Algebras associated with invariant means on the subnormal subgroups of an amenable group

Let G be an amenable group. We define and study an algebra ${\mathcal{A}}_{sn}(G)$, which is related to invariant means on the subnormal subgroups of G. For a just infinite amenable group G, we show that ${\mathcal{A}}_{sn}(G)$ is nilpotent if and only if G is not a branch group, and in the case that it is nilpotent we determine the index of nilpotence. We next study $\textrm{rad}\, \ell^1(G)^{**}$ for an amenable branch group G and show that it always contains nilpotent left ideals of arbitrarily large index, as well as non-nilpotent elements. This provides infinitely many finitely generated counterexamples to a question of Dales and Lau [4], first resolved by the author in [10], which asks whether we always have $(\textrm{rad}\, \ell^1(G)^{**})^{\Box 2} = \{0 \}$. We further study this question by showing that $(\textrm{rad}\, \ell^1(G)^{**})^{\Box 2} = \{0 \}$ imposes certain structural constraints on the group G.

VSTseed: periodic spaced seeds for reads with substitutions

Motivation: Technical progress in computer hardware made it possible to access and process large amounts of data even on budget workstations. Therefore new or existing alignment algorithms may use large index files to increase performance. Spaced seeds with large weights reduce the number of possible locations of a read within a reference sequence. Optimal patterns for spaced seeds may guarantee to align reads even with several substitutions. Results: For reads of 64-200 bp periodic spaced seeds of 32, 40, 48, 56, 64 weights are found that guarantee to locate all positions within a reference sequence for a specified number of point mutations. SIMD instructions to convert masked reads into 64, 80, 96, 112, 128-bit numbers are provided. Availability: C codes to generate spaced seeds and find optimal SIMD instructions for them are freely available under MIT license at https://github.com/vtman/VSTseed.

CM-types with large index of degeneracy

For an abelian variety [Formula: see text] of CM-type, the index of degeneracy is the minimum of [Formula: see text] such that the product [Formula: see text] holds an exceptional Hodge cycle. We present new examples with the index of degeneracy larger than [Formula: see text].

Tests for Price Indices in a Dynamic Item Universe

There is generally a need to deal with quality change and new goods in the consumer price index due to the underlying dynamic item universe. Traditionally axiomatic tests are defined for a fixed universe. We propose five tests explicitly formulated for a dynamic item universe, and motivate them both from the perspectives of a cost-of-goods index and a cost-of-living index. None of the indices that are currently available for making use of scanner data satisfies all the tests at the same time. The set of tests provides a rigorous diagnostic for whether an index is completely appropriate in a dynamic item universe, as well as pointing towards the directions of possible remedies. We thus outline a large index family that potentially can satisfy all the tests.

The Joint Dynamics of Liquidity and Volatility Across Small- and Large- index Indian Funds

The article explores the relationship between volatility and liquidity, as there is a change in market capitalisation (cap). Using three regimes of volatility, identified by the threshold vector auto-regression method, the results show that volatility affects liquidity differently for the three volatility regimes during the two periods (crisis and post-crisis) of study. The results show that there is inconsistency in how volatility affects liquidity across the Indian large-, mid- and small-cap indices. JEL Classification: G1 G17

International cooperation networks of the BRICS bloc

Since the BRICS Declaration in Cape Town in 2013, its five member countries have committed to cooperation programs in science, technology and innovation (STI), based on the five strategic thematic areas assigned to each signatory: climate change and mitigation of catastrophes (Brazil); water resources and pollution treatment (Russia); geospatial technology and its applications (India); new and renewable energy, and energy efficiency (China); and astronomy (South Africa). Five years after the Declaration and almost a decade after the First BRICS Summit, the evaluation of the strengthening of international cooperation among countries remains a challenge, due to their low presence in the large index databases commonly used for the collection of scientific data, such as Web of Science and Scopus. The proposal of this research is to carry out a study on international cooperation among the countries in the last five years through the Dimensions platform, based on the incidence of international co-authoring and co-financing of research agencies from the five countries, seeking to highlight the following points: the networks that consolidate themselves from the international cooperation among the BRICS countries, areas emerging in research with incidences of co-authorship, and how the research networks have been developed around the five strategic areas defined in the BRICS Cape Town Declaration. It aims to evaluate how the international cooperation of the BRICS bloc in strategic thematic areas has been growing, pointing to possible areas of strengthening of international partnerships that can be deployed through this study.