Letteratura scientifica selezionata sul tema "Projective code"

MDS code is a linear code that achieves equality in the Singleton bound, and projective MDS (PG-MDS) is MDS code with independents property of any two columns of its generator matrix. In this paper, elementary methods for modifying a PG-MDS code of dimensions 2, 3, as extending and lengthening, in order to find new incomplete PG-MDS codes have been used over . Also, two complete PG-MDS codes over of length and 28 have been found.

Abstract In this paper we estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We find the length of these codes and we give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishing ideal of the projective torus. Also we find an upper bound for the minimum distance and, in some cases, we give some lower bounds for the regularity index and the minimum distance. These lower bounds work in several cases, particularly for any projective parameterized code associated to the incidence matrix of uniform clutters and then they work in the case of graphs.

It has been known since the 1970’s that the difference of the non-zero weights of a projective Fq-linear two-weight code has to be a power of the characteristic of the underlying field. Here, we study non-projective two-weight codes and, e.g., show the same result under mild extra conditions. For small dimensions we give exhaustive enumerations of the feasible parameters in the binary case.

We propose a novel slot-pattern-control based coded compressed sensing for unsourced random access with an outer A-channel code capable of correcting t errors. Specifically, an RM extension code called patterned Reed–Muller (PRM) code is proposed. We demonstrate the high spectral efficiency due to its enormous sequence space and prove the geometry property in the complex domain that enhances the reliability and efficiency of detection. Accordingly, a projective decoder based on its geometry theorem is also proposed. Next, the “patterned” property of the PRM code, which partitions the binary vector space into several subspaces, is further extended as the primary principle for designing a slot control criterion that reduces the number of simultaneous transmissions in each slot. The factors affecting the chance of sequence collisions are identified. Finally, the proposed scheme is implemented in two practical outer A-channel codes: (i) the t-tree code and (ii) the Reed–Solomon code with Guruswami–Sudan list decoding, and the optimal setups are determined to minimize SNR by optimizing the inner and outer codes jointly. In comparison with the existing counterpart, our simulation results confirm that the proposed scheme compares favorably with benchmark schemes regarding the energy-per-bit requirement to meet a target error probability as well as the number of accommodated active users in the system.

AbstractThere is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a family of a ne cartesian codes. If 𝕏 is a set of projective points over a finite field we determine the basic parameters and the generalized Hamming weights of the Veronese type codes on 𝕏 and their dual codes in terms of the basic parameters and the generalized Hamming weights of the corresponding projective Reed–Muller-type codes on 𝕏 and their dual codes.

Projective Reed-Solomon code is an important class of maximal distance separable codes in reliable communication and deep holes play important roles in its decoding. In this paper, we obtain two classes of deep holes of projective Reed-Solomon codes over finite fields with even characteristic. That is, let [see formula in PDF] be finite field with even characteristic, [see formula in PDF], and let [see formula in PDF] be the Lagrange interpolation polynomial of the first [see formula in PDF] components of the received vector [see formula in PDF]. Suppose that the [see formula in PDF]-th component of [see formula in PDF] is 0, and [see formula in PDF],[see formula in PDF] where [see formula in PDF], and [see formula in PDF] is a polynomial over [see formula in PDF] with degree no more than [see formula in PDF]. Then the received vector [see formula in PDF] is a deep hole of projective Reed-Solomon codes [see formula in PDF]. In fact, our result partially solved an open problem on deep holes of projective Reed-Solomon codes proposed by Wan in 2020.

The goal of this paper was to study the applications of the projective plane PG (2, q) over a Galois field of order q in the projective q-ary (n, M, d) -code such that the parameters length of code n, the maximum value size code M, and the minimum distance d with the error-correcting e according to an incidence matrix have been calculated. Also, this research provides examples and theorems of links between the combinatorial structures and coding theory. The method of the research depends on the classification of the points and lines in PG (2, q).

A (n,r)-arc in a projective plane PG(2,q) is a set of n points such that some r, but no r+1 of them, are collinear. A (n,r)-arc is called complete if it is not contain in a (n+1,r)-arc. A linear -code over a finite field is a k-dimensional subspace of with minimum hamming distance d and length n. A code with parameters with Griesmer bound , is called Griesmer code. The major aim of this research is to find large size for the complete (k,3)-arcs in the projective plane of order nineteen PG(2,19) using the method of secants distributions, and the disjoint union of arcs, as well as, adding and removing points to (from) particular conic respectively. Also, we find the Griesmer codes that correspond to each large complete (k,3)-arcs, k=29,30,31. We introduced 20 inequivalent (29,3)-arcs up to secant distribution, 10 of them are complete. Also, we introduced 8 inequivalent (30,3)-arcs up to secant distribution, 2 of them are complete. Moreover, we construct 3 inequivalent complete (31,3)-arcs up to secant distribution, and then find the corresponding linear codes to some of the (29,3)-arcs, (30,3)-arcs and (31,3)-arcs. In particular, we established 3 types of Griesmer codes, and we find the weight enumerator that correspond to each one of them.

La théorie du codage algébrique sur les corps et les anneaux finis a une grande importance dans la théorie de l'information en raison de leurs diverses applications dans les schémas de partage de secrets, les graphes fortement réguliers, les codes d'authentification et de communication. Cette thèse aborde plusieurs sujets de recherche selon les orientations dans ce contexte, dont les méthodes de construction sont au cœur de nos préoccupations. Plus précisément, nous nous intéressons aux constructions de codes optimaux (ou codes asymptotiquement optimaux), aux constructions de codes linéaires à "hull" unidimensionnelle, aux constructions de codes minimaux et aux constructions de codes linéaires projectifs. Les principales contributions sont résumé comme suit. Cette thèse fournie une description explicite des caractères additifs et multiplicatifs sur les anneaux finis (précisément S\mathbb{F}_q+u\mathbb{F}_q~(u^2= 0)S et _\mathbb{F} _q +u\mathbb{F}_q~(u^2=u)s), utilise des sommes Gaussiennes, hyper Eisenstein et Jacobi et fournit plusieurs classes de nouveaux codes optimaux (ou asymptotiquement optimaux) avec des paramètres flexibles, propose des codes linéaires (optimaux ou quasi-optimal) avec une "hull" unidimensionnelle sur des corps finis en utilisant des outils de la théorie de la somme Gaussienne. De plus, cette thèse explore plusieurs classes de codes linéaires binaires (optimaux pour la borne de Griesmer bien connue) sur des corps finis basés sur deux constructions génériques utilisant des fonctions. Aussi, elle détermine leurs paramètres et leurs distributions de poids et en déduit plusieurs familles infinies de codes linéaires minimaux. Enfin, elle étudie des constructions optimales de plusieurs classes de codes linéaires binaires projectifs avec peu de poids et leurs codes duaux correspondants
Algebraic coding theory over finite fields and rings has always been an important research topic in information theory thanks to their various applications in secret sharing schemes, strongly regular graphs, authentication and communication codes.This thesis addresses several research topics according to the orientations in this context, whose construction methods are at the heart of our concerns. Specifically, we are interested in the constructions of optimal codebooks (or asymptotically optimal codebooks), the constructions of linear codes with a one-dimensional hull, the constructions of minimal codes, and the constructions of projective linear codes. The main contributions are summarized as follows. This thesis gives an explicit description of additive and multiplicative characters on finite rings (precisely _\mathbb{F}_q+u\mathbb{F}_q~(u^2= 0)s and S\mathbb{F}_q+u\mathbb{F}_q~(u^2=u)S), employees Gaussian, hyper Eisenstein and Jacobi sums and proposes several classes of optimal (or asymptotically optimal) new codebooks with flexible parameters. Next, it proposes(optimal or nearly optimal) linear codes with a one-dimensional hull over finite fields by employing tools from the theory of Gaussian sums. It develops an original method to construct these codes. It presents sufficient conditions for one-dimensional hull codes and a lower bound on its minimum distance. Besides, this thesis explores several classes of (optimal for the well-known Griesmer bound) binary linear codes over finite fields based on two generic constructions using functions. It determines their parameters and weight distributions and derives several infinite families of minimal linear codes. Finally, it studies (optimal for the sphere packing bound) constructions of several classes of projective binary linear codes with a few weight and their corresponding duals codes

Cette thèse porte sur différentes problématiques liées à la détection, l'ajustement et l'identification de structures elliptiques en images. Nous plaçons la détection de primitives géométriques dans le cadre statistique des méthodes a contrario afin d'obtenir un détecteur de segments de droites et d'arcs circulaires/elliptiques sans paramètres et capable de contrôler le nombre de fausses détections. Pour améliorer la précision des primitives détectées, une technique analytique simple d'ajustement de coniques est proposée ; elle combine la distance algébrique et l'orientation du gradient. L'identification d'une configuration de cercles coplanaires en images par une signature discriminante demande normalement la rectification Euclidienne du plan contenant les cercles. Nous proposons une technique efficace de calcul de la signature qui s'affranchit de l'étape de rectification ; elle est fondée exclusivement sur des propriétés invariantes du plan projectif, devenant elle même projectivement invariante
This thesis deals with different aspects concerning the detection, fitting, and identification of elliptical features in digital images. We put the geometric feature detection in the a contrario statistical framework in order to obtain a combined parameter-free line segment, circular/elliptical arc detector, which controls the number of false detections. To improve the accuracy of the detected features, especially in cases of occluded circles/ellipses, a simple closed-form technique for conic fitting is introduced, which merges efficiently the algebraic distance with the gradient orientation. Identifying a configuration of coplanar circles in images through a discriminant signature usually requires the Euclidean reconstruction of the plane containing the circles. We propose an efficient signature computation method that bypasses the Euclidean reconstruction; it relies exclusively on invariant properties of the projective plane, being thus itself invariant under perspective

Les fonctions de F_q dans lui-même sont des objets étudiés dans de divers domaines tels que la cryptographie, la théorie des codes correcteurs d'erreurs, la géométrie finie ainsi que la géométrie algébrique. Il est bien connu que ces fonctions sont en correspondance exacte avec les polynômes en une variable à coefficients dans F_q. Nous étudierons trois classes de polynômes particulières: les polynômes Presque Parfaitement Non linéaires (Almost Perfect Nonlinear (APN)), les polynômes planaires ou parfaitement non linéaire (PN) et les o-polynômes.Les fonctions APN sont principalement étudiées pour leurs applications en cryptographie. En effet, ces fonctions sont celles qui offre la meilleure résistance contre la cryptanalyse différentielle.Les polynômes PN et les o-polynômes sont eux liés à des problèmes célèbres de géométrie finie. Les premiers décrivent des plans projectifs et les seconds sont en correspondance directe avec les ovales et hyperovales de P^2(F_q). Néanmoins, leurs champ d'application a été récemment étendu à la cryptographie symétrique et à la théorie des codes correcteurs d'erreurs.L'un des moyens utilisé pour compléter la classification est de considérer les polynômes présentant l'une des propriétés recherchées sur une infinité d'extension de F_q. Ces fonctions sont appelées fonction APN (respectivement PN ou o-polynômes) exceptionnelles.Nous étendrons la classification des polynômes APN et PN exceptionnels et nous donneront une description complète des o-polynômes exceptionnels. Les techniques employées sont basées principalement sur la borne de Lang-Weil et sur des méthodes élémentaires
Functions from F_q to itself are interesting objects arising in various domains such as cryptography, coding theory, finite geometry or algebraic geometry. It is well known that these functions admit a univariate polynomial representation. There exists many interesting classes of such polynomials with plenty of applications in pure or applied maths. We are interested in three of them: Almost Perfect Nonlinear (APN) polynomials, Planar (PN) polynomials and o-polynomials. APN polynomials are mostly used in cryptography to provide S-boxes with the best resistance to differential cryptanalysis and in coding theory to construct double error-correcting codes. PN polynomials and o-polynomials first appeared in finite geometry. They give rise respectively to projective planes and ovals in P^2(F_q). Also, their field of applications was recently extended to symmetric cryptography and error-correcting codes.A complete classification of APN, PN and o-polynomials is an interesting open problem that has been widely studied by many authors. A first approach toward the classification was to consider only power functions and the studies were recently extended to polynomial functions.One way to face the problem of the classification is to consider the polynomials that are APN, PN or o-polynomials over infinitely many extensions of F_q, namely, the exceptional APN, PN or o-polynomials.We improve the partial classification of exceptional APN and PN polynomials and give a full classification of exceptional o-polynomials. The proof technique is based on the Lang-Weil bound for the number of rational points in algebraic varieties together with elementary methods

The M33 projectile has been analyzed using the ANSYS CFX code that is based on the numerical solution of the full Navier-Stokes equations. Simulation data were obtained against various Mach numbers ranging from M= 0.5 to M2.6 at 0 and 2 angles of attack. Simulation data were also obtained against various angles of attack from 0 to 85 for M= 0.5. For Mach numbers between M= 0.5 to 2.6, the results obtained using the combined k-epsilon and Shear Stress Transport model show good agreement with the experimental range data for the normal force and pitching moment coefficient. The drag coefficient at zero angle of attack tended to be over predicted by an average error of 11.6% with the highest error occurring at M= 1.5. For varying angle of attack up to 85 at M= 0.5, the results obtained from CFX code were compared with simulation results obtained from AP09. The data showed good agreement only up to 20 angles of attack.

We will discuss three ways to bound the chromatic number on a Cayley graph. 1. If the connection set contains information about a smaller graph, then these two graphs are related. Using this information, we will show that Cayley graphs cannot have chromatic number three. 2. We will prove a general statement that all vertex-transitive maximal triangle-free graphs on n vertices with valency greater than n/3 are 3-colourable. Since Cayley graphs are vertex-transitive, the bound of general graphs also applies to Cayley graphs. 3. Since Cayley graphs for abelian groups arise from vector spaces, we can view the connection set as a set of points in a projective geometry. We will give a characterization of all large complete caps, from which we derive that all maximal triangle-free cubelike graphs on 2ⁿ vertices and valency greater than 2ⁿ/4 are either bipartite or 4-colourable.

We apply the semidefinite programming method to obtain a new upper bound on the cardinality of codes made of subspaces of a linear vector space over a finite field. Such codes are of interest in network coding.Next, with the same method, we prove an upper bound on the cardinality of sets avoiding one distance in the Johnson space, which is essentially Schrijver semidefinite program. This bound is used to improve existing results on the measurable chromatic number of the Euclidean space.We build a new hierarchy of semidefinite programs whose optimal values give upper bounds on the independence number of a graph. This hierarchy is based on matrices arising from simplicial complexes. We show some properties that our hierarchy shares with other classical ones. As an example, we show its application to the problem of determining the independence number of Paley graphs.

This volume makes an intervention in the fields of film studies and visual culture by examining projection as a pivotal element in the continuing technological becoming of media systems. The chapters come together to paint a picture of projection that incorporates a range of practices across time and space. From studies of travelling projectionists in early twentieth-century Scotland and modern-day Uruguay to considerations of the (almost) lost mediums of the slide-tape and the magic lantern, the authors invite us to consider the varied nature of the technologies, apparatuses, practices, and histories of projection in a holistic manner. In doing so, the volume departs from the psychological metaphors of projection often employed by apparatus theory, instead emphasizing the performative character of the moving image and the labour of the various actors involved in the utterance of such texts.

Morality from an evolutionary perspective is a code of conduct that regulates behavior within a group in order to promote social cohesion and stability. Both religion and secularism are grounded in the same moral psychology. How should the distinction between secular and religious ethics be assessed? Religious morality is a late-comer to the natural history of morality, reinforcing much of morality with a worldview about unnatural powers that humans’ brains are prone to projecting onto reality. However, the natural history of morality reveals that religious moral traditions do not originate moral rules but instead reinforce ancient moral intuitions. Secularism as a worldview works within an immanent frame, compared to the transcendent frame of religious worldviews. This distinction is helpful in understanding the relationship between religious violence and secular-ideological driven violence.

This chapter maps the territory of the contemporary audiovisual cinematic avant-garde, which arose at the very moment of celluloid’s passage from mass use to obsolescence. It presents films that bear witness to the avant-garde’s ongoing interest in the formal organization of sound/image relationships. If one of the main concerns of sound in conventional film is to “naturalize” the image, experimental film is interested instead in ananti-naturalistic use of sound. Films without sound or even without images (which still can be called “films”), the use of audiovisual polysemy, asynchronous, or even synchronous sound, as well as the visualization of code-based music, are all means of revealing the constructed nature of the cinesonic event. The chapter examines the realm of the sound of technology itself, pointing out the creative potential ofoptically synthesized soundsas well aslive generated sounds and images, which attest to the agility of current projection performances.

The father-son relationship recurs as the central theme of Chapter 6, in which Etna powerfully symbolizes the generational tensions—Bernardo Bembo committed to traditional Venetian patrician civic duty, Pietro far more ambivalent about that calling—that underlie (and gently qualify) their congenial exchanges in De Aetna. Bernardo views Etna with studied detachment, resisting its wonder by systematically explaining its workings in terms of volcanic typology; Pietro’s Etna is as much a mountain of the mind as it is a formidable physical challenge. Bernardo objectifies nature; Pietro views Etna with a far more subjective eye for fabulist projection on to its slopes, for engaging with its air of mystery and enchantment, and above all for making the mountain his own as a figurative locus of self-expression. If Bernardo expounds de Aetna, Pietro exults de sua Aetna; whereas Bernardo deciphers the mountain, Pietro encrypts it in his own code of fantasy.

Laws and the use of induction to establish laws don’t require objects. The reasons for thinking this are analyzed and refuted. Next, the role of the principle of indiscernibles and Leibniz’s law in our projection of objects onto the world are given. This role is due to the fact that we characterize objects in functional ways, in terms of relations and properties we single out. Puzzles about the apparent modal properties of distinct objects that are otherwise categorically the same (statues and the clay they’re made of that come to be and are destroyed at the same time) arise because of these practices. These are explained and dissolved. The apparent role of objects in explanations is described; it’s shown that inferences to worldly objects don’t provide genuine explanations.

This book pays tribute to the unrecognized warriors and unsung heroes of human warfare: millions of animals from a surprising variety of species, ranging from rodents to dolphins to llamas. When one thinks of war, armies of soldiers and assaults with bullets and bombs delivered by deadly machinery typically come to mind. Throughout human history, however, animals have also played significant roles in our armed conflicts. In Animals in the Military: From Hannibal's Elephants to the Dolphins of the U.S. Navy, author John M. Kistler examines these contributions, describing the work of animals in human warfare throughout time, from lowly insects to birds to elephants. Drawing on both ancient and modern sources, the book reveals the full scope of heroics and horror committed by—and against—animal warriors in three unique areas: animals in combat, animals in support, and animals in incidental and experimental roles. Each chapter describes a single species, chronologically recounting its fascinating place in human warfare over time, from insects used as stinging projectiles to message-delivering pigeons.

The main aim of this paper is to introduce the relationship between the topic of coding theory and the projective space in field three and test the code. The maximum value of size of code over finite field of order three and an incidence matrix with the parameters, n (length of code), d (minimum distance of code) and e (error-correcting of code) have been constructed. With a theorem and a result that test the code if it is perfect or not.

Less-penetrating projectile has the capability of less penetration and high execution, it attracts international scientific interests for suitability for antiterrorism and anti-hijack. a new projectile which has the structure of pole mushroom shaped cap—premade separable half ring core—indenting jacket were designed for treatment and improving the capability of less penetration and high execution. Both testing and calculation data of 92A pistol projectile and 9mm pistol projectile proved the feasibility of new projectiles design. The result indicates that energy release of “jacket peeled—cap perturbed—core separated” is more effective than that of traditional projectile. The less penetration, high execution effect and degree of treatment difficulty of premade separable less-penetrating projectile is better than 92A pistol projectile and domestic 9mm low penetration pistol projectile.

To study the law of penetration action of small high-speed projectiles into the wall, three kinds of large caliber rifle projectiles were used to conduct armor penetration tests on the masonry walls, in which a mortar layer was applied inside and outside of the masonry wall, and the masonry was clay bricks and autoclaved aerated concrete blocks, respectively. High-speed photography of the impact velocity, residual velocity and motion attitude of the projectile, damage pattern, size and penetration process of the target body were obtained. Through the analysis of the kinetic energy loss ratio of the projectile and the wall penetration, it was revealed that the penetration effect of the projectile is mainly determined by the core structure (the single mass projectile is considered as the full core structure), the anti-penetration effect of the masonry wall mainly depends on the strength of the block itself, the anti-penetration effect of the lightweight masonry wall is weak, and the projectile penetrates more easily, the anti-penetration effect of the clay brick wall is the strongest, and also discovered the penetration depends on the thickness of the wall and the location of the projectile impact point. The results of the test and analysis can provide a basis for how to improve the lethality of light weapons against human targets behind the protection of brick walls.

In the December 2022 Summary of Economic Projections (SEP), the median projection for four-quarter core PCE inflation in the fourth quarter of 2025 is 2.1 percent. This same SEP has unemployment rising by nine-tenths, to 4.6 percent, by the end of 2023. We assess the plausibility of this projection using a specific nonlinear model that embeds an empirically successful nonlinear Phillips curve specification into a structural model, identifying it via an underutilized data-dependent method. We model core PCE inflation using three components that align with those noted by Chair Powell in his December 14, 2022, press conference: housing, core goods, and core-services-less-housing. Our model projects that conditional on the SEP unemployment rate path and a rapid deceleration of core goods prices, core PCE inflation moderates to only 2.75 percent by the end of 2025: inflation will be higher for longer. A deep recession would be necessary to achieve the SEP’s projected inflation path. A simple reduced-form welfare analysis, which abstracts from any danger of inflation expectations becoming unanchored, suggests that such a recession would not be optimal.

This paper examines the forecasting efficacy and implications of the recently popular breakdown of core inflation into three components: goods excluding food and energy, services excluding energy and housing, and housing. A comprehensive historical evaluation of the accuracy of point and density forecasts from a range of models and approaches shows that a BVAR with stochastic volatility in aggregate core inflation, its three components, and wage growth is an effective tool for forecasting inflation's components as well as aggregate core inflation. Looking ahead, the model's baseline projection puts core inflation at 2.6 percent in 2026, well below its 2023 level but still elevated relative to the Federal Reserve's 2 percent objective. The probability that core inflation will return to 2 percent or less is much higher when conditioning on goods or non-housing services inflation slowing to pre-pandemic levels than when conditioning on these components remaining above the same thresholds. Scenario analysis indicates that slower wage growth will likely be associated with reduced inflation in all three components, especially goods and non-housing services, helping to return core inflation to near the 2 percent target by 2026.

Terminal ballistics of concrete is of extreme importance to the military and civil communities. Over the past few decades, ultra‐high performance concrete (UHPC) has been developed for various applications in the design of protective structures because UHPC has an enhanced ballistic resistance over conventional strength concrete. Developing predictive numerical models of UHPC subjected to penetration is critical in understanding the material's enhanced performance. This study employs the advanced fundamental concrete (AFC) model, and it runs inside the reproducing kernel particle method (RKPM)‐based code known as the nonlinear meshfree analysis program (NMAP). NMAP is advantageous for modeling impact and penetration problems that exhibit extreme deformation and material fragmentation. A comprehensive experimental study was conducted to characterize the UHPC. The investigation consisted of fracture toughness testing, the utilization of nondestructive microcomputed tomography analysis, and projectile penetration shots on the UHPC targets. To improve the accuracy of the model, a new scaled damage evolution law (SDEL) is employed within the microcrack informed damage model. During the homogenized macroscopic calculation, the corresponding microscopic cell needs to be dimensionally equivalent to the mesh dimension when the partial differential equation becomes ill posed and strain softening ensues. Results of numerical investigations will be compared with results of penetration experiments.

This report documents the acquisition of source data, and calculation of land cover summary statistics datasets for ten National Park Service National Capital Region park units and three custom areas of analysis: Catoctin Mountain Park, Chesapeake & Ohio Canal National Historical Park, George Washington Memorial Parkway, Harpers Ferry National Historical Park, Manassas National Battlefield Park, Monocacy National Battlefield, National Capital Parks - East, Prince William Forest Park, Rock Creek Park, Wolf Trap National Park for the Performing Arts, and the three custom areas of analysis - National Capital Parks - East: Oxon Cove Park, Oxon Hill Farm, Piscataway Park, National Capital Parks - East: Greenbelt Park and Baltimore-Washington Parkway, and National Capital Parks - East: DC and Suitland Parkway. The source data and land cover calculations are available for use within the National Park Service (NPS) Inventory and Monitoring Program. Land cover summary statistics datasets can be calculated for all geographic regions within the extent of the NPS; this report includes statistics calculated for the conterminous United States. The land cover summary statistics datasets are calculated from multiple sources, including Multi-Resolution Land Characteristics Consortium products in the National Land Cover Database (NLCD) and United States Geological Survey?s (USGS) Earth Resources Observation and Science (EROS) Center products in the Land Change Monitoring, Assessment, and Projection (LCMAP) raster dataset. These summary statistics calculate land cover at up to three classification scales: Level 1, modified Anderson Level 2, and Natural versus Converted land cover. The output land cover summary statistics datasets produced here for the ten National Capital Region park units and three custom areas of analysis utilize the most recent versions of the source datasets (NLCD and LCMAP). These land cover summary statistics datasets are used in the NPS Inventory and Monitoring Program, including the NPS Environmental Settings Monitoring Protocol and may be used by networks and parks for additional efforts.

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%.

On the occasion of the thirtheenth bak'tun in the Maya calendar, the IDB Cultural Center and Country Department for Belize, Central America, México, Panama, and the Dominican Republic have come together to present this exhibition, which displays a rigorous selection of millennial pieces, allowing a glimpse into the artistic richness of a culture with stunning temples and cities, fascinating sculptures, advances organizational structure and the capacity to interpret its own historic projection. The exhibition was held at the Inter-American Development Bank headquarters in Washington, D.C., from December 2012 to February 2013.