Layered Exact-Repair Regenerating Codes via Embedded Error Correction and Block Designs

A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the help-by-transfer property where the helper nodes simply transfer part of the stored data directly, without performing any computation. This embedded error correction structure makes the decoding process straightforward, and in some cases the complexity is very low. We show that this construction is able to achieve performance better than space-sharing between the minimum storage regenerating codes and the minimum repair-bandwidth regenerating codes, and it is the first class of codes to achieve this performance. In fact, it is shown that the proposed construction can achieve a nontrivial point on the optimal functional-repair tradeoff, and it is asymptotically optimal at high rate, i.e., it asymptotically approaches the minimum storage and the minimum repair-bandwidth simultaneously.

The use of nonparametric contrasts in one-way layouts and random block designs

Nonparametric simple-contrast estimates for one-way layouts based on Hodges-Lehmann estimators for two samples and confidence intervals for all contrasts involving only two treatments are found in the literature.Tests for such contrasts are performed from the distribution of the maximum of the rank sum between two treatments. For random block designs, simple contrast estimates based on Hodges-Lehmann estimators for one sample are presented. However, discussions concerning the significance levels of more complex contrast tests in nonparametric statistics are not well outlined.This work aims at presenting a methodology to obtain p-values for any contrast types based on the construction of the permutations required by each design model using a C-language program for each design type. For small samples, all possible treatment configurations are performed in order to obtain the desired p-value. For large samples, a fixed number of random configurations are used. The program prompts the input of contrast coefficients, but does not assume the existence or orthogonality among them.In orthogonal contrasts, the decomposition of the value of the suitable statistic for each case is performed and it is observed that the same procedure used in the parametric analysis of variance can be applied in the nonparametric case, that is, each of the orthogonal contrasts has a chi(2) distribution with one degree of freedom. Also, the similarities between the p-values obtained for nonparametric contrasts and those obtained through approximations suggested in the literature are discussed.

Recursive Methods for Construction of Balanced N-ary Block Designs

2000 Mathematics Subject Classification: Primary 05B05; secondary 62K10.

Equitably coloured balanced incomplete block designs

In this thesis we determine necessary and sufficient conditions for the existence of an equitably ℓ-colourable balanced incomplete block design for any positive integer ℓ > 2. In particular, we present a method for constructing non-trivial equitably ℓ-colourable BIBDs and prove that these designs are the only non-trivial equitably ℓ-colourable BIBDs that exist. We also observe that every equitable ℓ-colouring of a BIBD yields both an equalised ℓ-colouring and a proper 2-colouring of the same BIBD. We also discuss generalisations of these concepts including open questions for further research. The main results presented in this thesis also appear in [7].

The extended metamorphosis of a complete bipartite design into a cycle system

A K-t,K-t-design of order n is an edge-disjoint decomposition of K-n into copies of K-t,K-t. When t is odd, an extended metamorphosis of a K-t,K-t-design of order n into a 2t-cycle system of order n is obtained by taking (t - 1)/2 edge-disjoint cycles of length 2t from each K-t,K-t block, and rearranging all the remaining 1-factors in each K-t,K-t block into further 2t-cycles. The 'extended' refers to the fact that as many subgraphs isomorphic to a 2t-cycle as possible are removed from each K-t,K-t block, rather than merely one subgraph. In this paper an extended metamorphosis of a K-t,K-t-design of order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is given for all odd t > 3. A metamorphosis of a 2-fold K-t,K-t-design of any order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is also given, for all odd t > 3. (The case t = 3 appeared in Ars Combin. 64 (2002) 65-80.) When t is even, the graph K-t,K-t is easily seen to contain t/2 edge-disjoint cycles of length 2t, and so the metamorphosis in that case is straightforward. (C) 2004 Elsevier B.V. All rights reserved.

Comparison of block and event-related experimental designs in diffusion-weighted functional MRI

PURPOSE To compare diffusion-weighted functional magnetic resonance imaging (DfMRI), a novel alternative to the blood oxygenation level-dependent (BOLD) contrast, in a functional MRI experiment. MATERIALS AND METHODS Nine participants viewed contrast reversing (7.5 Hz) black-and-white checkerboard stimuli using block and event-related paradigms. DfMRI (b = 1800 mm/s2 ) and BOLD sequences were acquired. Four parameters describing the observed signal were assessed: percent signal change, spatial extent of the activation, the Euclidean distance between peak voxel locations, and the time-to-peak of the best fitting impulse response for different paradigms and sequences. RESULTS The BOLD conditions showed a higher percent signal change relative to DfMRI; however, event-related DfMRI showed the strongest group activation (t = 21.23, P < 0.0005). Activation was more diffuse and spatially closer to the BOLD response for DfMRI when the block design was used. DfMRIevent showed the shortest TTP (4.4 +/- 0.88 sec). CONCLUSION The hemodynamic contribution to DfMRI may increase with the use of block designs.

Modeling of the hemodynamic responses in block design fMRI studies

The hemodynamic response function (HRF) describes the local response of brain vasculature to functional activation. Accurate HRF modeling enables the investigation of cerebral blood flow regulation and improves our ability to interpret fMRI results. Block designs have been used extensively as fMRI paradigms because detection power is maximized; however, block designs are not optimal for HRF parameter estimation. Here we assessed the utility of block design fMRI data for HRF modeling. The trueness (relative deviation), precision (relative uncertainty), and identifiability (goodness-of-fit) of different HRF models were examined and test-retest reproducibility of HRF parameter estimates was assessed using computer simulations and fMRI data from 82 healthy young adult twins acquired on two occasions 3 to 4 months apart. The effects of systematically varying attributes of the block design paradigm were also examined. In our comparison of five HRF models, the model comprising the sum of two gamma functions with six free parameters had greatest parameter accuracy and identifiability. Hemodynamic response function height and time to peak were highly reproducible between studies and width was moderately reproducible but the reproducibility of onset time was low. This study established the feasibility and test-retest reliability of estimating HRF parameters using data from block design fMRI studies.

λ-designs and related combinatorial configurations

This thesis deals with two problems. The first is the determination of λ-designs, combinatorial configurations which are essentially symmetric block designs with the condition that each subset be of the same cardinality negated. We construct an infinite family of such designs from symmetric block designs and obtain some basic results about their structure. These results enable us to solve the problem for λ = 3 and λ = 4. The second problem deals with configurations related to both λ -designs and (ѵ, k, λ)-configurations. We have (n-1) k-subsets of {1, 2, ..., n}, S₁, ..., S_n-1 such that S_i ∩ S_j is a λ-set for i ≠ j. We obtain specifically the replication numbers of such a design in terms of n, k, and λ with one exceptional class which we determine explicitly. In certain special cases we settle the problem entirely.

Zero-One Designs Produce Small Hard SAT Instances

Some basics of combinatorial block design are combined with certain constraint satisfaction problems of interest to the satisfiability community. The paper shows how such combinations lead to satisfiability problems, and shows empirically that these are some of the smallest very hard satisfiability problems ever constructed. Partially balanced (0,1) designs (PB01Ds) are introduced as an extension of balanced incomplete block designs (BIBDs) and (0,1) designs. Also, (0,1) difference sets are introduced as an extension of certain cyclical difference sets. Constructions based on (0,1) difference sets enable generation of PB01Ds over a much wider range of parameters than is possible for BIBDs. Building upon previous work of Spence, it is shown how PB01Ds lead to small, very hard, unsatisfiable formulas. A new three-dimensional form of combinatorial block design is introduced, and leads to small, very hard, satisfiable formulas. The methods are validated on solvers that performed well in the SAT 2009 and earlier competitions.

Large supersaturated designs

A supersaturated design (SSD) is an experimental plan, useful for evaluating the main effects of m factors with n experimental units when m > n - 1, each factor has two levels and when the first-order effects of only a few factors are expected to have dominant effects on the response. Use of these plans can be extremely cost-effective when it is necessary to screen hundreds or thousands of factors with a limited amount of resources. In this article we describe how to use cyclic balanced incomplete block designs and regular graph designs to construct E (s(2)) optimal and near optimal SSDs when m is a multiple of n - 1. We also provide a table that can be used to construct these designs for screening thousands of factors. We also explain how to obtain SSDs when m is not a multiple of n - 1. Using the table and the approaches given in this paper, SSDs can be developed for designs with up to 24 runs and up to 12,190 factors.

Variance dispersion graphs for comparing blocked response surface designs

In this paper, we extend the use of the variance dispersion graph (VDG) to experiments in which the response surface (RS) design must be blocked. Through several examples we evaluate the prediction performances of RS designs in non-orthogonal block designs compared with the equivalent unblocked designs and orthogonally blocked designs. These examples illustrate that good prediction performance of designs in small blocks can be expected in practice. Most importantly, we show that the allocation of the treatment set to blocks can seriously affect the prediction properties of designs; thus, much care is needed in performing this allocation.

Variance-balanced designs under interference for dependent observations

It is shown that variance-balanced designs can be obtained from Type I orthogonal arrays for many general models with two kinds of treatment effects, including ones for interference, with general dependence structures. These designs can be used to obtain optimal and efficient designs. Some examples and design comparisons are given. (C) 2002 Elsevier B.V. All rights reserved.

Combinatorial design of key distribution mechanisms for wireless sensor networks

Secure communications in wireless sensor networks operating under adversarial conditions require providing pairwise (symmetric) keys to sensor nodes. In large scale deployment scenarios, there is no prior knowledge of post deployment network configuration since nodes may be randomly scattered over a hostile territory. Thus, shared keys must be distributed before deployment to provide each node a key-chain. For large sensor networks it is infeasible to store a unique key for all other nodes in the key-chain of a sensor node. Consequently, for secure communication either two nodes have a key in common in their key-chains and they have a wireless link between them, or there is a path, called key-path, among these two nodes where each pair of neighboring nodes on this path have a key in common. Length of the key-path is the key factor for efficiency of the design. This paper presents novel deterministic and hybrid approaches based on Combinatorial Design for deciding how many and which keys to assign to each key-chain before the sensor network deployment. In particular, Balanced Incomplete Block Designs (BIBD) and Generalized Quadrangles (GQ) are mapped to obtain efficient key distribution schemes. Performance and security properties of the proposed schemes are studied both analytically and computationally. Comparison to related work shows that the combinatorial approach produces better connectivity with smaller key-chain sizes.

Combinatorial aspects of jump codes

We develop an approach to jump codes concentrating on their combinatorial and symmetry properties. The main result is a generalization of a theorem previously proved in the context of isodual codes. We show that several previously constructed jump codes are instances of this theorem.

Interação de microorganismos na solubilização de fósforo e potássio de rochas para produção de biofertilizantes

he present model of agriculture is based on intensive use of industrial inputs, due to its rapid response, but it brings harmful consequences to the environment, and it is necessary the use of modern inputs. And an alternative is the use of rock biofertilizers in agriculture, a product easy to use, with higher residual effect and does not harm the environment. The objective of study was to evaluate the inoculation and co-inoculation of different microorganisms in the solubilization of rock phosphate and potash ground microbial evaluating the best performance in the production of biofertilizers comparing with rocks pure in soil chemical properties and, verify effect of inoculation of the bacterium Paenibacillus polymyxa in the absorption of minerals dissolved in the development of cowpea (Vigna unguiculata [L.] Walp.). The first bioassay was conducted in Laboratory (UFRN) for 72 days in Petri dishes, where the rock powder was increased by 10% and sulfur co-inoculated and inoculated with bacterial suspension of Paenibacillus polymyxa grown in medium tryptone soy broth, Ralstonia solanacearum in medium Kelman, Cromobacterium violaceum in medium Luria-Bertani and Acidithiobacillus thiooxidans in medium Tuovinen and Kelly,and fungi Trichoderma humatum and Penicillium fellutanum in malt extract. Every 12 days, samples were removed in order to build up the release curve of minerals. The second bioassay was conducted in a greenhouse of the Agricultural Research Corporation of Rio Grande do Norte in experimental delineation in randomized block designs, was used 10 kg of an Yellow Argissolo Dystrophic per pot with the addition of treatments super phosphate simple (SS), potassium chloride (KCl), pure rock, biofertilizers in doses 40, 70, 100 and 200% of the recommendation for SS and KCl, and a control, or not inoculated with bacteria P. polymyxa. Were used seeds of cowpea BRS Potiguar and co-inoculated with the bacterial suspension of Bradyrhizobium japonicum and P. polymyxa. The first crop was harvested 45 days after planting, were evaluated in the dry matter (ADM), macronutrients (N, P, K, Ca, Mg) and micronutrients (Zn, Fe, Mn) in ADM. And the second at 75 days assessing levels of macro end micronutrients in plants and soil, and the maximum adsorption capacity of P in soil. The results showed synergism in co-inoculations with P. polymyxa+R. solanacearum and, P. polymyxa+C. violaceum solubilizations providing higher P and K, respectively, and better solubilization time at 36 days. The pH was lower in biofertilizers higher doses, but there was better with their addition to P at the highest dose. Significant reduction of maximum adsorption capacity of phosphorus with increasing dose of biofertilizer. For K and Ca was better with SS+KCl, and Mg to pure rock. There was an effect of fertilization on the absorption, with better results for P, K and ADM with SS+KCL, and N, Ca and Mg for biofertilizers. Generally, the P. polymyxa not influence the absorption of the elements in the plant. In treatments with the uninoculated P. polymyxa chemical fertilizer had an average significantly higher for weight and number of grains. And in the presence of the bacteria, biofertilizers and chemical fertilizers had positive values in relation to rock and control. The data show that the rocks and biofertilizers could meet the need of nutrients the plants revealed as potential for sustainable agriculture