Quantile correlations and quantile autoregressive modeling

In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the classical Box-Jenkins approach to quantile autoregressive models. Specifically, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the fitted model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR, QPCOR, QACF, and PQACF, but also show the large sample results of the QAR estimates and the quantile version of the Ljung-Box test. Simulation studies indicate that the proposed methods perform well in finite samples, and an empirical example is presented to illustrate usefulness

Finite-time Convergent Gossiping

Gossip algorithms are widely used in modern distributed systems, with applications ranging from sensor networks and peer-to-peer networks to mobile vehicle networks and social networks. A tremendous research effort has been devoted to analyzing and improving the asymptotic rate of convergence for gossip algorithms. In this work we study finite-time convergence of deterministic gossiping. We show that there exists a symmetric gossip algorithm that converges in finite time if and only if the number of network nodes is a power of two, while there always exists an asymmetric gossip algorithm with finite-time convergence, independent of the number of nodes. For $n=2^m$ nodes, we prove that a fastest convergence can be reached in $nm=n\log_2 n$ node updates via symmetric gossiping. On the other hand, under asymmetric gossip among $n=2^m+r$ nodes with $0\leq r<2^m$, it takes at least $mn+2r$ node updates for achieving finite-time convergence. It is also shown that the existence of finite-time convergent gossiping often imposes strong structural requirements on the underlying interaction graph. Finally, we apply our results to gossip algorithms in quantum networks, where the goal is to control the state of a quantum system via pairwise interactions. We show that finite-time convergence is never possible for such systems.Comment: IEEE/ACM Transactions on Networking, In Pres

Formal specification of MPI 2.0: case study in specifying a practical concurrent programming API

technical reportWe describe the rst formal speci cation of a non-trivial subset of MPI, the dominant communication API in high performance computing. Engineering a formal speci cation for a non-trivial concurrency API requires the right combination of rigor, executability, and traceability, while also serving as a smooth elaboration of a pre-existing informal speci - cation. It also requires the modularization of reusable speci cation components to keep the length of the speci cation in check. Long-lived APIs such as MPI are not usually `textbook minimalistic' because they support a diverse array of applications, a diverse community of users, and have ef cient implementations over decades of computing hardware. We choose the TLA+ notation to write our speci cations, and describe how we organized the speci - cation of 150 of the 300 MPI 2.0 functions. We detail a handful of these functions in this paper, and assess our speci cation with respect to the aforesaid requirements. We close with a description of possible approaches that may help render the act of writing, understanding, and validating speci cations much more productive

Application of Improved Packing Method in the Repair of Infectious Wounds in Special Body Parts

Objective: To investigate the effect of improved packing method in the repair of infectious wounds in special parts. Methods: From December 2017 to December 2020, 68cases of infectious wounds in special body parts were treated with improved packing and dressing method (including 28 cases of hip abscess, 16 cases of sacrococcygeal pressure ulcer, 12 cases of buttock pressure ulcer, 8 cases of perineal necrotizing fasciitis and 4 cases of hip pressure ulcer). After active anti infection, abscess incision and drainage, and debridement of necrotic tissue, the wound inflammation subsided, necrotic tissue was removed, and granulation tissue grew. The wound edge was fully dissociated, and the wound was directly closed and sutured or transferred to the adjacent skin flap to repair the wound. The drainage tube was prevented according to the condition of the wound. Meilan marked the area of the basal cavity of the wound, and the packing suture was placed outside the edge of the cavity to fix the wound. Result: Of the 68 patients, 58 had primary wound healing; 8 cases of partial wound dehiscence after removal of packing and bandage were treated with secondary suture combined with improved packing and bandage method; Two patient's wound was uncooperative due to the poor consciousness of the patient. The bandage was completely loose and the wound split again. Conclusion It has the advantages of simple operation, easy nursing and less hospitalization cost