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A recurrent neural network (RNN) can generate a sequence of patterns as the temporal evolution of the output vector. This paper focuses on a continuous-time RNN model with a piecewise-linear activation function that has neither external inputs nor hidden neurons, and studies the problem of finding the parameters of the model so that it generates a given sequence of bipolar vectors. First, a sufficient condition for the model to generate the desired sequence is derived, which is expressed as a system of linear inequalities in the parameters. Next, three approaches to finding solutions of the system of linear inequalities are proposed: One is formulated as a convex quadratic programming problem and others are linear programming problems. Then, two types of sequences of bipolar vectors that can be generated by the model are presented. Finally, the case where the model generates a periodic sequence of bipolar vectors is considered, and a sufficient condition for the trajectory of the state vector to converge to a limit cycle is provided.

In this paper, we present a new hybrid spectral-conjugate gradient (SCG) algorithm for finding approximate solutions to nonlinear monotone operator equations. The hybrid conjugate gradient parameter has the Polak–Ribiere–Polyak (PRP), Dai–Yuan (DY), Hestenes–Stiefel (HS) and Fletcher–Reeves (FR) as special cases. Moreover, the spectral parameter is selected such that the search direction has the descent property. Also, the search directions are bounded and the sequence of iterates generated by the new hybrid algorithm converge globally. Furthermore, numerical experiments were conducted on some benchmark nonlinear monotone operator equations to assess the efficiency of the proposed algorithm. Finally, the algorithm is shown to have the ability to recover disturbed signals.

Nearest neighbor (NN) is a simple machine learning algorithm, which is often used in classification problems. In this paper, a concept of modified nearest neighbor (MNN) is proposed to strengthen the optimization capability of artificial bee colony (ABC) algorithm. The new approach is called ABC based on modified nearest neighbor sequence (NNSABC). Firstly, MNN is used to construct solution sequences. Unlike the original roulette selection, NNSABC randomly chooses a solution from the corresponding nearest neighbor sequence to generate offspring. Then, two novel search strategies based on the modified nearest neighbor sequence are employed to build a strategy pool. In the optimization process, different search strategies are dynamically chosen from the strategy pool according to the current search status. In order to study the optimization capability of NNSABC, two benchmark sets including 22 classical problems and 28 CEC 2013 complex problems are tested. Experimental results show NNSABC obtains competitive performance when compared with twenty-three other ABCs and evolutionary algorithms.

We introduce an object called a tree growing sequence (TGS) in an effort to generalize bijective correspondences between G -parking functions, spanning trees, and the set of monomials in the Tutte polynomial of a graph G . A tree growing sequence determines an algorithm which can be applied to a single function, or to the set P G , q of G -parking functions. When the latter is chosen, the algorithm uses splitting operations – inspired by the recursive definition of the Tutte polynomial – to iteratively break P G , q into disjoint subsets. This results in bijective maps τ and ρ from P G , q to the spanning trees of G and Tutte monomials, respectively. We compare the TGS algorithm to Dhar’s algorithm and the family described by Chebikin and Pylyavskyy in 2005. Finally, we compute a Tutte polynomial of a zonotopal tiling using analogous splitting operations.

Various crowdsourced logistics platforms are forming rapidly along with the booming mobile Internet. Motivated by modern crowdsourced truck logistics platforms, we introduce the online crowdsourced truck delivery (OCTD) problem and reformulate it as the online bipartite hyper-matching problem. We then explore the possibility of accommodating historical information to design efficient online algorithms to serve online orders. To the best of our knowledge, it is the first work on incorporating historical information to solve the online bipartite hyper-matching problem. Depending on whether orders can be partially served, we investigate two practical situations, i.e. separable and inseparable cases. For the inseparable case, we propose a randomized online algorithm, named Hyper-Matching , whose competitive ratio is a non-decreasing function of the amount of historical information. For the separable case, we modify Hyper-Matching to present another randomized online algorithm, named Separable-Hyper-Matching . It is worth noting that the competitive ratios of Hyper-Matching and Separable-Hyper-Matching either beat or match the current best online algorithms when no historical information is considered. We then present four computationally efficient heuristic algorithms, including a greedy variant and a batch-processing variant for each of the inseparable and separable cases. We perform a sequence of experiments using synthetic and real-world datasets, with an emphasis on the influence that historical information has on algorithm performance. The experiment results demonstrate the effectiveness of our algorithms and particularly the positive influence of historical information on our algorithms.

Let G be a finite group. For a positive integer d, let s d N ( G ) denote the smallest integer l such that every sequence S over G of length | S | ≥ l has a nonempty product-one subsequence T with | T | ≡ 0 (mod d). In this paper, we mainly study this invariant for dihedral groups D 2 n and metacyclic groups C p ⋉ s C q .

We define and analyze the notion of variational Wardrop equilibrium for nonatomic aggregative games with an infinity of players types. These equilibria are characterized through an infinite-dimensional variational inequality. We show, under monotonicity conditions, a convergence theorem enables to approximate such an equilibrium with arbitrary precision. To this end, we introduce a sequence of nonatomic games with a finite number of players types, which approximates the initial game. We show the existence of a symmetric Wardrop equilibrium in each of these games. We prove that those symmetric equilibria converge to an equilibrium of the infinite game, and that they can be computed as solutions of finite-dimensional variational inequalities. The model is illustrated through an example from smart grids: the description of a large population of electricity consumers by a parametric distribution gives a nonatomic game with an infinity of different players types, with actions subject to coupling constraints., arXiv admin note: substantial text overlap with arXiv:1806.06230

In this paper we study time-dependent scheduling problems where activities consume a resource with limited availability. Activity durations as well as resource consumptions are assumed to be time-dependent and the resource can be replenished between activities. Because of the interaction of time-dependent activity durations and resource consumptions, scheduling policies based on starting all activities as early as possible may fail due to unnecessarily high resource consumptions. We propose a dynamic discretization discovery algorithm that generates a partially time-expanded network during the search. We propose preloading techniques allowing to significantly reduce the computational effort if the approach is embedded in an iterative solution procedure that frequently evaluates activity sequences that start with the same activities. We evaluate our approaches on a case of routing a fleet of electric vehicles in which vehicles can recharge batteries during the route., 40 pages

This paper introduces the multiphase course timetabling problem and presents mathematical formulations and effective solution algorithms to solve it in a real case study. Consider a pool of lessons and a number of students who are required to take a subset of these lessons to graduate. Each lesson consists of a predetermined and consecutive sequence of phases with possibly different resource requirements and duration. Students who take a lesson must be present in certain phases of the lesson. Similarly, resources that are allocated to the lesson must be present in certain phases of the lesson depending on their roles. The objective is to maximize the weighted sum of student-lesson allocations subject to some capacity, availability and prerequisite constraints. The problem is formulated as an integer linear program called the session-index formulation. The formulation is then extended by introducing various side constraints that capture business requirements of a pilot training program. An enhanced branch-and-check algorithm is proposed to solve the problem more efficiently. Large instances of the problem are solved by utilizing an effective fix-and-optimize matheuristic. Results of a computational study on a set of real-world instances of the problem demonstrate the efficacy of the proposed exact and matheuristic algorithms. Due to the novelty and complexity of the problem, the efficacy of the proposed methodology to solve its real-world instances, and the implementation and realization of these contributions within a decision support system, this work was recognized as a semi-finalist of INFORMS Franz Edelman Award (2021).

N6,2'-O-dimethyladenosine (m6Am) is a reversible modification widely occurred on varied RNA molecules. The biological function of m6Am is yet to be known though recent studies have revealed its influences in cellular mRNA fate. Precise identification of m6Am sites on RNA is vital for the understanding of its biological functions. We present here m6AmPred, the first web server for in silico identification of m6Am sites from the primary sequences of RNA. Built upon the eXtreme Gradient Boosting with Dart algorithm (XgbDart) and EIIP-PseEIIP encoding scheme, m6AmPred achieved promising prediction performance with the AUCs greater than 0.954 when tested by 10-fold cross-validation and independent testing datasets. To critically test and validate the performance of m6AmPred, the experimentally verified m6Am sites from two data sources were cross-validated. The m6AmPred web server is freely accessible at: https://www.xjtlu.edu.cn/biologicalsciences/m6am, and it should make a useful tool for the researchers who are interested in N6,2'-O-dimethyladenosine RNA modification.

The primary sequences of DNA, RNA and protein have been used as the dominant information source of existing machine learning tools, especially for contexts not fully explored by wet-experimental approaches. Since molecular markers are profoundly orchestrated in the living organisms, those markers that cannot be unambiguously recovered from the primary sequence often help to predict other biological events. To the best of our knowledge, there is no current tool to build and deploy machine learning models that consider genomic evidence. We therefore developed the WHISTLE server, the first machine learning platform based on genomic coordinates. It features convenient covariate extraction and model web deployment with 46 distinct genomic features integrated along with the conventional sequence features. We showed that, when predicting m6A sites from SRAMP project, the model integrating genomic features substantially outperformed those based on only sequence features. The WHISTLE server should be a useful tool for studying biological attributes specifically associated with genomic coordinates, and is freely accessible at: www.xjtlu.edu.cn/biologicalsciences/whi2.

International audience; PURPOSE: Using large French retrospective study cohort of chemotherapy-naïve metastatic castration-resistant prostate cancer patients (mCRPC; n = 10,308) comparing survival between patients who initiated abiraterone (ABI; 64%) and those initiating enzalutamide (ENZ; 36%), the present objective was to describe treatment patterns in the 2 years following initiation. METHOD: Using the national health data system (SNDS) from 2014 to 2018, we first explored the number of treatment lines, and secondly, patterns of patient management using state sequence analysis; cluster analyses were performed on the 0 to 12 month and 13 to 24 month periods. Age, Charlson score, and duration of androgen deprivation therapy (ADT) were obtained for each cluster in the first year of follow-up. RESULTS: Patients with only 1 treatment line accounted for 52%. In the 0 to 12 month sequence analysis, the main clusters among ABI/ENZ new users involved patients who continued the initial treatment (54% of 65% respectively) and discontinued active treatment (14.5% for both). Less than 2 years exposure to ADT prior to ABI/ENZ initiation was frequently observed for noncontrolled mCRPC, as shown in the death and switch from ABI/ENZ to docetaxel clusters. The clusters for a switch ABI/ENZ to ENZ/ABI involved 6% to 11% of the patients. CONCLUSION: Our study suggested fairly similar patterns between ABI and ENZ initiation. The cluster of patients with active treatment discontinuation needs to be further investigated, as well as factors influencing therapeutic choice. Better understanding for the use of second-generation hormone therapy in mCRPC in real life, could improve its implementation by clinicians in the early stages of prostate cancer.

We define a new metric between natural numbers induced by the $\ell_\infty$ norm of their unique prime signatures. In this space, we look at the natural analog of the number line and study the arithmetic function $L_\infty(N)$, which tabulates the cumulative sum of distances between consecutive natural numbers up to $N$ in this new metric. Our main result is to identify the positive and finite limit of the sequence $L_\infty(N)/N$ as the expectation of a certain random variable. The main technical contribution is to show with elementary probability that for $K=1,2$ or $3$ and $\omega_0,\ldots,\omega_K\geq 2$ the following asymptotic density holds $$ \lim_{n\to\infty}\frac{\big|\big\{M\leq n:\; \|M-j\|_\infty, Comment: This article supersedes arXiv:1711.02903. v3: accepted version in J. Number Theory with additional Appendix. v2: Conjecture 1 and 2 of v1 are now proved, major revision of exposition

A portmanteau-type statistic based on sample covariance is proposed to test for the existence of the unit-root of an autoregressive model under a heavy-tailed linear noise, where the noise ɛ t = ∑ j = 0 ∞ d j η t − j and { η t } is a sequence of i.i.d. innovations belonging to the domain of attraction of an α -stable distribution for some α ∈ ( 0 , 2 ) . The proposed procedure is nonparametric and easy to implement. Under certain regular assumptions, the limit distribution of the statistics is shown to be a functional of a standard stable distribution. Further, the good finite sample studies show that the new test outperforms PP, DF and ADF tests in size and power. Applications to the daily world crude oil price and 3-month AA financial commercial paper rate are also given to illustrate the performance of the new test.

Urban public transportation agencies sometimes have to operate mixing vehicles of different sizes on their routes, due to resource limitations or historical reasons. Services with different passenger-carrying capacities are provided to passengers during a mixed-fleet operation. A fundamental question arising here is how to optimally deploy a given fleet of different bus sizes to provide services that minimize passenger waiting time. We formulate a mixed-fleet vehicle dispatching problem as a Mixed-Integer Nonlinear Programming (MINLP) model to optimize dispatching schemes (dispatching orders and times) when a given set of buses of different sizes are available to serve demand along a route. The objective is to minimize the average passenger waiting time under time-dependent demand volumes. Stochastic travel times between stops and vehicle capacity constraints (i.e., introducing extra waiting time due to denied boarding) are explicitly modeled. A Simulated Annealing (SA) algorithm coupled with a Monte Carlo simulation framework is developed to solve large real-world instances in the presence of stochastic travel times. Results show that, in addition to dispatching headway, bus dispatching sequence can strongly affect waiting times under a mixed-fleet operation. Indeed, with an optimal dispatching sequence, a more accurate adjustment of supply to demand is possible in accordance with time-dependent demand conditions, and the total savings in waiting time are mainly driven by a further reduction in the number of passengers left behind. The optimality of uneven dispatching headways stems from two elements: having a mixed fleet and having localized peaks on demand that make buses run full.

Let $s_0,s_1,s_2,\ldots$ be a sequence of rational numbers whose $m$th divided difference is integer-valued. We prove that $s_n$ is a polynomial function in $n$ if $s_n \ll \theta^n$ for some positive number $\theta$ satisfying $\theta < e^{1 + \tfrac{1}{2} + \cdots+ \tfrac{1}{m}} -1$., Comment: 18 pages; revised for clarity

The unweighed oriented variable-sized two-dimensional guillotine bin packing problem consists in packing without overlap small rectangular items into large non-identical rectangular bins, with the items obtained via guillotine cuts. It minimizes the waste of the used bins. It is herein approximately solved using a hybrid matheuristic, which applies a sequence of low-level mixed-integer programs that reserve space for unpacked items and that are guided by feasibility constraints and by upper bounds on the objective function. The embedded constraints constitute a lookahead mechanism that prohibits the investigation of infeasible directions and constrains the search to improving ones. The matheuristic further employs high-level diversification and intensification mechanisms. The diversification incorporates a sequential value correction algorithm that tags a pseudo-price to each item to govern the fitness functions of mixed integer programs and subsequently their solution construction process. The intensification is a local search that investigates the neighbourhood of promising solutions. The extensive computational experiments provide evidence of the good performance of the proposed matheuristic. For the variable-sized bin packing benchmark instances, the matheuristic matches and improves 90.8% of the upper bounds. For the single bin-size bin packing benchmark instances, the matheuristic further proves the optimality of 82.6% upper bounds while it matches 14.4% and improves 2.6% existing bounds.

In this paper we consider the fractional parts of a general sequence, for example the sequence $\alpha \sqrt{n}$ or $\alpha n^2$. We give a general method, which allows one to show that long-range correlations (correlations where the support of the test function grows as we consider more points) are Poissonian. We show that these statements about convergence can be reduced to bounds on associated Weyl sums. In particular we apply this methodology to the aforementioned examples. In so doing, we recover a recent result of Technau-Walker (2020) for the triple correlation of $\alpha n^2$ and generalize the result to higher moments. For both of the aforementioned sequences this is one of the only results which indicates the pseudo-random nature of the higher level ($m \ge 3$) correlations., Comment: 132 pages

Open-source pulse sequence programs offer an accessible and transparent approach to sequence development and deployment. However, a common framework for testing, documenting, and sharing open-source sequences is still needed to ensure sequence usability and repeatability. We propose and demonstrate such a framework by implementing two sequences, Inversion Recovery Spin Echo (IRSE) and Turbo Spin Echo (TSE), with PyPulseq, and testing them on a commercial 3 T scanner. We used the ACR and ISMRM/NIST phantoms for qualitative imaging and T1/T2 mapping, respectively. The qualitative sequences show good agreement with vendor-provided counterparts (mean Structural Similarity Index Measure (SSIM) = 0.810 for IRSE and 0.826 for TSE). Both sequences passed five out of the seven standard ACR tests, performing at similar levels to vendor counterparts. Compared to reference values, the coefficient of determination R2 was 0.9946 for IRSE T1 mapping and 0.9331 for TSE T2 mapping. All sequences passed the scanner safety check for a 70 kg, 175 cm subject. The framework was demonstrated by packaging the sequences and sharing them on GitHub with data and documentation on the file generation, acquisition, reconstruction, and post-processing steps. The same sequences were tested at a second site using a 1.5 T scanner with the information shared. PDF templates for both sequence developers and users were created and filled.

Let M be a positive integer and q ∈ ( 1 , M + 1 ] . A q-expansion of a real number x is a sequence ( c i ) = c 1 c 2 ⋯ with c i ∈ { 0 , 1 , … , M } such that x = ∑ i = 1 ∞ c i q − i . Let U q j denote the set of numbers having exactly j expansions. Contrary to the unique expansions, we prove for each j ≥ 2 that the set U q j is closed only if it is empty. Then we generalize an important example of Sidorov by exhibiting many non-trivial bases q for which the Hausdorff dimension of U q j is independent of j.

This work presents a derivative-free trust-region algorithm for probability maximization problems. We assume that the probability function is continuously differentiable with Lipschitz continuous gradient, but no derivatives are available. The algorithm explores the particular structure of the probability objective function through models based on copulae. Under reasonable assumptions, the global convergence of the algorithm is analyzed: we prove that all accumulation points of the sequence generated by the algorithm are stationary. The proposed approach is validated by encouraging numerical results on academic and industrial problems.

A multi-party quantum key distribution protocol based on repetitive code is designed for the first time in this paper. First we establish a classical (t, n) threshold protocol which can authenticate the identity of the participants, and encode the classical key sequence in accordance with this repetitive code. Then unitary transformation of the quantum state sequence corresponding to this encoded sequence is carried out by using the parameters from this (t, n) threshold protocol. Furthermore, we derive two thresholds for whether or not reserving the measured values of the received sequence, and extract the classical subkey sequence from the measured values conforming to these two threshold conditions. This protocol can authenticate the identity of the participant, resist the attack from the internal and external participants, and do not need the decoy state particles when testing the eavesdropper, which is more efficient than the similar protocols, and also saves the quantum resources.

The aim of this work is to give some fixed point results based on the technique of measure of noncompactness which extend the classical Darbo’s theorem. With the help of our Darbo-type theorem, we obtain the existence of solution of implicit fractional integral equations in C ( I , l p α ) (collection of all continuous functions from I = [ 0 , a ] ( a > 0 ) to l p α ), where l p α is a tempered sequence space. Finally, we present a numerical example to see the validity and practicability of our existence result.

The problem of constructing the most powerful test for random number generators (RNGs) is considered, where the generators are modelled by stationary ergodic processes. At present, RNGs are widely used in data protection, modelling and simulation systems, computer games, and in many other areas where the generated random numbers should look like binary numbers of a Bernoulli equiprobable sequence. Another problem considered is that of constructing effective statistical tests for random number generators (RNG). Currently, effectiveness of statistical tests for RNGs is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the p -value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the p -value for any (unknown) stationary ergodic source. This model appears to be acceptable for binary sequences generated by physical devices that are used in cryptographic data protection systems.

In this work, we investigate deterministic mechanisms that generate and perpetuate flutter and fibrillation in the right atrium of the human heart using mathematical models and high-performance computational simulations. Using a GPU, the solutions of systems of as much as 360 000 cells of 29 variables each were distributed among the available processors to simulate a cell-to-cell electric behavior of heart tissue. Moreover, in a smaller array of 462 cells, we showed that fibrillation, fluttering, and fibrillation-to-fluttering can be modeled even by using the simplest excitable cell models including only a few variables as well as with realistic models of heart cells, simply by implementing aperiodicity and fractality to the connections network. Micro-reentries which may be identified with fibrillation of the systems can be simulated in silico experiments where emerge several self-perpetuating, colliding waves associated with non-periodic and mathematically calculated pseudo-EG.

Based on the two-point Hermite interpolation technique, the paper proposes a two-point generalized Hermite interpolation and its inversion in terms of weight functions. We prove that upon combining fourth-order optimal iterative scheme to the double Newton’s method (DNM), we can yield a generalized Hermite interpolation formula to relate the first-order derivatives at two points, and the converse is also true. Resorted on the DNM and the derived formula for the generalized inverse Hermite interpolation, some new third-order iterative schemes of quadrature type are constructed. Then, the fourth-order optimal iterative schemes are devised by using a double-weight function. A functional recursion formula is developed which can generate a sequence of two-point generalized Hermite interpolations for any two given weight functions with certain constraints; hence, a more general class of fourth-order optimal iterative schemes is developed from the functional recursion formula. The constructions of fourth-order optimal iterative schemes by using the techniques of double-weight function and the recursion formula obtained from a single weight function are appeared in the literature at the first time. The novelties involve deriving a two-point generalized Hermite interpolation and its inversion in terms of weight functions subjected to two conditions and through the recursion formula, relating the DNM to the third-order iterative schemes by the inverse Hermite interpolation, formulating a functional recursion formula, deriving a broad class fourth-order optimal iterative schemes through double-weight functions rather than the previous technique with a single-weight function, and finding that the new double-weight function and the newly developed fourth-order optimal iterative schemes are inclusive being convergent faster and competitive to other iterative schemes.

Today's volatile market conditions in electronic industries have lead to a new production system, seru (which is the Japanese pronunciation for cell), and has been widely implemented in hundreds of Japan and other Asia companies. In particular, the rotating seru has been widely implemented, where workers are fully cross-trained with the same skill level but may be different on the proficiency of performing tasks. The rotating seru production problem, which determines the rotating sequence of workers as well as the assembling sequence of jobs, is difficult to solve due to conflicting objectives and dynamic release of customer demands. To solve this problem, we propose a dynamic multi-objective NSGA-II based memetic algorithm. Moreover, to preserve desirable population diversity and improve the searching efficiency, we propose different problem-specific evolutionary strategies. Finally, we test the performance of our proposed memetic algorithm with other state-of-the-art multi-objective evolutionary algorithms and demonstrate the effectiveness of our proposed algorithm.

A temporal graph is a pair ( G , λ ) where G is a simple graph and λ is a function assigning to each edge time labels telling at which snapshots each edge is active. As recently defined by Mertzios, Molter and Zamaraev (2021), a temporal coloring of ( G , λ ) is a sequence of colorings of the vertices of the snapshots such that each edge is properly colored at least once. We first focus on t-persistent and t-occurrent temporal graphs. The former (resp. the latter) are temporal graphs where each edge of G stays active for at least t consecutive (resp. not-necessarily consecutive) snapshots. We study which values of t make the problem polynomial-time solvable. We also investigate the complexity of the problem when restricted to temporal graphs ( G , λ ) such that G has bounded treewidth.

Implicit curve and surface reconstruction has wide applications in computer graphics, which attracts great attention of many researchers. In this paper, we propose the relaxed implicit randomized algebraic reconstruction technique (RIR-ART) for curve and surface reconstruction. The RIR-ART method generates a sequence of curves and surfaces by adjusting the control coefficients with the relaxation parameters iteratively. It is proved that the sequence of curves and surfaces generated by the RIR-ART method with the suitable relaxation parameters converge to the least-norm results in terms of the mean square error. The RIR-ART method can eliminate the extra zero-level sets effectively during its iterative process, and converge faster than the implicit progressive-iterative approximation method (Hamza et al. 2020). Numerical examples present the efficiency and effectiveness of the proposed method.

Assume the initial data of compressible Euler equations has finite energy and total mass. We can construct a sequence of solutions of one-dimensional compressible Navier-Stokes equations (density-dependent viscosity) with stress-free boundary conditions, so that, up to a subsequence, the sequence of solutions of compressible Navier-Stokes equations converges to a finite-energy weak solution of compressible Euler equations. Hence the inviscid limit of the compressible Navier-Stokes is justified. It is worth pointing out that our result covers the interesting case of the Saint-Venant model for shallow water (i.e., α = 1 , γ = 2 ).

In this paper, we propose two inertial projection methods to solve mixed variational inequalities without assuming monotonicity on the cost operator. Consequently, we show that the sequence of iterates generated by our proposed methods converge globally to a solution of the mixed variational inequality under the condition that the set of solutions of the dual mixed variational inequality is nonempty. Our convergence results are obtained without assuming any further stringent condition imposed in other related results in the literature. Moreover, our results improve on many important related results in the literature. Some numerical illustrations are given to show the efficiency of our proposed methods.

An online algorithm is typically unaware of the length of the input request sequence that it is called upon. Consequently, it cannot determine whether it has already processed most of its input or whether the bulk of work is still ahead. In this paper, we are interested in whether some sort of orientation within the request sequence is nevertheless possible. For a real number 0 f 1 , our objective is to preemptively guess the position f n within the request sequence of unknown length n : While processing the input, the online algorithm maintains a guess and is only allowed to update its guess to the position of the current element under investigation. We give a complete characterization of the optimal guessing strategies with respect to f : For f ≤ f 0 ≈ 0 . 1867 , the trivial algorithm that never updates its initial guess is (asymptotically) optimal. For f > f 0 , we give a randomized algorithm that in expectation places the guess at distance β ( f ) n from f n , where β is a non-elementary function, and we prove that this is optimal. Our findings show that the position f max n ≈ 0 . 2847 n is hardest to guess. We also give upper and lower bounds for a natural extension to weighted sequences. Our work can also be seen as the first randomized approach to the online checkpointing problem.

The Multidimensional Multiple-choice Knapsack Problem (MMKP) is a complex combinatorial optimization problem for which finding high quality feasible solutions is very challenging. Recently, several heuristic approaches and a few exact algorithms have been proposed for its solution. These methods have been able to provide new best-known values for benchmark instances although many of them still remain unclosed to optimality. In this paper, we provide a new variant of the heuristic framework Kernel Search and apply it to the MMKP. The proposed variant keeps the method’s main idea of solving a sequence of restricted mixed-integer subproblems but innovates by partitioning the solution process into two different phases with complementary goals. The first phase strives for feasibility and collects important information to dynamically adapt subproblems’ dimension and solution time in the second phase that is focused on getting high quality solutions. This makes the global approach more scalable and efficient. Computational results on different sets of benchmark instances demonstrate that our method is extremely effective outperforming all state-of-the-art heuristics for the MMKP. The method compares extremely well also with respect to exact approaches running for five hours. The proposed algorithm is able to improve the best-known value of 185 out of 276 open benchmark instances and gets 8 out of 17 optimal solutions for the closed ones. The average deviation from optimality is always negligible.

One of the most interesting properties of Pascal’s triangle is that the sequence of the sums of the elements on its diagonals is the best known recurrence sequence, the Fibonacci sequence. It is also known that other diagonals can be associated with other relevant recurrence sequences, such as the Padovan and k -Padovan sequences. In this paper, we see that similar properties also hold for diagonals of generalized Pascal’s triangles. We show that the diagonal sums in generalized Pascal’s triangles belong to the family of the so-called ‘ k -Padovan-like sequences’ which are linear recurrences of order k with constant coefficients. A recurrence connection between the k -Padovan and k -Padovan-like sequences is derived.

We introduce a new graph-theoretic paradigm called a graph signature that describes persistent patterns in a sequence of graphs. This framework is motivated by the need to detect subgraphs of significance in temporal networks, e.g., social and biological networks that evolve over time. Because the subgraphs of interest may not all “look alike” in the snapshots of the temporal network, the framework deems a subgraph to be persistent if it satisfies one of several preselected properties in each snapshot of a consecutive subsequence. The persistency requirement is parameterized by the length of this subsequence. This discrete mathematical framework can be viewed more broadly as a way to generalize classical graph properties and invariants associated with a single graph to a sequence of graphs. In this introductory article, we formulate the graph signature identification problem as a mixed-integer program and propose an algorithmic framework based on dynamic programming. This methodology is applicable to any collection of mixed-integer representable graph properties. We also demonstrate how this framework can be tailored to exploit property-specific decomposition and scale reduction techniques through three different computational case-studies. Our experiments show that the dynamic programming algorithm solves this problem across most instances in our test bed to optimality. Moreover, for the instances in our test bed, the optimal signature sizes are comparable to those of their static counterparts, suggesting that our new framework can identify subgraphs of significance in complex dynamic networks.

We prove an asymptotic result on the maximum number of k -vertex subtrees in binary trees of given order. This problem turns out to be equivalent to determine the maximum number of k + 2 -cycles in n -vertex outerplanar graphs, thus we settle the generalised outerplanar Turan number for all cycles. We also determine the exponential growth of the generalised outerplanar Turan number of paths P k as a function of k which implies the order of magnitude of the generalised outerplanar Turan number of arbitrary trees. The bounds are strongly related to the sequence of Catalan numbers.

This paper proposes an intelligent STEP-NC-compliant setup planning method with the combination of rules, analytic hierarchy process (AHP) and improved back propagation neural network (IBPNN). In the method, the STEP-NC-compliant manufacturing features are firstly automatically and reasonably grouped based on tool approach direction (TAD) selection rules. Then, the AHP is used to intelligently and accurately determine the sequence between STEP-NC-compliant manufacturing feature groups in consideration of machining stability. Next, with the combination of firefly algorithm, chaos algorithm and back propagation neural network, an IBPNN algorithm for the locating datum decision-making of STEP-NC-compliant manufacturing feature groups is presented. Further, the locating datum decision-making of STEP-NC-compliant manufacturing feature groups is intelligently and efficiently made after the machining information of a part is normalized and input into the IBPNN. At the end, the effectivity and feasibility of the proposed method are verified by case study.

This paper studies centralized fusion estimation over a wireless sensor-actuator network, where packet dropouts cannot be observed by the fusion estimator. For such a system, we obtain an optimal linear fused estimation of system states, also known as optimal linear estimator. Then, we establish a necessary and sufficient condition for the stability of the optimal linear estimator. Finally, we show that the estimation performance is monotonically decreasing with respect to the observation packet-arrival rate. By analyzing a sequence that converges to the covariance of the optimal linear estimator, an analytical relationship between the estimation performance and the control packet-arrival rate is obtained. Simulation examples are given to illustrate the main results.

In this paper, we consider a new family of multivariate copulas described by a sequence of functions, named as AMO copula. The set of AMO copulas corresponds to a class of multivariate shock models with the Archimedean type of dependence. Sufficient conditions on the involved sequence of functions to obtain a multivariate copula are given and the probabilistic structure of the AMO copula is provided. We show that the family of AMO copulas is a generalization of Archimedean and Marshall-Olkin copulas family, and it includes some well-known copulas as specific cases. An alternative method for generating random vectors from AMO copulas via distortion functions is provided. In addition, a singular component along the main diagonal of the AMO copula is also verified. Finally, the tail behaviors of AMO copulas are discussed and some numerical illustrations are provided.

Time series prediction is important for financial analysis, climate forecasting, and so on. Existing works mainly focus on the prediction of target time series based on the prior of the sequence itself, but ignore the background information behind the sequences. Such ignored information is usually essential to build a robust prediction model in complex real-world applications. However, how to extract the shared background information behind multiple sequences and how to incorporate the extracted information in the prediction model are two main challenges. To address the above two challenges, we propose a shared state space model (SSSM) by introducing a shared background information component into the state space model. In SSSM, we consider all sequences as a whole and model each target series by utilizing a state space model with shared same parameters and background information. First, we employ two recurrent neural networks to extract the temporal characteristic of the target sequence as well as the background information. Second, the above extracted information is integrated into a state space model in the form of a linear Gaussian component, whose inference procedure is accomplished by Kalman Filter. Finally, the model is optimized following a log-likelihood of the model with the above two components. Experiments on real-world applications show that our model can extract the share information behind the data and outperforms the state-of-the-art methods.

Relation extraction is a critical natural language processing task. Existing dependency-based models captured long-range syntactic relations, but they usually cannot fully exploit information from sentences. They often used hand-crafted rules to prune redundant edges from dependency trees, but suffer from the imbalance of including and removing contents. When incorporating sequence models, they usually ignored the semantic and syntactic interactions between words. In this paper, we propose to automatically learn relational dependency structures with a fine-grained gating strategy. We decompose the dependency tree into differently informative parts and apply different gating methods to each part. To further capture the word-level interactions, we propose to apply the co-attention mechanism to combine structure and sequence models. We apply a neural network to learn the affinity matrix and derive mutual attention weights between semantic and syntactic representations. We conduct experiments on two benchmark datasets and the results indicate the effectiveness of our method.

In computer-assisted diagnosis of dermoscopy images, skin lesion segmentation is a critical but difficult process. Many segmentation methods fail to extract correct lesion boundaries due to the lack of pre-processing steps or a very few number of pre-processing steps that aren't in the right order. This paper demonstrates the significant of Multi-level pre-processing steps and its proper sequence before SegCaps segmentation of Lesion images. In the proposed work author have planned four pre-processing steps before segmentation of skin lesion images in the sequence of first is a 2nd Order grey edge algorithm is used to achieve color consistency;. Second process consists of two sub-processes in the hair removal procedure. To get started, we use the Prewitt filter, which is adaptable to the hair pixel level. The following procedure is the Repairing Operation, which is carried out using the anisotropic Fast Marching Method. Third process is a noise filtering with the Improved Switching Bilateral Filter (ISBF), which uses the Sorted Quadrant Median Vector (SQMV) to determine best median value and the last process is The Directed Edge Enhancer algorithm is used to perform edge enhancement. The proposed model is tested Over MatlabR2017b, using the HAM10000 dataset. The proposed method's output is assessed by comparing segmentation effects with and without pre-processing, as well as visual appearances of pre-processed images from input images. From the results it has been concludes that when pre-processing steps are used in the correct order and proper sequence, segmentation accuracy is very high, as compared to segmentation without pre-processing steps.

Composite materials are attracting increasing interest from many industrial sectors, and their use is becoming more widespread. The naval industry, for example, remains a large field of investigation for composite materials due to their mechanical properties, able to reach very interesting performance levels. Composites are often composed of plies arranged according to loading directions and forming structures called laminates; these directions can have a great effect on the structural behavior of the composite. For this, the study carried out in this article, consists in determining orientations and stacking sequences effect on the mechanical performance of a glass/epoxy composite panel, with a thickness of 8 mm containing 12 plies of the same thickness and different orientations, inclined at an angle of 10° and impacting the water at a velocity of V = 8 m/s.

Given a real number α ∈ ( 0 , 1 ) , we define the Webster sequence of density α to be W α = ( ⌈ ( n − 1 / 2 ) / α ⌉ ) n ∈ N , where ⌈ x ⌉ is the ceiling function. It is known that if α and β are irrational with α + β = 1 , then W α and W β partition N . On the other hand, an analogous result for three-part partitions does not hold: There does not exist a partition of N into sequences W α , W β , W γ with α , β , γ irrational. In this paper, we consider the question of how close one can come to a three-part partition of N into Webster sequences with prescribed densities α , β , γ . We show that if α , β , γ are irrational with α + β + γ = 1 , there exists a partition of N into sequences of densities α , β , γ , in which one of the sequences is a Webster sequence and the other two are “almost” Webster sequences that are obtained from Webster sequences by perturbing some elements by at most 1. We also provide two efficient algorithms to construct such partitions. The first algorithm outputs the n th element of each sequence in O ( 1 ) time and the second algorithm gives the assignment of the m th positive integer to a sequence in O ( 1 ) time. We show that the results are best-possible in several respects. Moreover, we describe applications of these results to apportionment and optimal scheduling problems.

We study entropy as a measure of randomness in a sequential clinical trial. For any randomization design, we consider the well-known sequence of conditional treatment assignment probabilities, P n , which complements the random allocation proportion. We then use P n to formulate and prove a statement about conditions for the asymptotic mean entropy of a randomization design to achieve its optimum value. We compare both response-adaptive and non response adaptive randomization designs with respect to the asymptotic mean entropy, connecting the variance of P n to the asymptotic mean entropy under normality. Then we explore whether both P n , as well as the allocation proportion, may have zero asymptotic variance.

The problem consists in bounding the number of tetrahedra that share the same volume V, circumradius R, and face areas A 1 , A 2 , A 3 , A 4 . A symbolic computation approach is used to prove that the upper bound of the number of tetrahedra is eight. First, the problem is reduced to a counting root problem using the Cayley-Menger determinant formula for the volume of a simplex and some metric equations of the tetrahedron to construct a system of algebraic equations. Then, an investigation of its real roots is done by analyzing the discriminant sequence and extensive numerical computations.

The features of carrier-based aircraft’s navigation systems during the approach and landing phases are investigated. A new adaptive Kalman filter with unknown state noise statistics is proposed to improve the accuracy of the INS/GNSS integrated navigation system. The adaptive filtering algorithm aims to estimate and adapt the unknown state noise covariance Q in high dynamic conditions, when the measurement noise covariance R is assumed to be known empirically in advance. The new adaptive Kalman filter based on the innovation sequence and pseudo-measurement vector approach makes it more effective to estimate and adapt Q. The simulation results and semi-physical experiments show that the application of the proposed adaptive Kalman filter can guarantee a higher estimation accuracy of the state variables.

Despite the robust findings indicating the positive role of spatial skills in a variety of mathematics skills (e.g., calculation), no empirical evidence has been provided concerning the longitudinal reciprocal relations between spatial skills and oral counting – perhaps the earliest form of symbolic representation. The purpose of the present study was to investigate the reciprocal longitudinal relations between spatial skills and three types of counting sequence knowledge (counting range, counting forward, and counting backward), which were measured at three time points between ages 3 to 4 years in a group of 109 young Hong Kong children. A series of family background and domain-general variables (i.e., family SES, vocabulary knowledge and behavioral regulation) were measured as covariates. Results from the cross-lagged panel analyses showed a reciprocal relationship between the children's counting sequence knowledge and their spatial skills, but this relationship only occurred between Time 2 (i.e., fall semester in the first year of kindergarten) and Time 3 (i.e., spring semester in the first year of kindergarten) and not between Time 1 (i.e., end of the nursery year) and Time 2. Further analyses showed that this pattern of results was task dependent. Reciprocal relations were found only in the counting range task and the counting backward task; no reciprocal relationship was found between spatial skills and the counting forward task. The findings reveal the developmental reciprocal link between spatial skills and early mathematics competency (i.e., the production of counting lists) and further highlight that this link varies according to children's conceptual levels of counting knowledge. Implications for classroom practices and teaching strategies are discussed.

News-driven stock prediction investigates the correlation between news events and stock price movements. Previous work has considered effective ways for representing news events and their sequences, but rarely exploited the representation of underlying equity states. We address this issue by making use of a recurrent neural network to represent an equity state transition sequence, integrating news representation using contextualized embeddings as inputs to the state transition mechanism. Thanks to the separation of news and equity representations, our model can accommodate additional input factors. We design a novel random noise factor for modeling influencing factors beyond news events, and a future event factor to address the delay of news information (e.g., insider trading). Results show that the proposed model outperforms strong baselines in the literature.