Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memory

In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy, price impact and price volatility are obtained explicitly. The volatility of the price volatility appears excessive, which is a result of the fact that a more aggressive trading strategy is chosen by the insider when uninformed volume is higher. The optimal trading strategy turns out to possess the property of long memory, and the price impact is also affected by the fractional noise.Comment: 21 pages; 2 figure

Discrepancy of coordinate system selection in backscattering Mueller matrix polarimetry: exploring photon coordinate system transformation invariants

In biomedical studies, Mueller matrix polarimetry is gaining increasing attention because it can comprehensively characterize polarization-related vectorial properties of the sample, which are crucial for microstructural identification and evaluation. For backscattering Mueller matrix polarimetry, there are two photon coordinate selection conventions, which can affect the following Mueller matrix parameters calculation and information acquisition quantitatively. In this study, we systematically analyze the influence of photon coordinate system selection on the backscattering Mueller matrix polarimetry. We compare the Mueller matrix elements in the right-handed-nonunitary and non-right-handed-unitary coordinate systems, and specifically deduce the changes of Mueller matrix polar decomposition, Mueller matrix Cloude decomposition and Mueller matrix transformation parameters widely used in backscattering Mueller matrix imaging as the photon coordinate system varied. Based on the theoretical analysis and phantom experiments, we provide a group of photon coordinate system transformation invariants for backscattering Mueller matrix polarimetry. The findings presented in this study give a crucial criterion of parameters selection for backscattering Mueller matrix imaging under different photon coordinate systems

TICK: Tiny Client for Blockchains

In Bitcoin-like systems, when a payee chooses to accept zero-confirmation transactions, it needs to verify the validity of the transaction. In particular, one of the steps is to verify that each referred output of the transaction is not previously spent. The conventional lightweight client design can only support such operation in the complexity of O($N_T$), where $N_T$ is the total number of transactions in the system. This is impractical for lightweight clients. The latest proposals suggest to summarize all the unspent outputs in an ordered Merkle tree. Therefore, a light client can request proof of presence and/or absence of an element in it to prove whether a referred output is previously spent or not, in the complexity of O(log($N_U$)), where $N_U$ is the total number of unspent output in the system. However, updating such ordered Merkle tree is slow, thus making the system impractical --- by our evaluation, when a new block is generated in Bitcoin, it takes more than one minute to update the ordered Merkle tree. We propose a practical client, TICK, to solve this problem. TICK uses the AVL hash tree to store all the unspent outputs. The AVL hash tree can be update in the time of O(M*log($N_U$)), where $M$ is the number of elements that need to be inserted or removed from the AVL hash tree. By evaluation, when a new block is generated, the AVL hash tree can be updated within $1$ second. Similarly, the proof can also be generated in the time of O(log($N_U$)). Therefore, TICK brings negligible run-time overhead, and thus it is practical. Benefited by the AVL hash tree, a storage-limited device can efficiently and cryptographically verify transactions. In addition, rather than requiring new miners to download the entire blockchain before mining, TICK allows new miners to download only a small portion of data to start mining. We implement TICK for Bitcoin and provide an experimental evaluation on its performance by using the current Bitcoin blockchain data. Our result shows that the proof for verifying whether an output of a transaction is spent or not is only several KB. The verification is very fast -- generating a proof generally takes less than $1$ millisecond, and verifying a proof even takes much less time. In addition, to start mining, new miners only need to download several GB data, rather than downloading over 230 GB data

Identification of open crack of beam using model based method

This research aims at identifying the position and depth of the open transverse crack of the beam using the model based method. The stiffness matrix of the cracked beam element and the basic principle of the model based method are introduced. It is discussed to estimate the generalized displacement of all nodes of the beam by the measured displacements of a few degrees of freedom. The relative change rate of the equivalent external load between the intact and cracked elements is compared with that of mode shape, nature frequency and displacement amplitude between the intact and cracked beam. The position and depth of the crack are identified by the model based method in two cases. In first case, the measured displacement is assumed not to include noise. The identification results based on the actual displacement and rotation of all nodes are compared with the results using the estimated generalized displacement. In second case, the measured displacement includes noise and the generalized displacement of all nodes is estimated by the displacement of two measurement points. The simulation results shown there is no error to identify the position, the relative depth identification error of the crack with 1 μm depth is 2.34 % without noise, and the relative depth identification error of the crack with 200 μm depth could be down to about 5 % with the energy signal to noise ratio being about 7.00 before denoising