Cascaded Code Distributed Computing With Low Complexity and Improved Flexibility

Coded distributed computing (CDC), proposed by Li et al., offers significant potential for reducing the communication load in MapReduce computing systems. In the setting of the cascaded CDC that consisting of $K$ nodes, $N$ input files, and $Q$ output functions, the objective is to compute each output function through $s\geq 1$ nodes with a computation load $r\geq 1$, enabling the application of coding techniques during the Shuffle phase to achieve minimum communication load. However, a significant limitation in most existing cascaded CDC schemes is their demand for splitting the original data into an exponentially growing number of input files and requiring an exponentially large number of output functions, which imposes stringent requirements for implementation. In this paper, we focus on the cascaded case of $K/s\in\mathbb{N}$, deliberately designing the strategy of data placement and output functions assignment based on a grouping method, such that a low-complexity Shuffle strategy is achievable. The main advantages of the proposed scheme include: 1) the multicast gains equal to $(r+s-1)(1-1/s)$ and $r+s-1$ which is approximate to $r+s-1$ when $s$ is relatively large, and the communication load is quite approximate to or surprisingly better than the optimal state-of-the-art scheme proposed by Li et al.; 2) the proposed scheme requires significantly less number of input files and output functions; 3) all the operations are implemented over the minimum binary field $\mathbb{F}_2$ in the one-shot fashion. Finally, we derive a new converse bound for the cascaded CDC framework, under the given strategies of data placement and output functions assignment. We demonstrate that the communication load of the proposed scheme is order optimal within a factor of $2$; and is also approximately optimal when $K$ is sufficiently large for a given $r$

Existence of APAV(q,k) with q a prime power ≡5(mod8) and k≡1(mod4)

AbstractStinson introduced authentication perpendicular arrays APAλ(t,k,v), as a special kind of perpendicular arrays, to construct authentication and secrecy codes. Ge and Zhu introduced APAV(q,k) to study APA1(2,k,v) for k=5, 7. Chen and Zhu determined the existence of APAV(q,k) with q a prime power ≡3(mod4) and odd k>1. In this article, we show that for any prime power q≡5(mod8) and any k≡1(mod4) there exists an APAV(q,k) whenever q>((E+E2+4F)/2)2, where E=[(7k−23)m+3]25m−3, F=m(2m+1)(k−3)25m and m=(k−1)/4

Immunohistochemical Expression and Prognostic Value of CD97 and Its Ligand CD55 in Primary Gallbladder Carcinoma

Background. CD97 as a member of the EGF-TM7 family with adhesive properties plays an important role in tumor aggressiveness by binding its cellular ligand CD55, which is a complement regulatory protein expressed by cells to protect them from bystander complement attack. Previous studies have shown that CD97 and CD55 both play important roles in tumor dedifferentiation, migration, invasiveness, and metastasis. The aim of this study was to investigate CD97 and CD55 expression in primary gallbladder carcinoma (GBC) and their prognostic significance. Methods. Immunohistochemistry was used to investigate the expression of CD97 and CD55 proteins in 138 patients with GBC. Results. CD97 and CD55 were absent or only weakly expressed in the normal epithelium of the gallbladder but in 69.6% (96/138) and 65.2% (90/138) of GBC, respectively, remarkably at the invasive front of the tumors. In addition, CD97 and CD55 expressions were both significantly associated with high histologic grade (both P = 0.009), advanced pathologic T stage (P = 0.01 and 0.009, resp.) and clinical stage (both P = 0.009), and positive venous/lymphatic invasion (both P = 0.009). Multivariate analyses showed that CD97 (hazard ratio, 3.236; P = 0.02) and CD55 (hazard ratio, 3.209; P = 0.02) expressions and clinical stage (hazard ratio, 3.918; P = 0.01) were independent risk factor for overall survival. Conclusion. Our results provide convincing evidence for the first time that the expressions of CD97 and CD55 are both upregulated in human GBC. The expression levels of CD97 and CD55 in GBC were associated with the severity of the tumor. Furthermore, CD97 and CD55 expressions were independent poor prognostic factors for overall survival in patients with GBC

A Programmable Real-Time Data Processor

International Telemetering Conference Proceedings / October 24-27, 1983 / Sheraton-Harbor Island Hotel and Convention Center, San Diego, CaliforniaA new type of programmable data processor for a telemetry system is described, in which the functional tables constructed by EPROM’s was employed for fast conversion of the measured binary code to easily understood data results by people, and a printer/plotter made in our country was used as Recordin device. Synchronization problems between the printer/plotter turning in high speed and the telemetry system have been solved fairly good. The data processing speed is 13200 characters per second. All of the circuit elements were mounted on a printed circuit board and we enclosed it in the case of the printer/plotter. The processor is directly linked to the synchnizer of telemetry system and the timer, and can process all the data obtainned from certain telemetry system in real-time.International Foundation for TelemeteringProceedings from the International Telemetering Conference are made available by the International Foundation for Telemetering and the University of Arizona Libraries. Visit http://www.telemetry.org/index.php/contact-us if you have questions about items in this collection

Relative difference families with variable block sizes and their relatedOOCs

Seven infinite classes of relative difference families with variable block sizes are presented explicitly. In particular, a balanced (gv,g,K,1)-DF with $g=\sum_{k\in K}{k^2-k\over2}$ is explicitly given for: (i) K={3,4,5} and every v coprime to 6; (ii) K={3,4,6} or {3,5,6} or {3,4,5,6} and every v coprime to 30. As far as the authors are aware, these difference families can be viewed as the first explicit constructions of infinite classes of optimal variable-weight optical orthogonal codes with more than two weights. It is observed, however, that there are infinitely many values of v for which an optimal (v.W,1,Q) -OOC exists, whatever the set of weights W and the weight distribution sequence Q are