12880164
Packings and coverings of the complete directed multigraph with 3- and 4-circuits
Abstract Let λDK v denote the complete directed multigraph with v vertices, where any two distinct vertices x and y are joined by λ arcs ( x , y ) and λ arcs ( y , x ). By a k -circuit we mean a directed cycle of length k . In this paper, we consider the problem of finding maximal packings and minimal coverings of λDK v with k -circuits. In particular, we completely determine the packing number and covering number for the cases k = 3 and 4.
14835961
North-Holland On the existence of perfect Mendelsohn designs with k = 7 and A even
Let v, k and I be positive integers. A (v, k, A)-Mendelsohn design (briefly (v, k, A)-MD) is a pair (X, 3) where X is a v-set (of points) and !?8 is a collection of cyclically ordered k-subsets of X (called blocks) such that every ordered pair of points of X are consecutive in exactly il blocks of 3. A set of k distinct elements {a,, a-,, . . . , ak} is said to be cyclically ordered by a,Ca,C.‘<a&a, and the pair a,, a,,, are said to be t-apart in a cyclic k-tuple (a,, az, . . . , ak) where i + I is taken modulo k. If for all t = 1, 2, . . . , k 1, every ordered pair of points of X are t-apart in exactly )L blocks of 3, then the (v, k, A)-MD is called perfect and is denoted briefly by (v, k, A)-PMD. A necessary condition for the existence of a (v, k, A)-PMD is Av(v 1) = 0 (mod k). In this paper, we shall be concerned mostly with the case k = 7 and il even. It will be shown ttat the necessary condition for the existence of a (v, 7, A)-PMD, namely Av(v 1) = 0 (mod 7), is also sufficient for all even A 2 16, with at most 29 possible exceptions for the pair (v, A) where A is even and E. < 16. In the process, we shall also establish that the necessary condition v = 0 or 1 (mod 7) for the existence of a (v, 7, I)-PMD is also sufficient for all v 2 421 with at most 40 possible exceptions below this value, which improves the earlier results.
11507660
Existence of perfect Mendelsohn designs with k=5 and lambda>1
Abstract Let υ, k , and λ be positive integers. A (υ, k , λ )- Mendelsohn design (briefly (υ, k , λ )-MD) is a pair ( X , B ) where X is a υ-set (of points ) and B is a collection of cyclically ordered k -subsets of X (called blocks ) such that every ordered pair of points of X are consecutive in exactly λ blocks of B . A set of k distinct elements { a 1 , a 2 ,…, a k } is said to be cyclically ordered by a 1 a 2 a k a 1 and the pair a i , a i + t is said to be t -apart in cyclic k -tuple ( a 1 , a 2 ,…, a k ) where i + t is taken modulo k . It for all t =1,2,…, k -1, every ordered pair of points of X is t -apart in exactly λ blocks of B , then the (υ, k , λ )-MD is called a perfect design and is denoted briefly by (υ, k , λ )-PMD. In this paper, we shall be concerned mainly with the case where k =5 and λ >1. It will be shown that the necessary condition for the existence of a (υ, 5, λ )-PMD, namely, λv ( υ -1)≡0 (mod 5), is also sufficient for λ >1 with the possible exception of pairs (υ, λ ) where λ =5 and υ =18 and 28.
29194002
On the existence of perfect Mendelsohn designs with k = 7 and lambda even
Abstract Let v, k and λ be positive integers. A ( v, k , λ)- Mendelsohn design (briefly ( v, k , λ)-MD) is a pair ( X ,B) where X is a v -set (of points ) andBis a collection of cyclically ordered k -subsets of X (called blocks ) such that every ordered pair of points of X are consecutive in exactly λ blocks of B. A set of k distinct elements { a 1 , a 2 , ..., a k } is said to be cyclically ordered by a 1 a 2 a k a 1 and the pair a i , a i + t are said to be t -part in a cyclic k -tuple ( a 1 , a 2 ,..., a k ) where i + t is taken modulo k . If for all t = 1, 2,..., k − 1, every ordered pair of points of X are t -apart in exactly λ blocks of B, then the ( v, k , λ)-MD is called perfect and is denoted briefly by ( v, k , λ)-PMD. A necessary condition for the existence of a ( v, k , λ)-PMD is λ v ( v −1)≡0 (mod k ). In this paper, we shall be concerned mostly with the case k = 7 and λ even. It will be shown that the necessary condition for the existence of a v , 7, λ)-PMD, namely λ v ( v −1)≡0 (mod 7), is also sufficient for all even λ ⪖ 16, with at most 29 possible exceptions for the pair ( v , λ) where λ is even and λ v ≡0 or 1 (mod 7) for the existence of a ( v , 7, 1)-PMD is also sufficient for all v ⪖ 421 with at most 40 possible exceptions below this value, which improves the earlier results.
5254546
Constructions for Perfect 5-Deletion-Correcting Codes of Length$7$
There are two kinds of perfect (k-t)-deletion-correcting codes with words of length k over an alphabet of size v, those where the coordinates may be equal and those where all coordinates must be different. We call these two kinds of codes T*(t,k,v)-codes and T(t,k,v)-codes respectively. Both a T*(t,k,v)-code and a T(t,k,v)-code are capable of correcting any combination of up to (k-t) deletions and insertions of letters occurred in transmission of codewords. In this correspondence, we consider constructions for the codes from directed designs. By means of these constructions, the existence of a T(2,7,v)-code is settled for all positive integers v with the exception of 68 values of v; T*(2,7,v)-codes are constructed for all integers vges2350. A large number of explicit constructions for T*(2,7,v)-codes with v<2350 are also presented
18873920
Signal Sets From Functions With Optimum Nonlinearity
Signal sets with the best correlation property are desirable in code-division multiple-access (CDMA) systems. In this paper, the construction of Wootters and Fields for mutually unbiased bases is extended into a generic construction of signal sets using planar functions. Then, specific classes of planar functions and almost bent functions are employed to obtain (q2+q,q) signal sets. The signal sets derived from planar functions are optimal with respect to the Levenstein bound, and those obtained from almost bent functions nearly meet the Levenstein bound. The signal sets constructed in this paper could have a very small alphabet size, and have applications in synchronous DS-CDMA systems, where the number of users is greater than the signal space dimension or the spreading factor
123278
Enhanced speech in noisy multiple speaker environment
Noisy environments seriously degrade the performance of speech recognition systems. Here we implement a high performance speech enhancement algorithm. Data from speech separation challenge were used to evaluate the method. It was observed that the enhanced speech significantly improved the recognition performance. In 2 out of 4 SNR cases, over 100% relative percentage improvements were achieved. Standalone software prototype has been developed and evaluated.
109716942
A nanoscale nonvolatile memory device made from RbAg4I5 solid electrolyte grown on a Si substrate
A nanoscale nonvolatile memory device made from RbAg"4I"5 solid electrolyte has been made directly on a Si substrate with lateral size scaled down to 100nm. By applying voltages with different polarity, the device could be switched between high- and low-resistance states. The ratio between the high and low resistances could reach ~10^3, and the low-resistance state showed rectifying diode characteristics. The configured resistances remained nonvolatile after switching, and the device could be switched repeatedly for ~10^3 times. Our results show that the nanoscale nonvolatile memory device can be integrated directly with Si-based circuit and can be potentially used for high-density memory application.
18219094
Nonuniform sequential sampling for signal analysis
New electronic technologies for signal analysis raise the possibility of sampling very rapidly, with a time-varying density, and determining empirically both the sampling rate and the window width as the signal evolves in time. These opportunities also point to the possibility of sequentially sampling in a time-varying way in more traditional problems. Motivated by these ideas, we establish a sampling formula, valid in cases where both sampling rate and window width may be varied. The formula states that, in terms of the ways in which these quantities should alter with time, optimal performance is achieved when the window width is inversely proportional to squared sampling rate, and sampling rate is directly proportional to squared bias.
14742588
Reducing Complexity of Software Deployment with Delta Configuration
Deploying a modern software service usually involves installing several software components, and configuring these components properly to realize the complex interdependencies between them. This process, which accounts for a significant portion of information technology (IT) cost, is complex and error-prone. In this paper, we propose delta configuration - an approach that reduces the cost of software deployment by eliminating a large number of choices on parameter values that administrators have to make during deployment. In delta configuration, the complex software stack of a distributed service is first installed and tested in a test environment. The resulting software images are then captured and used for deployment in production environments. To deploy a software service, we only need to copy these pre-configured software images into a production environment and modify them to account for the difference between the test environment and a production environment. We have implemented a prototype system that achieves software deployment using delta configuration of the configuration state captured inside virtual machines. We perform a case study to demonstrate that our scheme leads to substantial reduction in complexity for the customer, over the traditional software deployment method.
17275266
On Gauss quadrature and partial cross validation
New estimators of expected values Ew(X) of functions of a random variable X are introduced. The new estimators are based on Gauss quadrature, a numerical method frequently used to approximate integrals over finite intervals. The estimators need a small number of numerical evaluations and hence are useful in partial cross validation (PCV) a numerical method for finding optimal smoothing parameters in nonparametric curve estimation. The PCV can considerably reduce the computational cost of the generalized cross validation method typically used to determine the optimal smoothing parameter.