Academic literature on the topic 'Normal basis'

We give several generalizations of the normal basis and primitive element theorems for a finite Galois field extension, with an infinite base field. These generalizations are obtained by considering polynomial expressions of conjugates of a fixed element.

Cardiac action potential characteristics are known to vary in different species, but also in the different regions of the heart within a given species and in cardiovascular disease. The heterologous expression of voltage-gated ion currents is believed to underlie these differences. The purpose of this thesis is to elucidate the molecular mechanisms which may underlie some of the observed current changes in different species, as well as regions and diseases of the heart.
Here, we describe the variable dependence on repolarizing K+ currents in different species as being the result of the lack of Ito subunits in guinea pig heart with a greater expression of IK subunits, while rabbits express all hypothesized Ito subunits, but express IK subunits at low levels. Humans are found to lie in between these two species in terms of the expression of these voltage-gated K+ channel subunits. The specialized function of certain regions of the heart, such as the ventricles and the SAN, have been attributed to the heterologous expression of Ito and the pacemaker current (I f) respectively. Here were demonstrate that both Kv4.3 and KchIP2 gradients underlie an observed Ito transmural gradient and contribute to the dispersion of repolarization, while a greater expression of HCN2 and HCN4 subunits in the SAN compared to the right atrium account for the larger I f current in this region. Cardiovascular diseases such as congestive heart failure (CHF) have been associated with ion channel remodelling. Here, we report the finding of changes in Nav1.5, Kv4.3, HCN2 and HCN4 expression which may underlie some of the electrophysiological changes associated with this disease. Furthermore, we characterise a genetic polymorphism which is associated with another disease, atrial fibrillation.
The heterologous expression of voltage-gated ion channel subunits may account for many of the species-, region- and disease-specific differences which have been observed in the heart. Such heterogeneity contributes to the proper functioning of the heart under normal conditions, but may also contribute to the pathogenesis of cardiovascular disease.

This thesis investigates architectures for multiplying elements in Galois rings of the size 4^m, where m is an integer.

The main question is whether known architectures for multiplying in Galois fields can be used for Galois rings also, with small modifications, and the answer to that question is that they can.

Different representations for elements in Galois rings are also explored, and the performance of multipliers for the different representations is investigated.

This work is concerned with the genetic basis of normal human pigmentation variation. Specifically, the role of polymorphisms within the solute carrier family 45 member 2 (SLC45A2 or membrane associated transporter protein; MATP) gene were investigated with respect to variation in hair, skin and eye colour ― both between and within populations. SLC45A2 is an important regulator of melanin production and mutations in the gene underly the most recently identified form of oculocutaneous albinism. There is evidence to suggest that non-synonymous polymorphisms in SLC45A2 are associated with normal pigmentation variation between populations. Therefore, the underlying hypothesis of this thesis is that polymorphisms in SLC45A2 will alter the function or regulation of the protein, thereby altering the important role it plays in melanogenesis and providing a mechanism for normal pigmentation variation. In order to investigate the role that SLC45A2 polymorphisms play in human pigmentation variation, a DNA database was established which collected pigmentation phenotypic information and blood samples of more than 700 individuals. This database was used as the foundation for two association studies outlined in this thesis, the first of which involved genotyping two previously-described non-synonymous polymorphisms, p.Glu272Lys and p.Phe374Leu, in four different population groups. For both polymorphisms, allele frequencies were significantly different between population groups and the 272Lys and 374Leu alleles were strongly associated with black hair, brown eyes and olive skin colour in Caucasians. This was the first report to show that SLC45A2 polymorphisms were associated with normal human intra-population pigmentation variation. The second association study involved genotyping several SLC45A2 promoter polymorphisms to determine if they also played a role in pigmentation variation. Firstly, the transcription start site (TSS), and hence putative proximal promoter region, was identified using 5' RNA ligase mediated rapid amplification of cDNA ends (RLM-RACE). Two alternate TSSs were identified and the putative promoter region was screened for novel polymorphisms using denaturing high performance liquid chromatography (dHPLC). A novel duplication (c.–1176_–1174dupAAT) was identified along with other previously described single nucleotide polymorphisms (c.–1721C>G and c.–1169G>A). Strong linkage disequilibrium ensured that all three polymorphisms were associated with skin colour such that the –1721G, +dup and –1169A alleles were associated with olive skin in Caucasians. No linkage disequilibrium was observed between the promoter and coding region polymorphisms, suggesting independent effects. The association analyses were complemented with functional data, showing that the –1721G, +dup and –1169A alleles significantly decreased SLC45A2 transcriptional activity. Based on in silico bioinformatic analysis that showed these alleles remove a microphthalmia-associated transcription factor (MITF) binding site, and that MITF is a known regulator of SLC45A2 (Baxter and Pavan, 2002; Du and Fisher, 2002), it was postulated that SLC45A2 promoter polymorphisms could contribute to the regulation of pigmentation by altering MITF binding affinity. Further characterisation of the SLC45A2 promoter was carried out using luciferase reporter assays to determine the transcriptional activity of different regions of the promoter. Five constructs were designed of increasing length and their promoter activity evaluated. Constitutive promoter activity was observed within the first ~200 bp and promoter activity increased as the construct size increased. The functional impact of the –1721G, +dup and –1169A alleles, which removed a MITF consensus binding site, were assessed using electrophoretic mobility shift assays (EMSA) and expression analysis of genotyped melanoblast and melanocyte cell lines. EMSA results confirmed that the promoter polymorphisms affected DNA-protein binding. Interestingly, however, the protein/s involved were not MITF, or at least MITF was not the protein directly binding to the DNA. In an effort to more thoroughly characterise the functional consequences of SLC45A2 promoter polymorphisms, the mRNA expression levels of SLC45A2 and MITF were determined in melanocyte/melanoblast cell lines. Based on SLC45A2’s role in processing and trafficking TYRP1 from the trans-Golgi network to stage 2 melanosmes, the mRNA expression of TYRP1 was also investigated. Expression results suggested a coordinated expression of pigmentation genes. This thesis has substantially contributed to the field of pigmentation by showing that SLC45A2 polymorphisms not only show allele frequency differences between population groups, but also contribute to normal pigmentation variation within a Caucasian population. In addition, promoter polymorphisms have been shown to have functional consequences for SLC45A2 transcription and the expression of other pigmentation genes. Combined, the data presented in this work supports the notion that SLC45A2 is an important contributor to normal pigmentation variation and should be the target of further research to elucidate its role in determining pigmentation phenotypes. Understanding SLC45A2’s function may lead to the development of therapeutic interventions for oculocutaneous albinism and other disorders of pigmentation. It may also help in our understanding of skin cancer susceptibility and evolutionary adaptation to different UV environments, and contribute to the forensic application of pigmentation phenotype prediction.

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The purpose of this study is to examine the participation of the State University of Montes Claros (UNIMONTES) in the context of education policies of the country as regards its participation and proposition of training teachers in the Superior Normal mode in the post- LDBEN. Delineamos object of study as the training of teachers of the course Normal Superior / Modular offered by UNIMONTES. I reviewed the theoretical assumptions and economic education in the proposals of neoliberal Miltom Friedrick Hayek and Friedman. This study if it bases on the contributions of Karl Marx. The methodology is guided by qualitative research-quantitative, combining data: questionnaires, interviews, official documents of the course Normal Superior, matches of students and production of texts. The considerations possible, this research is that UNIMONTES, contributed to the access of a significant contingent of teachers of elementary school, following the decisions of LDBEN 9394/96. However, the university changes its role in training teachers when relegates to the background the course of teaching that has historical tradition in the training of professional education in the north of Minas.
O objetivo deste estudo é analisar a participação da Universidade Estadual de Montes Claros (UNIMONTES) no contexto das políticas de educação do país, no que se refere a sua participação e proposição de programas de formação de professores na modalidade Normal Superior no cenário pós-LDBEN. Delineamos como objeto de estudo a formação de professores do curso Normal Superior/Modular oferecido pela UNIMONTES. Analiso a origem da universidade, crises, tensões e desafios para preservar sua identidade e as repercussões históricas na universidade contemporânea no Brasil. A metodologia orientou-se pela pesquisa qualitativo-quantitativa, conjugando os dados: questionários, entrevistas, documentos oficiais do curso Normal Superior, correspondências de alunos e produção de textos. As considerações possíveis, a partir desta investigação, é a de que a UNIMONTES contribuiu com o acesso de um contingente significativo de professores do ensino fundamental, obedecendo às determinações da LDBEN 9394/96. Entretanto, a universidade altera o seu papel na formação de professores quando o relega a segundo plano o curso de Pedagogia, que tem tradição histórica na formação de profissionais da educação no norte de Minas.

Dans la première partie de la thèse on étudie un algorithme combinatoire qui correspond à l'itération de la modification de Nash d'une variété torique. On montre que, dans le cas de la dimension deux, cet algorithme s'arrête pour certains choix de cartes affines de la modification de Nash. De plus, on donne une borne pour le nombre d'itérations nécessaire pour que l'algorithme s'arrête dans les cas que l'on considère. Soit C(x_1,x_2) le corps des fonctions d'une surface torique. Alors notre résultat implique que pour toute valuation v centrée sur la surface torique tel que v(x_1) n'est pas un multiple irrationnel de v(x_2), une itération finie de la modification de Nash donne une uniformisation locale le long de cette valuation. Dans la deuxième partie on étudie la notion d'éclatement de Nash supérieur d'une variété algébrique. Cette notion consiste à remplacer des points singuliers par des limites de certains espaces vectoriels associés aux points non singuliers de la variété. On donne une description combinatoire de l'éclatement de Nash supérieur dans le cas de variétés toriques normales. En utilisant cette description, on montre que l'analogue du théorème de Nobile sur l'éclatement de Nash usuel est aussi valide dans ce contexte. Plus précisément, on montre que pour une variété torique normale, l'éclatement de Nash supérieur est un isomorphisme si et seulement si la variété est non singulière
In the first part of the thesis we explore a combinatorial algorithm that corresponds to the iteration of Nash modification on not necessarily normal toric varieties. We show that for toric surfaces this algorithm stops for certain choices of affine charts of the Nash modification. In addition, we give a bound on the number of steps required for the algorithm to stop in the cases we consider. Let C(x_1,x_2) be the field of rational functions of a toric surface. Then our result implies that for any valuation v centered on the toric surface such that v(x_1) is not an irrational multiple of v(x_2), a finite iteration of Nash modification gives local uniformization along this valuation. In the second part of the thesis we explore the notion of higher Nash blowup of an algebraic variety which is a modification that replaces singular points with limits of certain spaces carrying higher order data associated to the variety at non-singular points. In the case of normal toric varieties we give a combinatorial description of the higher Nash blowup in terms of a Groebner fan. This description allow us to prove the analogous of Nobile's theorem on the usual Nash blowup in this context. More precisely, we prove that for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular

Let p be a prime and q = pk. The polynomial gn,q isin Fp[x] defined by the functional equation Sigmaa isin Fq (x+a)n = gn,q(xq- x) gives rise to many permutation polynomials over finite fields. We are interested in triples (n,e;q) for which gn,q is a permutation polynomial of Fqe. In Chapters 2, 3, and 4 of this dissertation, we present many new families of permutation polynomials in the form of gn,q. The permutation behavior of gn,q is becoming increasingly more interesting and challenging. As we further explore the permutation behavior of gn,q, there is a clear indication that gn,q is a plenteous source of permutation polynomials. We also describe a piecewise construction of permutation polynomials over a finite field Fq which uses a subgroup of Fq*, a “selection” function, and several “case” functions. Chapter 5 of this dissertation is devoted to this piecewise construction which generalizes several recently discovered families of permutation polynomials.

Orientador: Pedro Antonio Muniz Vazquez
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Quimica
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Resumo: O presente trabalho aborda o desenvolvimento de metodologias para o cálculo das intensidades absolutas do espalhamento Raman vibracional produzido por moléculas em fase gasosa. Com o objetivo de reduzir a demanda por recursos computacionais nestes cálculos, foram desenvolvidas duas novas famílias de funções de base compactas pela aplicação do método de polarização elétrica de Sadlej às bases para uso com potenciais efetivos de caroço SBKJC e de Stuttgart-Colônia. Utilizando estas novas funções de base, as intensidades Raman podem ser obtidas com a mesma qualidade das bases Sadlej-pVTZ, que são referência no cálculo destas propriedades, porém com um custo computacional sensivelmente menor. Além disso, como estes pseudopotenciais foram modelados para descrever os efeitos relativísticos sobre os elétrons internos, as polarizabilidades e intensidades Raman obtidas no nível Hartree-Fock com estas novas bases concordam, dentro de um erro médio de 6%, com seus respectivos valores relativísticos Dirac-Hartree-Fock/Sadlei-pVTZ com hamiltoniano de Dirac-Coulomb. Também foi desenvolvida uma metodologia para o estudo das intensidades das transições Raman fundamentais, de combinação e sobretom, que inclui as correções para a anarmonicidade cúbica do potencial, introduzidas através de uma transformação de contato. Os resultados obtidos para a molécula de acetileno e seus isotopômeros deuterados mostram que a anarmonicidade mecânica exerce grande influência sobre as intensidades Raman, particularmente das transições de segunda ordem. Excetuando as transições de combinação, em geral, as correções de anarmoniciadade melhoram a concordância dos valores teóricos com os experimentais. Uma terceira parte deste trabalho trata do efeito Raman em condições ressonantes, onde uma expressão para estas intensidades foi derivada, implementada no programa PLACZEK e aplicada no cálculo do espectro Raman da molécula de trans-butadieno nas vizinhanças de sua transição eletrônica 1Bu. Este estudo mostrou que as aproximações utilizadas com maior frequência para simplificar o cálculo desta propriedade afetam significativamente as seções de choque desta molécula, sugerindo que estas aproximações devem ser evitadas em estudos desta natureza.
Abstract: In this work new methodologies for the calculation of absolute vibrational Raman intensities of gaseous systems are presented. In order to reduce the computational requirements in these calculations two families of compact basis functions were generated from the effective core potential valence basis sets SBKJC and Stuttgart-Cologne through the Sadlej's electric polarization procedure. The Raman intensities evaluated with the new bases are close to those obtained with the well successful Sadlej-pVTZ basis but the computational requirements are significatively reduced. Furthermore, since the effective core potentials SBKJC and Stuttgart-Cologne were developed to account for the relativistic effects on the inner electrons, the polarizabilities and Raman intensities evaluated at the Hartree-Fock level with the new bases agree with the relativistic Dirac-Hartree-Fock values, obtained using the Dirac-Coulomb Hamiltonian and the Sadlej-pVTZ set, within the mean error of 6%. In the second part of this work a methodology was developed for the study of fundamental, combination and overtone Raman transitions including a treatment based on the contact transform formalism for the mechanical anharmonicity from the cubic potential energy terms. The results obtained for acetylene and its deutered isotopomers show that anharmonicity effects on the Raman intensities can be very strong, particularly in the second order transitions. With the exception of the combination transitions, in general the corrections for mechanical anharmonicity improve the agreement between ab initio and experimental values. The resonance Raman scattering is the subject of the third part of this work where an expression for the resonance cross section was derived, implemented in the PLACZEK program and applied to the calculation of the resonance Raman spectrum of the trans-butadiene molecule in the region of its.
Doutorado
Físico-Química
Doutor em Ciências

The monograph is devoted to describing the methods of catastrophe theory and building on the basis of these methods, phenomenological models of phase transitions in solids. Methods of constructing structurally stable normal forms of functions, including functions that are imposed on the symmetry conditions. The classification of phenomenological models of phase transitions for two interacting one-component order parameter, two-component and three-component order parameters the number of control parameters varied in the experiment. Theoretical dependence of the anomalies of the physical properties of the models are compared with experimental data in ferroelectrics, magnetic materials, solid solutions of rare earth metals, multiferroics and other solids that are experiencing phase transitions. For professionals in the field of solid state physics and phase transitions.

The thesis of this essay is that the current schooling paradigm is in need of review and that the answer may lie in a shift in how we think about teaching and learning. Under the prevailing paradigm, the role of teachers is to deliver the year-level curriculum to all students in a year level. This mismatch has unfortunate consequences for both teaching and learning. Currently, many students are not ready for their year-level curriculum because they lack prerequisite knowledge, skills and understandings. The basis for an alternative paradigm and a 'new normal' is presented. The essay addresses concerns raised about changes to curriculum, including that: changing the structure of the curriculum will mean abandoning year levels; teachers will be unable to manage classrooms in which students are not all working on the same content at the same time; some students will be disadvantaged if students are not all taught the same content at the same time; a restructured curriculum will result in ‘streaming’ and/or require the development of individual learning plans; a restructured curriculum will lower educational standards; and it will not be possible to do this in some subjects.

Around the world, people with disabilities can be the most marginalised in society. Having a disability and being a member of a religious minority or an excluded social group can compound the reasons why some people find themselves on the outskirts of social systems which normally provide financial and moral support and a sense of identity and belonging. A recent study from India found that identity markers such as religion, caste and gender can exacerbate the exclusion already experienced by people with disabilities. Taking deliberate steps to strengthen the social inclusion of people with disabilities who also come from minority religious groups and socioeconomically marginalised backgrounds can help them fulfil their potential to fully and effectively participle in society on an equal basis with others, and strengthen community ties, making the society in which they live more inclusive.

Hanne Darboven’s (1941-2009) Opus 17a is a composition for solo double bass that is rarely performed due to the physical and mental challenges involved in its performance. It is one of four opuses from the composers monumental 1008 page Wünschkonzert (1984), and was composed during her period of making “mathematical music” based on mathematical systems where numbers were assigned to certain notes and translated to musical scores. It can be described as large-scale minimalism and it is highly repetitive, but even though the same notes and intervals keep repeating, the patterns slightly change throughout the piece. This is an attempt to unfold the many challenges of both interpreting, preparing and performing this 70 minute long solo piece for double bass consisting of a continuous stream of eight notes. It is largely based on my own experiences of preparing, rehearsing and performing Opus 17a, but also on interviews I have conducted with fellow bass players Robert Black and Tom Peters, who have both made recordings of this piece as well as having performed it live. One is met with few instrumental technical challenges such as fingering, string crossing and bowing when performing Opus 17a, but because of its long duration what one normally would take for granted could possibly prove to be challenging.

In the article researched the experience of licensing of nuclear power plants of member states of the EAEU, both already having functioning nuclear power plants and planning its construction. It noted the different approaches of states to the licensing of the activity in this area, which can lead to increased time and unnecessary increase in the cost of construction of nuclear power plants. On the basis of the analysis it makes the conclusion on the necessity of harmonization of the process of licensing activity of nuclear power plants in member states of the EAEU, as well as it exprecces an opinion on the expediency of developing unified norms of licensing of activity in the field of usage of atomic energy withing the integration unification and reflection of its in the relevant international-legal act of the EAEU.

In the countries of the Lake Chad Basin, Boko Haram’s emergence has created major new security challenges for the region’s governments. Cameroon’s Far North region, the most populous in the country, is at the heart of these security issues. Since late 2020, Boko Haram has intensified attacks in Far North localities with assassinations targeting civilians, kidnappings, and looting in small towns along the Nigerian border. In response, the Cameroonian government has pursued a hardline strategy and militarized the affected localities. In addition to arbitrary arrests, prolonged pre-trial detention, prison overcrowding, and the death penalty are all sources of concern. This policy note outlines core findings from a case study of the Boko Haram ex-associates reintegration process in Cameroon. The note examines how existing community norms or mechanisms might be as useful as more standard approaches to disarmament, demobilization, and reintegration (DDR) in addressing challenges presented by Boko Haram ex-associates in Cameroon.

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%.