workshop, the uses of information products, their benefits, the conditions for their introduction and development opportunities were mapped. According to the results, diverse uses and benefits of information products and services were seen. Information products would make it possible to develop proactive forest management, which would reduce the economic costs caused by wind and snow damages. A more up-to-date understanding of harvesting conditions, enabled by information products, would enhance the implementation of harvesting and harvesting operations and the management of timber stocks, as well as reduce terrain, trunk and root damage. According to the study, the introduction of information is particularly affected by the availability of timeliness. Although the interviewees were not currently willing to pay for the information products developed in the project, the interviews highlighted several suggestions for the development of information products, which could make it possible to commercialize them.

The function of the 30-kilodalton movement protein (MP) of tobacco mosaic virus (TMV) is to facilitate cell-to-cell movement of viral progeny in infected plants. Our earlier findings have indicated that this protein has a direct effect on plasmodesmal function. In addition, these studies demonstrated that constitutive expression of the TMV MP gene (under the control of the CaMV 35S promoter) in transgenic tobacco plants significantly affects carbon metabolism in source leaves and alters the biomass distribution between the various plant organs. The long-term goal of the proposed research was to better understand the factors controlling carbon translocation in plants. The specific objectives were: A) To introduce into tobacco and potato plants a virally-encoded (TMV-MP) gene that affects plasmodesmal functioning and photosynthate partitioning under tissue-specific promoters. B) To introduce into tobacco and potato plants the TMV-MP gene under the control of promoters which are tightly repressed by the Tn10-encoded Tet repressor, to enable the expression of the protein by external application of tetracycline. C) To explore the mechanism by which the TMV-MP interacts with the endogenous control o~ carbon allocation. Data obtained in our previous project together with the results of this current study established that the TMV-MP has pleiotropic effects when expressed in transgenic tobacco plants. In addition to its ability to increase the plasmodesmal size exclusion limit, it alters carbohydrate metabolism in source leaves and dry matter partitioning between the various plant organs, Expression of the TMV-MP in various tissues of transgenic potato plants indicated that sugars and starch levels in source leaves are reduced below those of control plants when the TMV-MP is expressed in green tissue only. However, when the TMV-MP was expressed predominantly in PP and CC, sugar and starch levels were raised above those of control plants. Perhaps the most significant result obtained from experiments performed on transgenic potato plants was the discovery that the influence of the TMV-MP on carbohydrate allocation within source leaves was under developmental control and was exerted only during tuber development. The complexity of the mode by which the TMV-MP exerts its effect on the process of carbohydrate allocation was further demonstrated when transgenic tobacco plants were subjected to environmental stresses such as drought stress and nutrients deficiencies, Collectively, these studies indicated that the influence of the TMV-MP on carbon allocation L the result of protein-protein interaction within the source tissue. Based on these results, together with the findings that plasmodesmata potentiate the cell-to-cell trafficking of viral and endogenous proteins and nucleoproteins complexes, we developed the theme that at the whole plant level, the phloem serves as an information superhighway. Such a long-distance communication system may utilize a new class of signaling molecules (proteins and/or RNA) to co-ordinate photosynthesis and carbon/nitrogen metabolism in source leaves with the complex growth requirements of the plant under the prevailing environmental conditions. The discovery that expression of viral MP in plants can induce precise changes in carbon metabolism and photoassimilate allocation, now provide a conceptual foundation for future studies aimed at elucidating the communication network responsible for integrating photosynthetic productivity with resource allocation at the whole-plant level. Such information will surely provide an understanding of how plants coordinate the essential physiological functions performed by distantly-separated organs. Identification of the proteins involved in mediating and controlling cell-to-cell transport, especially at the companion cell-sieve element boundary, will provide an important first step towards achieving this goal.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.