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Positioning disk-shaped sensors to optimize certain coverage parameters is a fundamental problem in ad hoc sensor networks. The hexagon lattice arrangement is known to be optimally efficient in the plane, even though 20.9% of the area is unnecessarily covered twice, however, the arrangement is very rigid—any movement of a sensor from its designated grid position (due to, e.g., placement error or obstacle avoidance) leaves some region uncovered, as would the failure of any one sensor. In this article, we consider how to arrange sensors in order to guarantee multiple coverage, that is, k -coverage for some value k > 1. A naive approach is to superimpose multiple hexagon lattices, but for robustness reasons, we may wish to space sensors evenly apart. We present two arrangement methods for k -coverage: (1) optimizing a Riesz energy function in order to evenly distribute nodes, and (2) simply shrinking the hexagon lattice and making it denser. The first method often approximates the second, and so we focus on the latter. We show that a density increase tantamount to k copies of the lattice can yield k ′-coverage, for k ′ > k (e.g., k = 11, k ′ = 12 and k = 21, k ′ = 24), by exploiting the double-coverage regions. Our examples' savings provably converge in the limit to the ≈ 20.9% maximum. We also provide analogous results for the square lattice and its ≈ 57% inefficiency (e.g., k = 3, k ′ = 4 and k =5, k ′ = 7) and show that for multi-coverage for some values of k ′, the square lattice can actually be more efficient than the hexagon lattice. We also explore other benefits of shrinking the lattice: Doing so allows all sensors to move about their intended positions independently while nonetheless guaranteeing full coverage and can also allow us to tolerate probabilistic sensor failure when providing 1-coverage or k -coverage. We conclude by construing the shrinking factor as a budget to be divided among these three benefits.

Local Resilience and Hamiltonicity Maker–Breaker Games in Random Regular Graphs

For an increasing monotone graph propertythelocal resilienceof a graphGwith respect tois the minimalrfor which there exists a subgraphH⊆Gwith all degrees at mostr, such that the removal of the edges ofHfromGcreates a graph that does not possess. This notion, which was implicitly studied for somead hocproperties, was recently treated in a more systematic way in a paper by Sudakov and Vu. Most research conducted with respect to this distance notion focused on the binomial random graph model(n, p) and some families of pseudo-random graphs with respect to several graph properties, such as containing a perfect matching and being Hamiltonian, to name a few. In this paper we continue to explore the local resilience notion, but turn our attention to random and pseudo-randomregulargraphs of constant degree. We investigate the local resilience of the typical randomd-regular graph with respect to edge and vertex connectivity, containing a perfect matching, and being Hamiltonian. In particular, we prove that for every positive ϵ and large enough values ofd, with high probability, the local resilience of the randomd-regular graph,n, d, with respect to being Hamiltonian, is at least (1−ϵ)d/6. We also prove that for the binomial random graph model(n, p), for every positive ϵ > 0 and large enough values ofK, ifp>$\frac{K\ln n}{n}$then, with high probability, the local resilience of(n, p) with respect to being Hamiltonian is at least (1−ϵ)np/6. Finally, we apply similar techniques to positional games, and prove that ifdis large enough then, with high probability, a typical randomd-regular graphGis such that, in the unbiased Maker–Breaker game played on the edges ofG, Maker has a winning strategy to create a Hamilton cycle.

Dynamic entropy-compressed sequences and full-text indexes

We give new solutions to the Searchable Partial Sums with Indels problem. Given a sequence of n k -bit numbers, we present a structure taking kn + o ( kn ) bits of space, able of performing operations sum , search , insert , and delete , all in O (log n ) worst-case time, for any k = O (log n ). This extends previous results by Hon et al. [2003c] achieving the same space and O (log n /log log n ) time complexities for the queries, yet offering complexities for insert and delete that are amortized and worse than ours, and supported only for k = O (1). Our result matches an existing lower bound for large values of k . We also give new solutions to the Dynamic Sequence problem. Given a sequence of n symbols in the range [1,σ] with binary zero-order entropy H 0 , we present a dynamic data structure that requires nH 0 + o ( n log σ) bits of space, which is able of performing rank and select , as well as inserting and deleting symbols at arbitrary positions, in O (log n log σ) time. Our result is the first entropy-bound dynamic data structure for rank and select over general sequences. In the case σ = 2, where both previous problems coincide, we improve the dynamic solution of Hon et al. [2003c] in that we compress the sequence. The only previous result with entropy-bound space for dynamic binary sequences is by Blandford and Blelloch [2004], which has the same complexities as our structure, but does not achieve constant 1 multiplying the entropy term in the space complexity. Finally, we present a new dynamic compressed full-text self-index, for a collection of texts over an alphabet of size σ, of overall length n and h th order empirical entropy H h . The index requires nH h + o ( n log σ) bits of space, for any h ≤ α log sigma n and constant 0 < α < 1. It can count the number of occurrences of a pattern of length m in time O ( m log n log σ). Each such occurrence can be reported in O (log 2 n log log n ) time, and displaying a context of length ℓ from a text takes time O (log n (ℓ log σ + log n log log n )). Insertion/deletion of a text to/from the collection takes O (log n log σ) time per symbol. This significantly improves the space of a previous result by Chan et al. [2004] in exchange for a slight time complexity penalty. We achieve at the same time the first dynamic index requiring essentially nH h bits of space, and the first construction of a compressed full-text self-index within that working space. Previous results achieve at best O ( nH h space with constants larger than 1 [Ferragina and Manzini 2000; Arroyuelo and Navarro 2005] and higher time complexities. An important result we prove in this paper is that the wavelet tree of the Burrows-Wheeler transform of a text, if compressed with a technique that achieves zero-order compression locally (e.g., Raman et al. [2002]), automatically achieves h th order entropy space for any h . This unforeseen relation is essential for the results of the previous paragraph, but it also derives into significant simplifications on many existing static compressed full-text self-indexes that build on wavelet trees.

Relating complexity and precision in control flow analysis

We analyze the computational complexity of k CFA, a hierarchy of control flow analyses that determine which functions may be applied at a given call-site. This hierarchy specifies related decision problems, quite apart from any algorithms that may implement their solutions. We identify a simple decision problem answered by this analysis and prove that in the 0CFA case, the problem is complete for polynomial time. The proof is based on a nonstandard, symmetric implementation of Boolean logic within multiplicative linear logic (MLL). We also identify a simpler version of 0CFA related to η-expansion, and prove that it is complete for logarithmic space, using arguments based on computing paths and permutations. For any fixed k >0, it is known that k CFA (and the analogous decision problem) can be computed in time exponential in the program size. For k =1, we show that the decision problem is NP-hard, and sketch why this remains true for larger fixed values of k . The proof technique depends on using the approximation of CFA as an essentially nondeterministic computing mechanism, as distinct from the exactness of normalization. When k = n , so that the "depth" of the control flow analysis grows linearly in the program length, we show that the decision problem is complete for exponential time. In addition, we sketch how the analysis presented here may be extended naturally to languages with control operators. All of the insights presented give clear examples of how straightforward observations about linearity, and linear logic, may in turn be used to give a greater understanding of functional programming and program analysis.

A method for measuring mode I crack tip constraint under static and dynamic loading conditions

A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity factorK I , the crack tip biaxiality parameter\(\beta = T\sqrt {{{\pi a} \mathord{\left/ {\vphantom {{\pi a} K}} \right. \kern-\nulldelimiterspace} K}} \) is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out under plane stress conditions. Time histories ofK I andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK I and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing trend as β becomes more negative at higher impact velocities.

Study on the coercivity and step effect of mixed magnetic films by micromagnetism and Monte Carlo simulation

The magnetic properties of ferromagnetically and antiferromagnetically mixed fi lms are simulated by micromagnetism method based on the principle of energy mini mum and Monte Carlo technology. The hysteresis loops, spin configurations, and the influences of exchange constant JAA, uniaxial anisotropy constant K, dipolar interaction constant Dand diluted ratio of ferromagnetic ato m X on the coercivity Hc at the ground states are studied systematical ly for the systems studied. A t the same time, the temperature dependence of the coercivity is calculated. The simulated results indicate that: (1) a steplike hysteresis is evidently observed in the mixed magnetic films, and the result calculated by a simple Ising model reveals that the steplike effect can be attributed to the different response of the clusters with different size and different diluted ratio of antiferromagn etic atom on the external field; (2) at the ground states, as 0.5≤X≤1.0,the value of Hc increases with increasing values ofK, JAA, but decreases with increasing value of D; (3) a peak exists in the HcX curves. These simulated resu lts explain the experimental facts about the granular films with antiferromagnetic coupling. The T dependence of the value ofHc for the films with diffe rent magnitude of X can be well described by the law of Tα. But the value of α has a complex variation with the change of X.

Bayesian approach to parameter estimation of the generalized pareto distribution

Several methods have been used for estimating the parameters of the generalized Pareto distribution (GPD), namely maximum likelihood (ML), the method of moments (MOM) and the probability-weighted moments (PWM). It is known that for these estimators to exist, certain constraints have to be imposed on the range of the shape parameter,k, of the GPD. For instance, PWM and ML estimators only exist fork>−0.5 andk≤1, respectively. Moreover, and particularly for small sample sizes, the most efficient method to apply in any practical situation highly depends on a previous knowledge of the most likely values ofk. This clearly suggests the use of Bayesian techniques as a way of using prior information onk. In the present work, we address the issue of estimating the parameters of the GPD from a Bayesian point of view. The proposed approach is compared via a simulation study with ML, PWM and also with the elemental percentile method (EPM) which was developed by Castillo and Hadi (1997). The estimation procedure is then applied to two real data sets.

Thermochemistry of the biochemical reaction: { pyrophosphate(aq) + H2O(l) = 2 phosphate(aq)}

Calorimetric enthalpies of reaction have been measured for the overall biochemical reaction{pyrophosphate(aq) + H2O(l) = 2phosphate (aq)} . The reaction was catalyzed by alkaline phosphatase and, to simplify the thermochemistry, was carried out in the absence of Mg 2+(aq). Measurements were performed with phosphate buffer ( pH = 7.19 and 7.94), PIPES buffer ( pH = 7.13), and HEPES buffer ( pH = 7.86). The results of these measurements were analyzed by using an equilibrium model. These calculations lead to the standard molar enthalpy changeΔrHmo=−(17.3 ± 0.6)kJ·mol−1 (temperature T= 298.15 K and ionic strengthI= 0) for the reference reaction{HP2O73−(aq) + H2O(l) = 2HPO42−(aq) + H+(aq)} . Values of the apparent equilibrium constantK′ for the overall biochemical reaction from the literature were also analyzed by using the equilibrium model in order to obtain what is believed to be a reliable value for the equilibrium constantK= 4.7 · 10−4 for the reference reaction. The values ofK and ΔrHmo for the reference reaction have been used together with values from the CODATA tables to calculate standard molar formation properties for the pyrophosphate species.

Photochemical heterogeneous catalytic reaction at recirculated reactor system

A study was undertaken to examine the possibility of combining a batch-recirculated photoreactor with a ceramic membrane filter for heterogeneous photocatalysis applications. D-cargo red GS (GS) was used as the test substrate and titanium dioxide was used as photocatalyst for this study. The dark adsorption of GS on the TiO2 particle surface was also analyzed. The adsorption trends of GS at various initial concentrations followed the Langmuir isotherm trend. The GS were decolorized from 20% to 70% by the dark adsorption with various concentrations. The photodegradation of GS after the dark adsorption showed the behavior of Langmuir-Hinshelwood model. The variation of recirculation flow rate did not much influence photocatalysis. Variation tendencies of GS concentration were almost similar after about 90 minutes illumination in spite of the flow rate change. The values ofk (apparent first order rate constant) also varied with increase of the recirculation flow rate, but there were no observable significant differences between them.

Formation of excitons from free electron–hole pairs due to acoustic phonon interactions in quantum wells

A study of the process of exciton formation due to acoustic phonon interaction in quantum wells (QWs) is presented. Considering that excitons are formed from photoexcited free electron–hole pairs, we have derived the rate of such formation as a function of density and temperature of charge carriers and wavevectorK|| of the center-of-mass motion of exciton, and finally applied our theory to GaAs/AlGaAs QWs. We have found that the formation of an exciton due to acoustic phonon emission is more efficient at relatively large values ofK|| (hot excitons) whereas that due to longitudinal optical (LO) phonon emission is more efficient at relatively small values of K||.

Transitional behaviors of the average cost of quicksort with median-of-(2t + 1)

A fine analysis is given of the transitional behavior of the average cost of quicksort with median-of-three. Asymptotic formulae are derived for the stepwise improvement of the average cost of quicksort when iterating median-of-threek rounds for all possible values ofk. The methods used are general enough to apply to quicksort with median-of-(2t + 1) and to explain in a precise manner the transitional behaviors of the average cost from insertion sort to quicksort proper. Our results also imply nontrivial bounds on the expected height, "saturation level," and width in a random locally balanced binary search tree.

Effects of Poiseuille flow on peristaltic transport

The effects of Poiseuille flow on peristaltic transport in a cylindrical tube has been investigated. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio (wave amplitude/tube radius) is chosen as a small parameter. The results show that the fluid phase mean axial velocity increases with increasing the Poiseuille parameter k. The phenomena of reflux is discussed. Numerical results are reported for various values of k.

The sequential approach to the product of distribution

It is well known that the sequential approach is one of the main tools of dealing with product, power, and convolution of distribution (cf. Chen (1981), Colombeau (1985), Jones (1973), and Rosinger (1987)). Antosik, Mikusiński, and Sikorski in 1972 introduced a definition for a product of distributions using a delta sequence. However,δ2as a product ofδwith itself was shown not to exist (see Antosik, Mikusiński, and Sikorski (1973)). Later, Koh and Li (1992) chose a fixedδ-sequence without compact support and used the concept of neutrix limit of van der Corput to defineδkand(δ′)kfor some values ofk. To extend such an approach from one-dimensional space tom-dimensional, Li and Fisher (1990) constructed a delta sequence, which is infinitely differentiable with respect tox1,x2,…,xmandr, to deduce a non-commutative neutrix product ofr−kandΔδ. Li (1999) also provided a modifiedδ-sequence and defined a new distribution(dk/drk)δ(x), which is used to compute the more general product ofr−kandΔlδ, wherel≥1, by applying the normalization procedure due to Gel'fand and Shilov (1964). We begin this paper by distributionally normalizingΔr−kwith the help of distributionx+−n. Then we utilize several nice properties of theδ-sequence by Li and Fisher (1990) and an identity ofδdistribution to derive the productΔr−k⋅δbased on the results obtained by Li (2000), and Li and Fisher (1990).

Behaviors of anisotropic fluids in the vicinity of a wedge

The laminar boundary layer flow and heat transfer of anisotropic fluids in the vicinity of a wedge have been examined with constant surface temperature. The similarity variables found by Falkner and Skan are employed to reduce the streamwise-dependence in the coupled nonlinear boundary layer equations. The numerical solutions are presented using the fourth-order Runge-Kutta method and the distribution of velocity, micro-rotation, shear and couple stresses and temperature across the boundary layer are plotted. These results are also compared with the corresponding flow problems for Newtonian fluid over wedges. It is found that for a constant wedge angle, the skin friction coefficient is lower for micropolar fluid, as compared to Newtonian fluid. For the case of the constant material parameterK, however, the magnitude of velocity for anisotropic fluid is greater than that of Newtonian fluid. The numerical results also show that for a constant wedge angle with a given Prandtl number,P γ=1, the effect of increasing values ofK results in increasing thermal boundary layer thickness for anisotropic fluid, as compared with Newtonian fluid. For the case of the constant material parameterK, however, the heat transfer rate for anisotropic fluid is lower than that of Newtonian fluid.

A Rapid, Sensitive, and Nonradioactive Method for Assay of FHIT Ap3A Hydrolase Activity by Fluorescence Thin-Layer Chromatographic Image Analysis

Fhit, a member of the histidine triad superfamily of nucleotide-binding proteins, binds and cleaves diadenosine polyphosphates and functions as a tumor suppressor in human epithelial cancers. Function of Fhit in tumor suppression does not require diadenosine polyphosphate cleavage but correlates with the ability to form substrate complexes. As diadenosine polyphosphates are at lower cellular concentrations than mononucleotides, we sought to quantify interactions between Fhit and competitive inhibitors with the use of diadenosine polyphosphate analogs containing fluorophores in place of one nucleoside. Appp-S-(7-diethylamino-4-methyl-3-(4-succinimidylphenyl)) coumarin (ApppAMC), Appp-S-(4-4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-s-indacine-3-yl) methylaminoacetyl (ApppBODIPY), and GpppBODIPY, synthesized in high yield, are effective Fhit substrates, producing AMP or GMP plus fluorophore diphosphates. GpppBODIPY cleavage is accompanied by a 5.4-fold increase in fluorescence because BODIPY fluorescence is quenched by stacking with guanine. Titration of unlabeled diadenosine polyphosphates, inorganic pyrophosphate, mononucleotides, and inorganic phosphate into fluorescent assays provided values ofK m and KI as competitive inhibitors. The data indicate that Fhit discriminates between good substrates via k cat and against cellular competitors in equilibrium binding terms. Surprisingly, pyrophosphate competes better than purine mononucleotides.

Thermal boundary layer flow of a micropolar fluid past a wedge with constant wall temperature

The steady laminar flow of micropolar fluids past a wedge has been examined with constant surface temperature. The similarity variables found by Falkner and Skan are employed to reduce the streamwise-dependence in the coupled nonlinear boundary layer equation. Numerical solutions are presented for the heat transfer characteristics with Pr=1 using the fourth-order Runge-Kutta method, and their dependence on the material parameters is discussed. The distributions of dimensionless temperature and Nusselt number across the boundary layer are compared with the corresponding flow problems for a Newtonian fluid over wedges. Numerical results show that for a constant wedge angle with a given Prandtl number Pr=1, the effect of increasing values ofK results in an increasing thermal boundary thickness for a micropolar fluid, as compared with a Newtonian fluid. For the case of the constant material parameterK, however, the heat transfer rate for a micropolar fluid is lower than that of a Newtonian fluid.

Spouting and planform selection in the Rayleigh–Taylor instability of miscible viscous fluids

A weakly nonlinear analysis is used to study the initial evolution of the Rayleigh–Taylor instability of two superposed miscible layers of viscous fluid between impermeable and traction-free planes in a field of gravity. Analytical solutions are obtained to second order in the small amplitude of the initial perturbation of the interface, which consists of either rolls or squares or hexagons with a horizontal wavenumber k. The solutions are valid for arbitrary values of k, the viscosity ratio (upper/lower) γ, and the depth ratio r, but are presented assuming that k=kmax(γ, r), where kmax is the most unstable wavenumber predicted by the linear theory. For all planforms, the direction of spouting (superexponential growth of interfacial extrema) is determined by the balance between the tendency of the spouts to penetrate the less viscous layer, and a much stronger tendency to penetrate the thicker layer. When these tendencies are opposed (i.e. when γ>1 with r>1), the spouts change direction at a critical value of r=rc(γ). Hexagons with spouts at their centres are the preferred planform for nearly all values of γ and r, followed closely by squares; the most slowly growing planform is hexagons with spouts at corners. Planform selectivity is strongest when γ[ges ]10 and r[ges ]γ1/3. Application of the results to salt domes in Germany and Iran show that these correspond to points (γ, r) below the critical curve r=rc(γ), indicating that the domes developed from interfacial extrema having subexponential growth rates.

Intertwining operators and polynomials associated with the symmetric group

There is an algebra of commutative differential-difference operators which is very useful in studying analytic structures invariant under permutation of coordinates. This algebra is generated by the Dunkl operators\(T_i : = \frac{\partial }{{\partial x_i }} + k\sum\nolimits_{j \ne i} {\frac{{1 - (ij)}}{{x_i - x_j }}} \), (i=1, ...,N, where (ij) denotes the transposition of the variablesxixj andk is a fixed parameter). We introduce a family of functions {pα}, indexed bym-tuples of non-negative integers α = (α1, ..., αm) form≤N, which allow a workable treatment of important constructions such as the intertwining operatorV. This is a linear map on polynomials, preserving the degree of homogeneity, for which\(T_i V = V\frac{\partial }{{\partial x_i }}\),i = 1, ...,N, normalized byV1=1 (seeDunkl, Canadian J. Math.43 (1991), 1213–1227). We show thatTipα=0 fori>m, and $$V(x_1^{\alpha _1 } \cdots x_m^{\alpha _m } ) = \frac{{\lambda _1 !\lambda _2 ! \cdots \lambda _m !}}{{\left( {Nk + 1} \right)_{\lambda _1 } \left( {Nk - k + 1} \right)_{\lambda _2 } \cdots (Nk - (m - 1)k + 1)_{\lambda _m } }}p_\alpha + \sum\limits_\beta {A_{\beta \alpha } p_{\beta ,} } $$ where (λ1, λ2, ..., λm) is the partition whose parts are the entries of α (That is, λ1➮ λ2➮ ... λm➮0), β = (β1, ..., βm), ∑i=1m βi = ∑i=1m αm and the sorting of β is a partition strictly larger than λ in the dominance order. This triangular matrix representation ofV allows a detailed study. There is an inner product structure on span {pα} and a convenient set of self-adjoint operators, namelyTiρi, whereρipα ≔p(α1, ...., αi + 1, ..., αm). This structure has a bi-orthogonal relationship with the Jack polynomials inm variables. Values ofk for whichV fails to exist are called singular values and were studied byDe Jeu, Opdam, andDunkl in Trans. Amer. Math. Soc.346 (1994), 237–256. As a partial verification of a conjecture made in that paper, we construct, for anya=1,2,3,... such that gcd(N−m+1,a)<(N−m+1)/m andm≤N/2, a space of polynomials annihilated by eachTi fork=−a/(N−m+1) and on which the symmetric groupSN acts according to the representation (N−m, m).

Antisymmetric Amino-Wagging Band of Hydrazine up toK′ = 13 Levels

A newly recorded high-resolution infrared spectrum of hydrazine has been studied in the 729–1198 cm−1region (the ν12antisymmetric wagging band) with a resolution of 0.002 cm−1. About 1350 transitions withK′ from 7 to 13 have been newly assigned and about 2350 transitions with lower values ofK′ reanalyzed with the improved precision. The effective parameters have been calculated separately for each value ofK′ using the Hougen–Ohashi hamiltonian for hydrazine. The extended assignment completes the analysis of the ν12band of hydrazine.

Coins with Arbitrary Weights

Given a set ofmcoins out of a collection of coins ofkunknown distinct weights, we wish to decide if all themgiven coins have the same weight or not using the minimum possible number of weighings in a regular balance beam. Letm(n,k) denote the maximum possible number of coins for which the problem can be solved innweighings. It is known thatm(n,2)=n(1/2+o(1))n. Here we determine the asymptotic behavior ofm(n,k) for larger values ofk. Surprisingly it turns out that for all 3≤k≤n+1,m(n,k) is much smaller thanm(n,2) and satisfiesm(n,k)=Θ(nlogn/logk).