Derivative-free global ship design optimization using global/local hybridization of the DIRECT algorithm

The application of global/local hybrid DIRECT algorithms to the simulation-based hull form optimization of a military vessel is presented, aimed at the reduction of the resistance in calm water. The specific features of the black-box-type objective function make the problem suitable for the application of DIRECT-type algorithms. The objective function is given by numerical iterative procedures, which could lead to inaccurate derivative calculations. In addition, the presence of local minima cannot be excluded a priori. The algorithms proposed (namely DIRMIN and DIRMIN-2) are hybridizations of the classic DIRECT algorithm, with deterministic derivative-free local searches. The algorithms’ performances are first assessed on a set of test problems, and then applied to the ship optimization application. The numerical results show that the local hybridization of the DIRECT algorithm has beneficial effects on the overall computational cost and on the efficiency of the simulation-based optimization procedure.     

Construction of cyclic codes over \mathbb F _2+u\mathbb F _2 for DNA computing

We construct codes over the ring $\mathbb F _2+u\mathbb F _2$ with $u^2=0$ for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the $GC$ content constraint, and avoid the secondary structure. They are derived from cyclic reverse-complement codes over the ring $\mathbb F _2+u\mathbb F _2$ . We also construct an infinite family of BCH DNA codes.     

Derivation of constraint-dependent J–R curves based on modified T-stress parameter and GTN model for a low-alloy steel

In this paper, a modified load-independent $T$ -stress constraint parameter $\tau ^{*}$ was defined. The $\tau ^{*}$ of specimens with different crack-tip constraint levels at different $J$ -integrals was calculated, and its load-independence has been validated. Based on the modified constraint parameter $\tau ^{*}$ and the numerically calculated J–R curves by using the Gurson–Tvergaard–Needleman (GTN) model for the SENB specimens with different $a/W$ , the equations of constraint-dependent J–R curves for the A508 steel were obtained. The predicted J–R curves using the equations essentially agree with the experimental and calculated J–R curves. The transferability of the constraint-dependent J–R curves to the CT, SENT and CCT specimens was validated. The results show that the modified constraint parameter $\tau ^{*}$ and the GTN model can be effectively used to derive the constraint-dependent J–R curves for ductile materials.     

Heat transfer rates in sheared beds of inertial particles at high Biot numbers

We investigate heat conduction rates through the contact network of sheared granular materials that consist of particles with a density much larger than that of the ambient fluid. The tool ParScale, a finite difference solver for intra-particle transport processes, is coupled to the discrete element method solver LIGGGHTS to carry out the simulations. Heat transfer to the surrounding fluid is considered via a fixed heat transfer coefficient. We identify a combination of Biot and Peclet number as the key non-dimensional influence parameter to describe the non-dimensional heat flux through the particle bed and provide an analytical solution to calculate mean particle temperature profiles. Simulations over a wide range of particle volume fractions, Biot and Peclet numbers are then performed in order to develop a continuum model for the heat flux. We show that for Biot numbers below \(10^{-3}\) our results agree with a simple model based on a uniform particle temperature. However, for Biot numbers above a certain threshold, the conductive heat flux decreases substantially depending on the flow situation, and temperature gradients within the particle should be considered in order to correctly predict the heat transfer rate to the surrounding fluid.     

Nonclassical analysis of the nonlinear Kompaneets equation

The dimensional nonlinear Kompaneets (NLK) equation ${u_{t} = x^{-2}[x^{4}(\alpha{u}_{x} + \beta{u} + \gamma{u}^{2})]_{x}}$ describes the spectra of photons interacting with a rarefied electron gas. Recently, Ibragimov obtained some time-dependent exact solutions for several approximations of this equation. In this paper, we use the nonclassical method to construct time-dependent exact solutions for the NLK equation ${u_{t} = x^{-2}[x^{4}(\alpha{u}_{x} + \gamma{u}^{2})]_{x}}$ for arbitrary constants α > 0, γ > 0. Solutions arising from “nonclassical symmetries” are shown to yield wider classes of time-dependent exact solutions for the NLK equation ${u_{t} = x^{-2}[x^{4}(\alpha{u}_{x} + \gamma{u}^{2})]_{x}}$ beyond those obtained by Ibragimov. In particular, for five classes of initial conditions, each involving two parameters, previously unknown explicit time-dependent solutions are obtained. Interestingly, each of these solutions is expressed in terms of elementary functions. Three of the classes exhibit quiescent behavior, i.e., ${\lim_{t\rightarrow \infty}u(x,t) = 0}$ , and the other two classes exhibit blow-up behavior in finite time. As a consequence, it is shown that the corresponding nontrivial stationary solutions are unstable.     

The assembly line balancing and scheduling problem with sequence-dependent setup times: problem extension, model formulation and efficient heuristics

Assembly line balancing problems (ALBP) consist of distributing the total workload for manufacturing any unit of the products to be assembled among the work stations along a manufacturing line as used in the automotive or the electronics industries. Usually, theory assumes that, within each station, tasks can be executed in an arbitrary precedence-feasible sequence without changing station times. In practice, however, the task sequence may influence the station time considerably as sequence-dependent setups (e.g., walking distances, tool changes) have to be considered. Including this aspect leads to a joint balancing and scheduling problem, which we call SUALBSP (setup assembly line balancing and scheduling problem). In this paper, we modify the problem by modeling setups more realistically, give a new, more compact mathematical model formulation and develop effective heuristic solution procedures. Computational experiments based on existing and new data sets indicate that the new procedures outperform formerly proposed heuristics. They are able to solve problem instances of real-world size with small deviations from optimality in computation times short enough to be accepted in real-world decision support systems.     

Looking for the best modes helps solving the MRCPSP/max

The multi-mode resource-constrained project scheduling problem with minimum and maximum time lags MRCPSP/max is a very general project scheduling problem with multiple execution modes per activity, renewable and non-renewable resources and minimum and maximum time lags between activities. In this paper, we describe SA-EVA, an algorithm for the problem. SA-EVA first searches for the best mode for each activity, without considering renewable resources. In this phase a simulated annealing is applied. Once a mode vector has been chosen, the problem reduces to the RCPSP/max, which SA-EVA solves with EVA, an algorithm designed in Ballestín et al. [2009. An evolutionary algorithm for the resource-constrained project scheduling problem with minimum and maximum time-lags. Journal of Scheduling, 14 (4), online]. Computational results show that SA-EVA outperforms the state-of-the-art algorithms in medium and large instances.     

Preliminary Results of the MARE Experiment

The microcalorimeter array for a rhenium experiment (MARE) project aims at the direct and calorimetric measurement of the electron neutrino mass with sub-eV sensitivity. The design is based on large arrays of thermal detectors to study the beta decay of \(^{187}\) Re and the electron capture of \(^{163}\) Ho. One of the activities of the project, MARE 1 in Milan, has started in Milan using one array of 6  \(\times \)  6 silicon implanted thermistors equipped with AgReO \(_4\) absorbers. The purposes of MARE 1 in Milan are to achieve a sensitivity on the neutrino mass of a few eV and to investigate the systematics of \(^{187}\) Re neutrino mass measurements, focusing on those caused by the beta environmental fine structure and the beta spectrum theoretical shape. In parallel, the MARE collaboration is performing an R&D work for producing absorbers embedded with radioactive metal \(^{163}\) Ho. We report here the status of MARE using Re as beta source and the preliminary results obtained with \(^{163}\) Ho.     

Some results on the differential functions over finite fields

Let \(g\) be a function over \(\mathbb {F}_q\) . If there exist a function \(f\) and \(a\in \mathbb {F}_q^*\) such that \(g(x)=f(x+a)-f(x)\) , then we call \(g\) a differential function and call \(f\) a differential-inverse of \(g\) . We present two criteria to decide whether a given \(g\) is a differential function. The set of the degrees of all differential functions over \({\mathbb {F}}_q\) is determined. Then we give a lower bound and an upper bound on the number of differential functions over \({\mathbb {F}}_q\) . Besides, we show how to construct differential inverses of a given differential function. At last, some applications of our results are introduced.     

On the error linear complexity spectrum of p^{n}-periodic binary sequences

The error linear complexity spectrum of a periodic sequence is defined to be the ordered list of $k$ -error linear complexities of the sequence. In this paper, we present an algorithm which computes the error linear complexity spectrum for binary sequences with period $p^{n}$ , where $p$ is an odd prime and $2$ is a primitive root modulo $p^{2}$ .     

Block-simultaneous direction method of multipliers: a proximal primal-dual splitting algorithm for nonconvex problems with multiple constraints

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function f of multiple arguments with potentially multiple constraints \(g_\circ\) on each of them. The function f may be nonconvex as long as it is convex in every argument, while the constraints \(g_\circ\) need to be convex but not smooth. If f is smooth, the proposed Block-Simultaneous Direction Method of Multipliers (bSDMM) can be interpreted as a proximal analog to inexact coordinate descent methods under constraints. Unlike alternative approaches for joint solvers of multiple-constraint problems, we do not require linear operators \({{\mathsf {L}}}\) of a constraint function \(g({{\mathsf {L}}}\ \cdot )\) to be invertible or linked between each other. bSDMM is well-suited for a range of optimization problems, in particular for data analysis, where f is the likelihood function of a model and \({{\mathsf {L}}}\) could be a transformation matrix describing e.g. finite differences or basis transforms. We apply bSDMM to the Non-negative Matrix Factorization task of a hyperspectral unmixing problem and demonstrate convergence and effectiveness of multiple constraints on both matrix factors. The algorithms are implemented in python and released as an open-source package.     

Limit laws for the maxima of stationary chi-processes under random index

Let \(\{\chi _{k}(t), t\ge 0\}\) be a stationary \(\chi \) -process with \(k\) degrees of freedom. In this paper, we consider the maxima \(M_{k}(T)= \max \{\chi _{k}(t), \forall t\in [0,T]\}\) with random index \(\mathcal {T}_{T}\) , where \(\mathcal {T}_{T}/T\) converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of \(M_{k}(\mathcal {T}_{T})\) exists under some additional conditions.     

On the automorphism group of a binary self-dual [120, 60, 24] code

We prove that an automorphism of order 3 of a putative binary self-dual $[120, 60, 24]$ [ 120 , 60 , 24 ] code $C$ C has no fixed points. Moreover, the order of the automorphism group of $C$ C divides $2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$ 2 a · 3 · 5 · 7 · 19 · 23 · 29 with $a\in \mathbb N _0$ a ∈ N 0 . Automorphisms of odd composite order $r$ r may occur only for $r=15, 57$ r = 15 , 57 or $r=115$ r = 115 with corresponding cycle structures $3 \cdot 5$ 3 · 5 - $(0,0,8;0), 3\cdot 19$ ( 0 , 0 , 8 ; 0 ) , 3 · 19 - $(2,0,2;0)$ ( 2 , 0 , 2 ; 0 ) or $5 \cdot 23$ 5 · 23 - $(1,0,1;0)$ ( 1 , 0 , 1 ; 0 ) respectively. In case that all involutions act fixed point freely we have $|\mathrm{Aut}(C)| \le 920$ | Aut ( C ) | ≤ 920 , and $\mathrm{Aut}(C)$ Aut ( C ) is solvable if it contains an element of prime order $p \ge 7$ p ≥ 7 . Moreover, the alternating group $\mathrm{A}_5$ A 5 is the only non-abelian composition factor which may occur in $\mathrm{Aut}(C)$ Aut ( C ) .     

Toward a Detector/Readout Architecture for the Background-Limited Far-IR/Submm Spectrograph (BLISS)

We have built and tested 32-element linear arrays of absorber-coupled transition-edge sensors (TESs) read out with a time-division SQUID multiplexer. This detector/readout architecture is designed for the background-limited far-IR/submm spectrograph (BLISS) which is a broadband (35–433  \(\upmu \) m), grating spectrometer consisting of six wavebands each with a modest resolution of R \(\sim \) 700. Since BLISS requires the effective noise equivalent power (NEP) of the TESs to equal 1  \(\times \)  10 \(^{-19}\)  W/Hz \(^{1/2}\) , our detectors consist of very long (1–2 mm), narrow (0.4 \(\upmu \) m), and thin (0.25 \(\upmu \) m) Si \(_{x}\) N \(_{y}\) support beams that reduce the thermal conductance G between the substrate and the optical absorber. The thermistors of our lowest noise TESs consist of iridium with \(T_{c}=130\) mK. We have measured the electrical properties of arrays of these Ir TESs with various meander and straight support beams and absorber shapes and found that G is \(\sim \) 30 fW/K (meander) and \(\sim \) 110 fW/K (straight), the electrical NEP is 2–3  \(\times \)  10 \(^{-19}\) W/Hz \(^{1/2}\) (meander and straight), and the response time \(\tau \) is 10–30 ms (meander) and 2–5 ms (straight). To reduce spurious or “dark” power from heating the arrays, we mounted the arrays into light-tight niobium boxes and added custom L/R and L/C low-pass chip filters into these boxes to intercept dark power from the bias and readout circuit. We found the average dark power equals 1.3 and 4.6 fW for the boxes with L/R and L/C chip filters, respectively. We have built arrays with \(T_{c}= 70\)  mK using molybdenum/copper bilayers and are working to lower the dark power by an order of magnitude so we can demonstrate NEP \(~=~1~\times \)  10 \(^{-19}\)  W/Hz \(^{1/2}\) with these arrays. PACS numbers: 85.25.Pb; 95.85.Gn; 95.85.Fm; 63.22. \(+\) m     

Effect of anisotropic permeability on convective heat transfer through a porous river bed underlying a fluid layer

A study is made of convective heat transfer through packed porous beds which consist of a horizontal fluid layer (river bed) and a porous zone with anisotropic permeability and underlaid by a surface heated to a constant temperature $T_1$ . The free surface of the fluid layer overlying the horizontal porous layer is heated isothermally at temperature $T_2$ ( $>T_1$ ). Using the Navier–Stokes model for the fluid layer and the generalized Brinkman-extended Darcy model for the porous zone, an exact solution is found for a fully developed system of forced convective flow through the superposed layers. The Beavers–Joseph condition is applied at the interface between the two layers. The influence of hydrodynamic anisotropy on the convective phenomenon is investigated analytically. It is shown that the anisotropic permeability ratio $K^*$ , the inclination angle of the principal axes $\varphi $ of the porous medium, and the thickness of the porous lining $\epsilon $ have a strong influence on the convective flow and the heat transfer rate. This analysis helps to predict environmental aquatic behavior.     

Worst-case analysis of the LPT algorithm for single processor scheduling with time restrictions

We consider the following scheduling problem. We are given a set S of jobs which are to be scheduled sequentially on a single processor. Each job has an associated processing time which is required for its processing. Given a particular permutation of the jobs in S, the jobs are processed in that order with each job started as soon as possible, subject only to the following constraint: For a fixed integer \(B \ge 2\), no unit time interval \([x, x+1)\) is allowed to intersect more than B jobs for any real x. There are several real world situations for which this restriction is natural. For example, suppose in addition to the jobs being executed sequentially on a single main processor, each job also requires the use of one of B identical subprocessors during its execution. Each time a job is completed, the subprocessor it was using requires one unit of time to reset itself. In this way, it is never possible for more than B jobs to be worked on during any unit interval. In Braun et al. (J Sched 17: 399–403, 2014a) it is shown that this problem is NP-hard when the value B is variable and a classical worst-case analysis of List Scheduling for this situation has been carried out. We prove a tighter bound for List Scheduling for \(B\ge 3\) and we analyze the worst-case behavior of the makespan \(\tau _\mathrm{LPT}(S)\) of LPT (longest processing time first) schedules (where we rearrange the set S of jobs into non-increasing order) in relation to the makespan \(\tau _o(S)\) of optimal schedules. We show that LPT ordered jobs can be processed within a factor of \(2-2/B\) of the optimum (plus 1) and that this factor is best possible.     

An algorithm for computing the error sequence of p^{n}-periodic binary sequences

For binary sequences with period \(p^{n}\) , where \(p\) is an odd prime and 2 is a primitive root modulo \(p^{2}\) , we present an algorithm which computes the minimum number \(k\) so that the \(k\) -error linear complexity is not greater than a given constant \(c\) . An associated error sequence which gives the \(k\) -error linear complexity is also obtained.     

An extension of the (strong) primitive normal basis theorem

An extension of the primitive normal basis theorem and its strong version is proved. Namely, we show that for nearly all \(A = {\small \left( \begin{array}{cc} a&{}b \\ c&{}d \end{array} \right) } \in \mathrm{GL}_2(\mathbb {F}_{q})\) , there exists some \(x\in \mathbb {F}_{q^m}\) such that both \(x\) and \((-dx+b)/(cx-a)\) are simultaneously primitive elements of \(\mathbb {F}_{q^m}\) and produce a normal basis of \(\mathbb {F}_{q^m}\) over \(\mathbb {F}_q\) , granted that \(q\) and \(m\) are large enough.