Reconstructing the parameter space of non-analytical cosmological fixed points

Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a set of autonomous first-order differential equations. The fixed points of this autonomous set encode the asymptotic evolution of the model. Usually, these points can be written as analytical expressions for the variables in terms of the parameters of the model, which allows a complete characterization of the corresponding parameter space. However, a thoroughly analytical treatment is impossible in some cases. In this work, we give an example of a dark energy model, a scalar field coupled to a vector field in an anisotropic background, where not all the fixed points can be analytically found. Then, we put forward a general scheme that provides a numerical description of the parameter space. This allows us to find interesting accelerated attractors of the system with no analytical representation. This work may serve as a template for the numerical analysis of highly complicated dynamical systems.Comment: 13 pages, 13 figures, 1 table. Changes match the published versio

The effects of storage duration, temperature and cultivar on the severity of garlic clove rot caused by Fusarium proliferatum.

Diseases that affect garlic during storage can lead to severe economic losses for farmers worldwide. One causal agent of clove rot is Fusarium proliferatum. Here, the progress of clove rot caused by F. proliferatum and its dependence on different storage conditions and cultivar type were studied. The effect of temperature on mycelial growth, conidial viability, and fungal survival during garlic commercial storage was documented. Samples of 50 bulbs from a randomized field trial with three different clonal generations for purple garlic (F3, F4 and F5) and the F4 clonal generation for white garlic were labeled and stored for two months (short-term storage). In addition, another sample of the F5 clonal generation of purple garlic was stored for 6 months after harvest (long-term storage). The presence of the pathogen and the percentage of symptomatic cloves were evaluated. A notable difference in the rot severity index (RSI) of different garlic varieties was observed. In all studied cases, clove rot increased with storage time at 20 ◦ C, and the white garlic variety had a higher index of rot severity after two months of storage. Additionally, there were clear differences between the growth rates of F. proliferatum isolates. Studies conducted on the temperature responses of the pathogen propagules showed that expo- sure for at least 20 min at 50 ◦ C was highly effective in significantly reducing the viability of fungal conidia. Pathogenicity studies showed that the fungus is pathogenic in all commercial varieties. However, there were significant differences in varietal susceptibility between Chinese and white garlic type cultivars (81.84 ± 16.44% and 87.5 ± 23.19% symptomatic cloves, respectively) and purple cultivars (49.06 ± 13.42% symptomatic cloves

Phase-plane analysis of Friedmann-Robertson-Walker cosmologies in Brans-Dicke gravity

We present an autonomous phase-plane describing the evolution of Friedmann-Robertson-Walker models containing a perfect fluid (with barotropic index gamma) in Brans-Dicke gravity (with Brans-Dicke parameter omega). We find self-similar fixed points corresponding to Nariai's power-law solutions for spatially flat models and curvature-scaling solutions for curved models. At infinite values of the phase-plane variables we recover O'Hanlon and Tupper's vacuum solutions for spatially flat models and the Milne universe for negative spatial curvature. We find conditions for the existence and stability of these critical points and describe the qualitative evolution in all regions of the (omega,gamma) parameter space for 0-3/2. We show that the condition for inflation in Brans-Dicke gravity is always stronger than the general relativistic condition, gamma<2/3.Comment: 24 pages, including 9 figures, LaTe

Cortical thinning over two years after first-episode psychosis depends on age of onset

First-episode psychosis (FEP) patients show structural brain abnormalities at the first episode. Whether the cortical changes that follow a FEP are progressive and whether age at onset modulates these changes remains unclear. This is a multicenter MRI study in a deeply phenotyped sample of 74 FEP patients with a wide age range at onset (15–35 years) and 64 neurotypical healthy controls (HC). All participants underwent two MRI scans with a 2-year follow-up interval. We computed the longitudinal percentage of change (PC) for cortical thickness (CT), surface area (CSA) and volume (CV) for frontal, temporal, parietal and occipital lobes. We used general linear models to assess group differences in PC as a function of age at FEP. We conducted post-hoc analyses for metrics where PC differed as a function of age at onset. We found a significant age-by-diagnosis interaction effect for PC of temporal lobe CT (d = 0.54; p = 002). In a post-hoc-analysis, adolescent-onset (≤19 y) FEP showed more severe longitudinal cortical thinning in the temporal lobe than adolescent HC. We did not find this difference in adult-onset FEP compared to adult HC. Our study suggests that, in individuals with psychosis, CT changes that follow the FEP are dependent on the age at first episode, with those with an earlier onset showing more pronounced cortical thinning in the temporal lobe

Modified Gravity and Cosmology

In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f(R), general higher-order theories, Horava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.Comment: 312 pages, 15 figure

Feasibility and short-term outcomes in liver-first approach: a Spanish snapshot study (the RENACI project)

Producción CientíficaSimple Summary: Current evidence does not provide enough information for selecting a tailored approach pathway in patients with colorectal cancer and synchronous liver metastases. There are no randomized clinical trials or prospective series comparing the classical approach with the liver-first approach. In addition, information on the proportion of patients who actually complete the therapeutic regimen is limited. The RENACI Project was a prospective National Registry performed on patients with colorectal cancer and synchronous liver metastases undergoing the liver-first approach. This study aimed to present the data of feasibility and short-term outcomes of the Spanish National Registry of Liver First Approach (the RENACI Project).(1) Background: The liver-first approach may be indicated for colorectal cancer patients with synchronous liver metastases to whom preoperative chemotherapy opens a potential window in which liver resection may be undertaken. This study aims to present the data of feasibility and short-term outcomes in the liver-first approach. (2) Methods: A prospective observational study was performed in Spanish hospitals that had a medium/high-volume of HPB surgeries from 1 June 2019 to 31 August 2020. (3) Results: In total, 40 hospitals participated, including a total of 2288 hepatectomies, 1350 for colorectal liver metastases, 150 of them (11.1%) using the liver-first approach, 63 (42.0%) in hospitals performing <50 hepatectomies/year. The proportion of patients as ASA III was significantly higher in centers performing ≥50 hepatectomies/year (difference: 18.9%; p = 0.0213). In 81.1% of the cases, the primary tumor was in the rectum or sigmoid colon. In total, 40% of the patients underwent major hepatectomies. The surgical approach was open surgery in 87 (58.0%) patients. Resection margins were R0 in 78.5% of the patients. In total, 40 (26.7%) patients had complications after the liver resection and 36 (27.3%) had complications after the primary resection. One-hundred and thirty-two (89.3%) patients completed the therapeutic regime. (4) Conclusions: There were no differences in the surgical outcomes between the centers performing <50 and ≥50 hepatectomies/year. Further analysis evaluating factors associated with clinical outcomes and determining the best candidates for this approach will be subsequently conducted.Asociación Española de Cirujanos - (grant Research Projects 2020

Informe de Política Monetaria - Octubre 2020

Recent data suggest that the technical staff’s appraisals of the condition and development of economic activity, inflation and the labor market have been in line with current trends, marked by a decline in demand and the persistence of ample excess productive capacity. A significant projected fall in output materialized in the second quarter, contributing to a decline in inflation below the 3% target and reflected in a significant deterioration of the labor market. A slow recovery in output and employment is expected to continue for the remainder of 2020 and into next year, alongside growing inflation that should remain below the target. The Colombian economy is likely to undergo a significant recession in 2020 (GDP contraction of 7.6%), though this may be less severe than projected in the previous report (-8.5%). Output is expected to have begun a slow recovery in the second half of this year, though it is not projected to return to pre-pandemic levels in 2021 amid significant global uncertainty. The output decline in the first half of 2020 was less severe than anticipated, thanks to an upward revision in first-quarter GDP and a smaller contraction in the second quarter (-15.5%) than had been projected (-16.5%). Available economic indicators suggest an annual decline in GDP in the third quarter of around 9%. No significant acceleration of COVID-19 cases that would imply a tightening of social distancing measures is presumed for the remainder of this year or in 2021. In that context, a gradual opening of the economy would be expected to continue, with supply in sectors that have been most affected by the pandemic recovering slowly as restrictions on economic activity continue to be relaxed. On the spending side, an improvement in consumer confidence, suppressed demand for goods and services, low interest rates, and higher expected levels of foreign demand should contribute to a recovery in output. A low base of comparison would also help explain the expected increase in GDP in 2021. Based on the conditions laid out above, economic growth in 2020 is expected to be between -9% and -6.5%, with a central value of -7.6%. Growth in 2021 is projected to be between 3% and 7%, with a central value of 4.6% (Graph 1.1). Upward revisions compared to the July report take into account a lower-than-expected fall in first-semester growth and a somewhat faster recovery in the third quarter in some sectors. The forecast intervals for 2020 and 2021 growth tightened somewhat but continue to reflect a high degree of uncertainty over theevolution of the pandemic, the easures required to deal with it, and their effects on global and domestic economic activity.Box 1. Evaluation of the Predictive Capacity of Expected Inflation Measures. Authors: César Anzola-Bravo, Anderson Grajales-Olarte, Alexander Guarín-López, Julián Camilo Mateus-Gamboa, Jonathan Alexander Muñoz-Martínez, Carlos Andrés Quicazán-Moreno, Juan Sebastián Rojas-Moreno, Cristhian Hernando Ruiz-CardozoBox 2. Literature Review: Weighing the Drivers of Portfolio Flows to Emerging Market Economies. Authors: Andrés Sánchez-Jabb

Monetary Policy Report - January 2021

Macroeconomic Summary Overall inflation (1.61%) and core inflation (excluding food and regulated items) (1.11%) both declined beyond the technical staff’s expectations in the fourth quarter of 2020. Year-end 2021 forecasts for both indicators were revised downward to 2.3% and 2.1%, respectively. Market inflation expectations also fell over this period and suggested inflation below the 3% target through the end of this year, rising to the target in 2022. Downward pressure on inflation was more significant in the fourth quarter than previously projected, indicating weak demand. Annual deceleration among the main groups of the consumer price index (CPI) was generalized and, except for foods, was greater than projected in the October report. The CPI for goods (excluding foods and regulated items) and the CPI for regulated items were subject to the largest decelerations and forecasting discrepancies. In the first case, this was due in part to a greater-than-expected effect on prices from the government’s “VAT-fee day” amid weak demand, and from the extension of some price relief measures. For regulated items, the deceleration was caused in part by unanticipated declines in some utility prices. Annual change in the CPI for services continued to decline as a result of the performance of those services that were not subject to price relief measures, in particular. Although some of the overall decline in inflation is expected to be temporary and reverse course in the second quarter of 2021, various sources of downward pressure on inflation have become more acute and will likely remain into next year. These include ample excesses in capacity, as suggested by the continued and greater-than-expected deceleration in core inflation indicators and in the CPI for services excluding price relief measures. This dynamic is also suggested by the minimal transmission of accumulated depreciation of the peso on domestic prices. Although excess capacity should fall in 2021, the decline will likely be slower than projected in the October report amid additional restrictions on mobility due to a recent acceleration of growth in COVID-19 cases. An additional factor is that low inflation registered at the end of 2020 will likely be reflected in low price adjustments on certain indexed services with significant weight in the CPI, including real estate rentals and some utilities. These factors should keep inflation below the target and lower than estimates from the previous report on the forecast horizon. Inflation is expected to continue to decline to levels near 1% in March, later increasing to 2.3% at the end of 2021 and 2.7% at year-end 2022 (Graph 1.1). According to the Bank’s most recent survey, market analysts expect inflation of 2.7% and 3.1% in December 2021 and 2022, respectively. Expected inflation derived from government bonds was 2% for year-end 2021, while expected inflation based on bonds one year forward from that date (FBEI 1-1 2022) was 3.2%.Box I. Macroeconomic Expectations: Analysis of the Monthly Survey of Economic Analyst Expectations. Authors: Hernando Vargas, Alexander Guarín, Anderson Grajales, César Anzola, Jonathan Muño

Monetary Policy Report - April de 2021

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%.Box 1. The Transmission of Changes in the Monetary Policy Interest Rate (MPR) to Credit Institutions’ Interest Rates (CI). Authors: Isleny Carranza Amortegui, Deicy Cristiano Botia, Eliana González Molano, Carlos Huertas CamposBox 2. Analysis of Macroeconomic Expectations implicit in Financial Market Instruments. Authors: Hernando Vargas, Alexander Guarín, Anderson Grajales-Olarte, Jonathan Muño