Simple Irreducible Subgroups of Exceptional Algebraic Groups

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible subgroups of exceptional algebraic groups $G$ which are connected, closed and simple of rank at least $2$. Consequences are given concerning the representations of such subgroups on various $G$-modules: for example, with one exception, the conjugacy classes of irreducible simple connected subgroups of rank at least $2$ are determined by their composition factors on the adjoint module for $G$.Comment: 46 pages; version to appear in J. Al

Irreducible A_1 Subgroups of Exceptional Algebraic Groups

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible $A_1$ subgroups of exceptional algebraic groups $G$. Consequences are given concerning the representations of such subgroups on various $G$-modules: for example, the conjugacy classes of irreducible $A_1$ subgroups are determined by their composition factors on the adjoint module of $G$.Comment: 51 pages; published in J. Al

ConSole: using modularity of contact maps to locate solenoid domains in protein structures.

BackgroundPeriodic proteins, characterized by the presence of multiple repeats of short motifs, form an interesting and seldom-studied group. Due to often extreme divergence in sequence, detection and analysis of such motifs is performed more reliably on the structural level. Yet, few algorithms have been developed for the detection and analysis of structures of periodic proteins.ResultsConSole recognizes modularity in protein contact maps, allowing for precise identification of repeats in solenoid protein structures, an important subgroup of periodic proteins. Tests on benchmarks show that ConSole has higher recognition accuracy as compared to Raphael, the only other publicly available solenoid structure detection tool. As a next step of ConSole analysis, we show how detection of solenoid repeats in structures can be used to improve sequence recognition of these motifs and to detect subtle irregularities of repeat lengths in three solenoid protein families.ConclusionsThe ConSole algorithm provides a fast and accurate tool to recognize solenoid protein structures as a whole and to identify individual solenoid repeat units from a structure. ConSole is available as a web-based, interactive server and is available for download at http://console.sanfordburnham.org

On Mubayi's Conjecture and conditionally intersecting sets

Mubayi's Conjecture states that if $\mathcal{F}$ is a family of $k$-sized subsets of $[n] = \{1,\ldots,n\}$ which, for $k \geq d \geq 2$, satisfies $A_1 \cap\cdots\cap A_d \neq \emptyset$ whenever $|A_1 \cup\cdots\cup A_d| \leq 2k$ for all distinct sets $A_1,\ldots,A_d \in\mathcal{F}$, then $|\mathcal{F}|\leq \binom{n-1}{k-1}$, with equality occurring only if $\mathcal{F}$ is the family of all $k$-sized subsets containing some fixed element. This paper proves that Mubayi's Conjecture is true for all families that are invariant with respect to shifting; indeed, these families satisfy a stronger version of Mubayi's Conjecture. Relevant to the conjecture, we prove a fundamental bijective duality between $(i,j)$-unstable families and $(j,i)$-unstable families. Generalising previous intersecting conditions, we introduce the $(d,s,t)$-conditionally intersecting condition for families of sets and prove general results thereon. We conjecture on the size and extremal structures of families $\mathcal{F}\in\binom{[n]}{k}$ that are $(d,2k)$-conditionally intersecting but which are not intersecting, and prove results related to this conjecture. We prove fundamental theorems on two $(d,s)$-conditionally intersecting families that generalise previous intersecting families, and we pose an extension of a previous conjecture by Frankl and F\"uredi on $(3,2k-1)$-conditionally intersecting families. Finally, we generalise a classical result by Erd\H{o}s, Ko and Rado by proving tight upper bounds on the size of $(2,s)$-conditionally intersecting families $\mathcal{F}\subseteq 2^{[n]}$ and by characterising the families that attain these bounds. We extend this theorem for certain parametres as well as for sufficiently large families with respect to $(2,s)$-conditionally intersecting families $\mathcal{F}\subseteq 2^{[n]}$ whose members have at most a fixed number $u$ members

Capital Importers Pay More for their Imports

We examine the effects that a country’s net capital flows have on the (border) prices that a country pays for its imports of goods. Using data from 2000 to 2009 for 11 euro area countries we utilize a pricing-to-market specification to study exporters’ pricing behavior to the rest of the countries in the sample, at the industry level, for 900 goods disseminated at the 4- digit Standard International Trade Classification (SITC- revision 3) level. This allows us to construct a panel dataset which contains observations across exporters, importers, industries and time, ending up with a total of 594,327 observations. We find a strong influence of the importing country’s net capital inflows on the border prices of its imports of goods. This result is robust across different specifications of the underlying model, as well to different sample dis-aggregations across types of capital flows, product categories, and exporters.capital flows, import prices, pricing to market, globalization, euro area

Turkish Delight for Some, Cold Turkey for Others?: The Effects of the EU-Turkey Customs Union

Following Turkey’s application for EU membership in 1987, a Customs Union (CU) between Turkey and the EU, mainly covering trade in manufacturing goods and processed agricultural products, came into effect in 1995. In addition to a large agricultural sector, Turkey also specializes in the production and exportation of relatively low-price, low-quality varieties of manufactured products. We use a theoretical framework in order to demonstrate that these features of the Turkish economy imply asymmetric changes in the trade volumes of the incumbent countries of the EU as a result of the EU-Turkey CU. By examining disaggregated trade data we find that the technologically sophisticated EU countries (e.g., mainly the Northern European countries) are also least similar to Turkey in terms of their export structure, whereas the degree of export similarity between the less technologically sophisticated EU members and Turkey is high. Our econometric results indicate that, in contrast to the “Northern” group’s exports to other EU15 countries (which have remained intact), the Southern countries’s exports to the other EU15 countries have declined as a result of the EU-Turkey CU. Moreover, the extra penetration of the Turkish market by EU countries has not been more favourable to the Southern group. These findings also imply that technologically sophisticated countries may see no significant further benefits from Turkey’s full accession to the EU (whereas the migration and political influence related costs for these countries may be large).European Union, Turkey, customs union, exports, gravity, differentiated products

Complete Reducibility in Good Characteristic

Let $G$ be a simple algebraic group of exceptional type, over an algebraically closed field of characteristic $p \ge 0$. A closed subgroup $H$ of $G$ is called $G$-completely reducible ($G$-cr) if whenever $H$ is contained in a parabolic subgroup $P$ of $G$, it is contained in a Levi subgroup of $P$. In this paper we determine the $G$-conjugacy classes of non-$G$-cr simple connected subgroups of $G$ when $p$ is good for $G$. For each such subgroup $X$, we determine the action of $X$ on the adjoint module $L(G)$ and the connected centraliser of $X$ in $G$. As a consequence we classify all non-$G$-cr connected reductive subgroups of $G$, and determine their connected centralisers. We also classify the subgroups of $G$ which are maximal among connected reductive subgroups, but not maximal among all connected subgroups.Comment: 66 pages. To appear in Trans. Amer. Math. So