On the generic local Langlands correspondence for GSpin groups

In the case of split $GSpin$ groups, we prove an equality of $L$-functions between automorphic local $L$-functions defined by the Langlands-Shahidi method and local Artin $L$-functions. Our method of proof is based on previous results of the first author which allow to reduce the problem to supercuspidal representations of Levi subgroups of $GSpin$, by constructing Langlands parameters for general generic irreducible admissible representations of $GSpin$ from the one for generic irreducible supercuspidal representations of its Levi subgroups.Comment: 17 pages, To appear in Transactions of the AM

Statistical identification with hidden Markov models of large order splitting strategies in an equity market

Large trades in a financial market are usually split into smaller parts and traded incrementally over extended periods of time. We address these large trades as hidden orders. In order to identify and characterize hidden orders we fit hidden Markov models to the time series of the sign of the tick by tick inventory variation of market members of the Spanish Stock Exchange. Our methodology probabilistically detects trading sequences, which are characterized by a net majority of buy or sell transactions. We interpret these patches of sequential buying or selling transactions as proxies of the traded hidden orders. We find that the time, volume and number of transactions size distributions of these patches are fat tailed. Long patches are characterized by a high fraction of market orders and a low participation rate, while short patches have a large fraction of limit orders and a high participation rate. We observe the existence of a buy-sell asymmetry in the number, average length, average fraction of market orders and average participation rate of the detected patches. The detected asymmetry is clearly depending on the local market trend. We also compare the hidden Markov models patches with those obtained with the segmentation method used in Vaglica {\it et al.} (2008) and we conclude that the former ones can be interpreted as a partition of the latter ones.Comment: 26 pages, 12 figure

Dynamically Adjusting the Mining Capacity in Cryptocurrency with Binary Blockchain

Many cryptocurrencies rely on Blockchain for its operation. Blockchain serves as a public ledger where all the completed transactions can be looked up. To place transactions in the Blockchain, a mining operation must be performed. However, due to a limited mining capacity, the transaction confirmation time is increasing. To mitigate this problem many ideas have been proposed, but they all come with own challenges. We propose a novel parallel mining method that can adjust the mining capacity dynamically depending on the congestion level. It does not require an increase in the block size or a reduction of the block confirmation time. The proposed scheme can increase the number of parallel blockchains when the mining congestion is experienced, which is especially effective under DDoS attack situation. We describe how and when the Blockchain is split or merged, how to solve the imbalanced mining problem, and how to adjust the difficulty levels and rewards. We then show the simulation results comparing the performance of binary blockchain and the traditional single blockchain

Integration of Modules II: Exponentials

We continue our exploration of various approaches to integration of representations from a Lie algebra \mbox{Lie} (G) to an algebraic group $G$ in positive characteristic. In the present paper we concentrate on an approach exploiting exponentials. This approach works well for over-restricted representations, introduced in this paper, and takes no note of $G$-stability.Comment: Accepted by Transactions of the AMS. This paper is split off the earlier versions (1, 2 and 3) of arXiv:1708.06620. Some of the statements in these versions of arXiv:1708.06620 contain mistakes corrected here. Version 2 of this paper: close to the accepted version by the journal, minor improvements, compared to Version

Limit Orders, Trading Activity, and Transactions Costs in Equity Futures in an Electronic Trading Environment

The behaviour of limit order quotes and trading activity are studied using a unique and rich database that includes the identity of market participants from a fully automated derivatives market. The analysis is performed using transactions records for three aggregated trader types and three trade identifiers, with trades stamped in milliseconds for the SXF, the equity futures contract of the Montreal Exchange. The identifiers distinguish trades between principals; agency based trades, as well as transactions that are conducted for risk management as opposed to speculative purposes. Agency related trades are shown to represent the largest amount of trading activity relative to other account types. Over 90% of trades in this electronic market are limit orders. The limit order book, especially the depth 1 order, has a dominant role in providing liquidity and in explaining market participants’ trading behaviour. Participants in the SXF reference their trades to the best limit order depth. Hence, investors with large positions or investors who want to build a large position have to strategically split large orders to close/build their position, according to the depth of the best limit order, to ameliorate price impact and information leakage effects. In addition, the results show that traditionally measured spreads have no relationship with trading costs.Limit Orders, Trading Activity, Transactions Costs, Electronic Trading