On the representation theory of Galois and Atomic Topoi

We elaborate on the representation theorems of topoi as topoi of discrete actions of various kinds of localic groups and groupoids. We introduce the concept of "proessential point" and use it to give a new characterization of pointed Galois topoi. We establish a hierarchy of connected topoi: [1. essentially pointed Atomic = locally simply connected], [2. proessentially pointed Atomic = pointed Galois], [3. pointed Atomic]. These topoi are the classifying topos of, respectively: 1. discrete groups, 2. prodiscrete localic groups, and 3. general localic groups. We analyze also the unpoited version, and show that for a Galois topos, may be pointless, the corresponding groupoid can also be considered, in a sense, the groupoid of "points". In the unpointed theories, these topoi classify, respectively: 1. connected discrete groupoids, 2. connected (may be pointless) prodiscrete localic groupoids, and 3. connected groupoids with discrete space of objects and general localic spaces of hom-sets, when the topos has points (we do not know the class of localic groupoids that correspond to pointless connected atomic topoi). We comment and develop on Grothendieck's galois theory and its generalization by Joyal-Tierney, and work by other authors on these theories.Comment: This is a revised version of arXiv.org/math.CT/02008222 to appear in JPA

The fundamental progroupoid of a general topos

It is well known that the category of covering projections (that is, locally constant objects) of a locally connected topos is equivalent to the classifying topos of a strict progroupoid (or, equivalently, a localic prodiscrete groupoid), the \emph{fundamental progroupoid}, and that this progroupoid represents first degree cohomology. In this paper we generalize these results to an arbitrary topos. The fundamental progroupoid is now a localic progroupoid, and can not be replaced by a localic groupoid. The classifying topos in not any more a Galois topos. Not all locally constant objects can be considered as covering projections. The key contribution of this paper is a novel definition of covering projection for a general topos, which coincides with the usual definition when the topos is locally connected. The results in this paper were presented in a talk at the Category Theory Conference, Vancouver July 2004.Comment: 19 page

Muxama and other traditional food products obtained from tuna in south Portugal and Spain: review and future perspectives

There is evidence that consumers perceive fish as healthy (Carlucci D et.al, Appetite 84:212–27,2015; Vanhonacker F et.al, Br Food J 115:508–25,2013; Verbeke W et.al, Public Health Nutr 8:422–9,2005.). Historically, the development of (traditional) processing techniques allowed for the preservation of excess quantities of fresh fish for storage or transport. Those technologies are not well documented and are being lost with the trend to urbanization and consumption of convenience, ready-to-eat food. In the so-called developed world, there is still a considerable demand for traditionally processed (sea)food products, wherein the raw material and the final product are of high value. Muxama or mojama is a traditional, highly valued food product prepared from dry-cured tuna loins that is a delicatessen in the southern Iberian Peninsula: Algarve (Portugal) and Andalucía, Murcia, Alicante, and Valencia (Spain). The tuna (mostly Thunnus obesus and T. albacares) loins are salted and dried following a typically artisanal process that incorporates empirical knowledge passed down numerous generations since at least the tenth century Common Era (Aníbal J and Esteves E, Muxama and estupeta: traditional food products obtained from tuna loins in South Portugal and Spain, Traditional food products 2016, Lindkvist KB et.al, Can Geogr-Géogr Can 52:105–20,2008, Gallart-Jornet L et.al, La salazón de pescado, una tradición en la dieta mediterránea [The salting of fish, a tradition in the Mediterranean diet] 2005.). The production process changed little over the years but is different among locations, even supporting distinct certifications. The stability of muxama derives from the reduced water activity. Furthermore, the drying method has secondary effects on flavor, color, and nutritional value of the product. In southern Portugal and Spain, muxama is the prime food product obtained from tuna at the end of the traditional quartering of tunas, named ronqueamento in Portugal or ronqueo in Spain. Other food products obtained from tuna include Estupeta, Mormos, Rabinhos, Faceiras and Orelhas, Ventresca, Tarantela and Sangacho, Espinheta, Tripa, Bucho, and Ovas. These products result from employing different manufacturing procedures and processes. In this paper, we tentatively describe the main features of the processing stages and traditional food products obtained from tuna produced in the southern Iberian Peninsula (Portugal and Spain) and discuss the interactions of knowledge systems and transmission of traditional knowledge regarding its production.This study received national funds from FCT-Foundation for Science and Technology (Portugal) [UID/Multi/04326/2019] (EE) and [UID/MAR/00350/ 2019 CIMA] (JA).info:eu-repo/semantics/publishedVersio

Nonfractional Memory: Filtering, Antipersistence, and Forecasting

The fractional difference operator remains to be the most popular mechanism to generate long memory due to the existence of efficient algorithms for their simulation and forecasting. Nonetheless, there is no theoretical argument linking the fractional difference operator with the presence of long memory in real data. In this regard, one of the most predominant theoretical explanations for the presence of long memory is cross-sectional aggregation of persistent micro units. Yet, the type of processes obtained by cross-sectional aggregation differs from the one due to fractional differencing. Thus, this paper develops fast algorithms to generate and forecast long memory by cross-sectional aggregation. Moreover, it is shown that the antipersistent phenomenon that arises for negative degrees of memory in the fractional difference literature is not present for cross-sectionally aggregated processes. Pointedly, while the autocorrelations for the fractional difference operator are negative for negative degrees of memory by construction, this restriction does not apply to the cross-sectional aggregated scheme. We show that this has implications for long memory tests in the frequency domain, which will be misspecified for cross-sectionally aggregated processes with negative degrees of memory. Finally, we assess the forecast performance of high-order $AR$ and $ARFIMA$ models when the long memory series are generated by cross-sectional aggregation. Our results are of interest to practitioners developing forecasts of long memory variables like inflation, volatility, and climate data, where aggregation may be the source of long memory

Optimal Fear of Floating: The Role of Currency Mismatches and Fiscal Constraints

Evidence suggests that developing countries are more concerned with stabilizing the nominal exchange rate than developed countries. Some papers show not only that nominal exchange rates are less volatile, but also that international reserves and domestic interest rates are significantly more volatile. This paper presents a model with flexible prices that introduces a new channel through which the fear of floating is generated. It departs from the previous research in an important dimension; fears will come from nominal, as supposed to real, exchange rate volatility. Also, the model is able to explain the whole range of observed policies. The trade-off proposed in the paper is driven by two facts that proved to be crucial in recent financial crises: emerging market countries face fiscal restrictions during turbulent times, and they tend to have a mismatch in the currency denomination of their assets and their liabilities. These features make both interventions and depreciations costly. Thus, faced with these costs policymakers have to choose the optimal policy mix, such that the costs are minimized. Based on these intervention and depreciation costs, the model is able to rationalize as the outcome of an optimal policy decision, the observation that emerging markets end up with higher inflation rates and lower fluctuations in the nominal exchange rate. The results suggest that the amount of intervention depends on the degree of currency mismatch, the degree of flexibility on the fiscal side, the elasticity of money demand, and the relative size of the financial system. Estimations of a stylized econometric model support the effect of these variables on the variability of the exchange rate. Variability is negative correlated with the mismatch, the fiscal and the size variables; and positive correlated with elasticity, being in all these cases highly significant across most specifications.exchange rates, floating, currency mismatch, optimal policy

The effect of convolving families of L-functions on the underlying group symmetries

L-functions for GL_n(A_Q) and GL_m(A_Q), respectively, such that, as N,M --> oo, the statistical behavior (1-level density) of the low-lying zeros of L-functions in F_N (resp., G_M) agrees with that of the eigenvalues near 1 of matrices in G_1 (resp., G_2) as the size of the matrices tend to infinity, where each G_i is one of the classical compact groups (unitary, symplectic or orthogonal). Assuming that the convolved families of L-functions F_N x G_M are automorphic, we study their 1-level density. (We also study convolved families of the form f x G_M for a fixed f.) Under natural assumptions on the families (which hold in many cases) we can associate to each family L of L-functions a symmetry constant c_L equal to 0 (resp., 1 or -1) if the corresponding low-lying zero statistics agree with those of the unitary (resp., symplectic or orthogonal) group. Our main result is that c_{F x G} = c_G * c_G: the symmetry type of the convolved family is the product of the symmetry types of the two families. A similar statement holds for the convolved families f x G_M. We provide examples built from Dirichlet L-functions and holomorphic modular forms and their symmetric powers. An interesting special case is to convolve two families of elliptic curves with rank. In this case the symmetry group of the convolution is independent of the ranks, in accordance with the general principle of multiplicativity of the symmetry constants (but the ranks persist, before taking the limit N,M --> oo, as lower-order terms).Comment: 41 pages, version 2.1, cleaned up some of the text and weakened slightly some of the conditions in the main theorem, fixed a typ