Bosonic effective action for interacting fermions

We compare different versions of a bosonic description for systems of interacting fermions, with particular emphasis on the free energy functional. The bosonic effective action makes the issue of symmetries particularly transparent and we present for the Hubbard model an exact mapping between repulsive and attractive interactions. A systematic expansion for the bosonic effective action starts with a solution to the lowest order Schwinger-Dyson or gap equation. We propose a two particle irreducible formulation of an exact functional renormalization group equation for computations beyond leading order. On this basis we suggest a renormalized gap equation. This approach is compared with functional renormalization in a partially bosonized setting.Comment: new sections on exact mapping between attractive and repulsive Hubbard model and relation between two-particle-irreducible formalism, 32 pages,1 figure,LaTe

Country Diversification, Product Ubiquity, and Economic Divergence

Countries differ markedly in the diversification of their exports. Products differ in the number of countries that export them, which we define as their ubiquity. We document a new stylized fact in the global pattern of exports: there is a systematic relationship between the diversification of a country’s exports and the ubiquity of its products. We argue that this fact is not implied by current theories of international trade and show that it is not a trivial consequence of the heterogeneity in the level of diversification of countries or of the heterogeneity in the ubiquity of products. We account for this stylized fact by constructing a simple model that assumes that each product requires a potentially large number of non-tradable inputs, which we call capabilities, and that a country can only make the products for which it has all the requisite capabilities. Products differ in the number and specific nature of the capabilities they require, as countries differ in the number/nature of capabilities they have. Products that require more capabilities will be accessible to fewer countries (i.e., will be less ubiquitous), while countries that have more capabilities will have what is required to make more products (i.e., will be more diversified). Our model implies that the return to the accumulation of new capabilities increases exponentially with the number of capabilities already available in a country. Moreover, we find that the convexity of the increase in diversification associated with the accumulation of a new capability increases when either the total number of capabilities that exist in the world increases or the average complexity of products, defined as the number of capabilities products require, increases. This convexity defines what we term as a quiescence trap, or a trap of economic stasis: countries with few capabilities will have negligible or no return to the accumulation of more capabilities, while at the same time countries with many capabilities will experience large returns - in terms of increased diversification - to the accumulation of additional capabilities. We calibrate the model to three different sets of empirical data and show that the derived functional forms reproduce the empirically observed distributions of product ubiquity, the relationship between the diversification of countries and the average ubiquity of the products they export, and the distribution of the probability that two products are co-exported. This calibration suggests that the global economy is composed of a relatively large number of capabilities – between 23 and 80, depending on the level of disaggregation of the data – and that products require on average a relatively large fraction of these capabilities in order to be produced. The conclusion of this calibration is that the world exists in a regime where the quiescence trap is strong

The Network Structure of Economic Output

Much of the analysis of economic growth has focused on the study of aggregate output. Here, we deviate from this tradition and look instead at the structure of output embodied in the network connecting countries to the products that they export. We characterize this network using four structural features: the negative relationship between the diversification of a country and the average ubiquity of its exports, and the non-normal distributions for product ubiquity, country diversification and product co-export. We model the structure of the network by assuming that products require a large number of non-tradable inputs, or capabilities, and that countries differ in the completeness of the set of capabilities they have. We solve the model assuming that the probability that a country has a capability and that a product requires a capability are constant and calibrate it to the data to find that it accounts well for all of the network features except for the heterogeneity in the distribution of country diversification. In the light of the model, this is evidence of a large heterogeneity in the distribution of capabilities across countries. Finally, we show that the model implies that the increase in diversification that is expected from the accumulation of a small number of capabilities is small for countries that have a few of them and large for those with many. This implies that the forces that help drive divergence in product diversity increase with the complexity of the global economy when capabilities travel poorly

Estimates of air–sea feedbacks on sea surface temperature anomalies in the southern ocean

Sea surface temperature (SST) air–sea feedback strengths and associated decay time scales in the Southern Ocean (SO) are estimated from observations and reanalysis datasets of SST, air–sea heat fluxes, and ocean mixed layer depths. The spatial, seasonal, and scale dependence of the air–sea heat flux feedbacks is mapped in circumpolar bands and implications for SST persistence times are explored. It is found that the damping effect of turbulent heat fluxes dominates over that due to radiative heat fluxes. The turbulent heat flux feedback acts to damp SSTs in all bands and spatial scales and in all seasons, at rates varying between 5 and 25 W m⁻² K⁻¹, while the radiative heat flux feedback has a more uniform spatial distribution with a magnitude rarely exceeding 5 W m⁻² K⁻¹. In particular, the implied net air–sea feedback (turbulent + radiative) on SST south of the polar front, and in the region of seasonal sea ice, is as weak as 5–10 W m⁻² K⁻¹ in the summertime on large spatial scales. Air–sea interaction alone thus allows SST signals induced around Antarctica in the summertime to persist for several seasons. The damping effect of mixed layer entrainment on SST anomalies averages to approximately 20 W m⁻² K⁻¹ across the ACC bands in the summer-to-winter entraining season and thereby reduces summertime SST persistence to less than half of that predicted by air–sea interaction alone (i.e., 3–6 months).National Science Foundation (U.S.). Frontiers in Earth System Dynamic

Sex hormones modulate neurophysiological correlates of visual temporal attention

The functional cerebral asymmetry (FCA) in processing targets within rapid serial visual presentation (RSVP) streams has been reported to fluctuate across the menstrual cycle, with identification of the second of two closely spaced targets being impaired when both targets occur in the left or the right hemifield stream during the luteal phase, while during the menstrual phase identification of the second target is only impaired for target pairs presented in the right hemifield stream. This fluctuation has been proposed to result from variations in estradiol levels. The current study used EEG to investigated whether the cycle-related fluctuation in RSVP target identification FCA relates to changes in early, stimulus-driven, bottom-up or in later, top down-driven aspects of FCA. While the former would be expected to become evident in the early visual evoked potentials (VEPs) P1 or N1, the latter would be evident in later event-related potentials (ERPs) such as N2pc or P3. Women performed a dual-stream RSVP task once during the menstrual phase and once during the follicular phase. Estradiol levels were determined from saliva samples. In contrast to previous findings, FCA in RSVP target identification was not affected by cycle phase. However, the impairment in second-target identification when targets where closely spaced was generally smaller during the menstrual phase than during the follicular phase. This effect was matched by shorter peak latencies of P1 VEPs for the menstrual phase, and by a reduction in the latency of the second-target P3 ERP for closely spaced relative to widely spaced target pairs, again for the menstrual phase. Results suggest that in a dual-stream RSVP setup, target identification, early stage stimulus processing, and target consolidation are affected by cycle phase, but that the asymmetry of these effects does not differ between menstrual and follicular phase. The observed cycle-related modulations in neurophysiology and behavior could relate to the effects of estradiol on the locus ceruleus norepinephrine (LC-NE) system, which is known to play a major role in arousal, attention and stress response

Pointing errors in solar absorption spectrometry - correction scheme and its validation

A method for quantification of sun-pointing inaccuracies in solar absorption spectrometry is presented along with a correction scheme for the resulting errors in trace gas vertical column or profile retrievals. A posteriori correction of pointing errors requires knowledge of both coordinates of the mispointing vector on the solar disk. In principle, quantitative information on the mispointing can be retrieved from Doppler shifts of solar lines derived from measured spectra. However, this yields only one component of the mispointing vector, namely the one which is perpendicular to the solar rotation axis. Missing information on the second vector component has hindered a posteriori correction of mispointing errors so far. Our idea to overcome this problem is to obtain estimates of both coordinates of the mispointing by combining subsequent measurements with differing orientations of the solar rotation axis relative to the zenith direction. An implementation of this original concept is demonstrated using measurements from the solar absorption Fourier transform infrared (FTIR) spectrometer at the Zugspitze (47.42° N, 10.98° E, 2964 m a.s.l.). Soundings in the September 2012 to September 2014 time interval were impacted by mispointing problems due to a non-optimum solar tracking optics configuration. They show a mean mispointing in zenith direction of -0.063°. This causes biases in vertical soundings of trace gases, e.g. -2.82 ppb in monthly means of dry-air column-averaged mole fractions of methane (XCH4). Measurements made with the more stable pre-September 2012 and post-September 2014 optics configurations show considerably smaller mispointing effects. Applying the mispointing correction, the April 2006-March 2014 XCH4 trend determined from Zugspitze measurements is reduced from 6.45 [5.84, 7.04] to 6.07 [5.55, 6.59] ppb yr-1. The correction thereby restores consistency with results from the nearby Garmisch FTIR site (47.48° N, 11.06° E, 743 m a.s.l.). The mispointing correction is applicable to solar absorption measurements in the mid infrared and near infrared. It will be of particular benefit for refining existing records of high-accuracy-and-precision greenhouse gas soundings for the purpose of improved trend analysis or source-sink inversions

The Structure and Dynamics of International Development Assistance

We study the structure of international aid coordination by creating and analyzing a tripartite network of donor organizations, recipient countries and development issues using web-based information. We develop a measure of coordination and find that it is moderate, achieving about 60% of its theoretical maximum. Many countries are strongly connected to organizations that are related to the issues that are salient there. Nevertheless, we identify many countries that are poorly served, issues that are inadequately attended to, and organizations that focus on the wrong combination of places and issues. Our approach may be used to improve decentralized coordination