A first and second order progress rate analysis was conducted for the intermediate multi-recombinative Evolution Strategy (/, λ)-ES with isotropic scale-invariant mutations on the highly multimodal Rastrigin test function. Closed-form analytic solutions for the progress rates are obtained in the limit of large dimensionality and large populations. The first order results are able to model the one-generation progress including local attraction phenomena. Furthermore, a second order progress rate is derived yielding additional correction terms and further improving the progress model. The obtained results are compared to simulations and show good agreement, even for moderately large populations and dimensionality. The progress rates are applied within a dynamical systems approach, which models the evolution using difference equations. The obtained dynamics are compared to real averaged optimization runs and yield good agreement. The results improve further when dimensionality and population size are increased. Local and global convergence is investigated within given model showing that large mutations are needed to maximize the probability of global convergence, which comes at the expense of efficiency. An outlook regarding future research goals is provided.

The incorporation of ribonucleoside monophosphates (rNMPs) in genomic DNA is a frequent phenomenon in many species, often associated with genome instability and disease. The ribose-seq technique is one of a few techniques designed to capture and map rNMPs embedded in genomic DNA. The first step of ribose-seq is restriction enzyme (RE) fragmentation, which cuts the genome into smaller fragments for subsequent rNMP capture. The RE selection chosen for genomic DNA fragmentation in the first step of the rNMP-capture techniques determines the genomic regions in which the rNMPs can be captured. Here, we designed a computational method, Restriction Enzyme Set and Combination Optimization Tools (RESCOT), to calculate the genomic coverage of rNMP-captured regions for a given RE set and to optimize the RE set to significantly increase the rNMP-captured-region coverage. Analyses of ribose-seq libraries for which the RESCOT tools were applied reveal that many rNMPs were captured in the expected genomic regions. Since different rNMP-mapping techniques utilize RE fragmentation and purification steps based on size-selection of the DNA fragments in the protocol, we discuss the possible usage of RESCOT for other rNMP-mapping techniques. In summary, RESCOT generates optimized RE sets for the fragmentation step of many rNMP capture techniques to maximize rNMP capture rate and thus enable researchers to better study characteristics of rNMP incorporation.

Prefix normal words are binary words with the property that no factor has more 1s than the prefix of the same length. Finite prefix normal words were introduced in [Fici and Lipták, DLT 2011]. In this paper, we study infinite prefix normal words and explore their relationship to some known classes of infinite binary words. In particular, we establish a connection between prefix normal words and Sturmian words, between prefix normal words and abelian complexity, and between prefix normality and lexicographic order.

Social networks provide us a convenient platform to communicate and share information or ideas with each other, but it also causes many negative effects at the same time, such as, the spread of misinformation or rumor in social networks may cause public panic and even serious economic or political crisis. In this paper, we propose a Community-based Rumor Blocking Problem (CRBMP), i.e., selecting a set of seed users from all communities as protectors with the constraint of budget such that the expected number of users eventually not being influenced by rumor sources is maximized. We consider the community structure in social networks and solve our problem in two stages, in the first stage, we allocate budget for all the communities, this sub-problem whose objective function is proved to be monotone and DR-submodular, so we can use the method of submodular function maximization on an integer lattice, which is different from most of the existing work with the submodular function over a set function. Then a greedy community budget allocation algorithm is devised to get an approximation ratio; we also propose a speed-up greedy algorithm which greatly reduces the time complexity for the community budget allocation and can get an approximation guarantee meanwhile. Next we solve the Protector Seed Selection (PSS) problem in the second stage after we obtained the budget allocation vector for communities, we greedily choose protectors for each community with the budget constraints to achieve the maximization of the influence of protectors. The greedy algorithm for PSS problem can achieve a 1/2 approximation guarantee. We also consider a special case where the rumor just originates from one community and does not spread out of its own community before the protectors are selected, the proposed algorithm can reduce the computational cost than the general greedy algorithm since we remove the uninfected communities. Finally, we conduct extensive experiments on three real world data sets, the results demonstrate the effectiveness of the proposed algorithm and its superiority over other methods.

We study an optimization problem of a computational folding model, proving its hardness and proposing heuristic algorithms. RNA cotranscriptional folding refers to the phenomenon in which an RNA transcript folds upon itself while being synthesized out of a gene. An oritatami model (OM) is a computational model of this phenomenon that lets its sequence of beads (abstract molecules) fold cotranscriptionally by the interactions between beads, according to its ruleset. We study the problem of reducing the ruleset size, while keeping the terminal conformations geometrically the same. We first prove the hardness of finding the smallest ruleset, and then suggest two approaches that reduce the ruleset size efficiently.

Endovascular coiling is a primary treatment for intra-cranial aneurysm, which deploys a thin and detachable metal wire inside the aneurysm so as to prevent its rupture. Emerging evidence from medical research and clinical practice has suggested that the coil configuration inside the aneurysm plays a vital role in properly treating aneurysm and predicting its outcome. In this paper, we propose a novel virtual coiling technique, called , for generating a coil configuration with ensured blocking ability. It can be used as an automatic tool for virtually simulating coiling before its implantation and thus optimizes such treatments. Our approach is based on integer linear programming and computational geometry techniques, and takes into consideration the packing density and coil distribution as the performance measurements. The resulting coiling is deployable (with the help of coil pre-shaping) and with minimized energy. Experimental results on both random and real aneurysm data suggest that our proposed method yields near optimal solution.

We consider global dynamics of reaction systems as introduced by Ehrenfeucht and Rozenberg. The dynamics is represented by a directed graph, the so-called transition graph, and two reaction systems are considered equivalent if their corresponding transition graphs are isomorphic. We introduce the notion of a skeleton (a one-out graph) that uniquely determines a directed graph. We provide the necessary and sufficient conditions for two skeletons to define isomorphic graphs. This provides a necessary and sufficient condition for two reactions systems to be equivalent, as well as a characterization of the directed graphs that correspond to the global dynamics of reaction systems.

The famous Burrows-Wheeler Transform (BWT) was originally defined for a single string but variations have been developed for sets of strings, labeled trees, de Bruijn graphs, etc. In this paper we propose a framework that includes many of these variations and that we hope will simplify the search for more. We first define and show they have a property we call . We show that if the state diagram of a finite-state automaton is a Wheeler graph then, by its path coherence, we can order the nodes such that, for any string, the nodes reachable from the initial state or states by processing that string are consecutive. This means that even if the automaton is non-deterministic, we can still store it compactly and process strings with it quickly. We then rederive several variations of the BWT by designing straightforward finite-state automata for the relevant problems and showing that their state diagrams are Wheeler graphs.

Chemical reaction networks are a powerful means of specifying the intended behaviour of synthetic biochemical systems. A high-level formal specification, expressed as a chemical reaction network, may be compiled into a lower-level encoding, which can be directly implemented in wet chemistry and may itself be expressed as a chemical reaction network. Here we present conditions under which a lower-level encoding correctly emulates the sequential dynamics of a high-level chemical reaction network. We require that encodings are transactional, such that their execution is divided by a "commit reaction" that irreversibly separates the reactant-consuming phase of the encoding from the product-generating phase. We also impose restrictions on the sharing of species between reaction encodings, based on a notion of "extra tolerance", which defines species that may be shared between encodings without enabling unwanted reactions. Our notion of correctness is serializability of interleaved reaction encodings, and if all reaction encodings satisfy our correctness properties then we can infer that the global dynamics of the system are correct. This allows us to infer correctness of system constructed using verified encodings. As an example, we show how this approach may be used to verify two- and four-domain DNA strand displacement encodings of chemical reaction networks, and we generalize our result to the limit where the populations of helper species are unlimited.

DNA nanotechnology is a promising approach for engineering computation at the nanoscale, with potential applications in biofabrication and intelligent nanomedicine. DNA strand displacement is a general strategy for implementing a broad range of nanoscale computations, including any computation that can be expressed as a chemical reaction network. Modelling and analysis of DNA strand displacement systems is an important part of the design process, prior to experimental realisation. As experimental techniques improve, it is important for modelling languages to keep pace with the complexity of structures that can be realised experimentally. In this paper we present a process calculus for modelling DNA strand displacement computations involving rich secondary structures, including DNA branches and loops. We prove that our calculus is also sufficiently expressive to model previous work on non-branching structures, and propose a mapping from our calculus to a canonical representation, in which vertices represent DNA strands, ordered sites represent domains, and edges between sites represent bonds between domains. We define interactions between strands by means of strand graph rewriting, and prove the correspondence between the process calculus and strand graph behaviours. Finally, we propose a mapping from strand graphs to an efficient implementation, which we use to perform modelling and simulation of DNA strand displacement systems with rich secondary structure.

We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the ([Formula: see text] for short). This termination order entails a new syntactic method to analyse the innermost runtime complexity of term rewrite systems fully automatically: for any rewrite system compatible with [Formula: see text] that employs recursion up to depth , the (innermost) runtime complexity is polynomially bounded of degree . This bound is tight. Thus we obtain a direct correspondence between a syntactic (and easily verifiable) condition of a program and the asymptotic worst-case complexity of the program.

We describe a method to perform scalar multiplication on two classes of ordinary elliptic curves, namely [Formula: see text] in prime characteristic [Formula: see text], and [Formula: see text] in prime characteristic [Formula: see text]. On these curves, the 4-th and 6-th roots of unity act as (computationally efficient) endomorphisms. In order to optimise the scalar multiplication, we consider a width--NAF (Non-Adjacent Form) digit expansion of positive integers to the complex base of , where is a zero of the characteristic polynomial [Formula: see text] of the Frobenius endomorphism associated to the curve. We provide a precomputationless algorithm by means of a convenient factorisation of the unit group of residue classes modulo in the endomorphism ring, whereby we construct a digit set consisting of powers of subgroup generators, which are chosen as efficient endomorphisms of the curve.

Designing algorithms for distributed systems that provide a round abstraction is often simpler than designing for those that do not provide such an abstraction. Further, distributed systems need to tolerate various kinds of failures. The concept of a synchronizer deals with both: It constructs rounds and allows masking of transmission failures. One simple way of dealing with transmission failures is to retransmit a message until it is known that the message was successfully received. We calculate the of the average rate of a retransmission-based synchronizer in environments with probabilistic message loss, within which the synchronizer shows nontrivial timing behavior. We show how to make this calculation efficient, and present analytical results on the convergence speed. The theoretic results, based on Markov theory, are backed up with Monte Carlo simulations.

In this work the number of occurrences of a fixed non-zero digit in the width-[Formula: see text] non-adjacent forms of all elements of a lattice in some region (e.g. a ball) is analysed. As bases, expanding endomorphisms with eigenvalues of the same absolute value are allowed. Applications of the main result are on numeral systems with an algebraic integer as base. Those come from efficient scalar multiplication methods (Frobenius-and-add methods) in hyperelliptic curves cryptography, and the result is needed for analysing the running time of such algorithms. The counting result itself is an asymptotic formula, where its main term coincides with the full block length analysis. In its second order term a periodic fluctuation is exhibited. The proof follows Delange's method.

We extend the methodology in Baaz and Fermüller (1999) [5] to systematically construct analytic calculi for semi-projective logics-a large family of (propositional) locally finite many-valued logics. Our calculi, defined in the framework of sequents of relations, are proof search oriented and can be used to settle the computational complexity of the formalized logics. As a case study we derive sequent calculi of relations for Nilpotent Minimum logic and for Hajek's Basic Logic extended with the [Formula: see text]-contraction axiom ([Formula: see text]). The introduced calculi are used to prove that the decidability problem in these logics is Co-NP complete.

Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own interest in the design and synthesis of resource-constrained omega-regular specifications, energy parity games provide one of the simplest model of games with combined qualitative and quantitative objectives. Our main results are as follows: (a) exponential memory is sufficient and may be necessary for winning strategies in energy parity games; (b) the problem of deciding the winner in energy parity games can be solved in NP [Formula: see text] coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games. We also show that the problem of deciding the winner in energy parity games is logspace-equivalent to the problem of deciding the winner in mean-payoff parity games, which can thus be solved in NP [Formula: see text] coNP. As a consequence we also obtain a conceptually simple algorithm to solve mean-payoff parity games.

To theoretically compare the behavior of different algorithms, compatible performance measures are necessary. Thus in the first part, an analysis approach, developed for evolution strategies, was applied to simultaneous perturbation stochastic approximation on the noisy sphere model. A considerable advantage of this approach is that convergence results for non-noisy and noisy optimization can be obtained simultaneously. Next to the convergence rates, optimal step sizes and convergence criteria for 3 different noise models were derived. These results were validated by simulation experiments. Afterward, the results were used for a comparison with evolution strategies on the sphere model in combination with the 3 noise models. It was shown that both strategies perform similarly, with a slight advantage for SPSA if optimal settings are used and the noise strength is not too large.

When investigating the complexity of cut-elimination in first-order logic, a natural subproblem is the elimination of quantifier-free cuts. So far, the problem has only been considered in the context of general cut-elimination, and the upper bounds that have been obtained are essentially double exponential. In this note, we observe that a method due to Dale Miller can be applied to obtain an exponential upper bound.

Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer n as a sum n=∑kεkUk, where the digits εk are taken from a finite alphabet Σ and (Uk)k is a linear recurrent sequence of Pisot type with U0=1. The most prominent example of a base sequence (Uk)k is the sequence of Fibonacci numbers. We prove that the representations of minimal weight ∑k|εk| are recognised by a finite automaton and obtain an asymptotic formula for the average number of representations of minimal weight. Furthermore, we relate the maximal number of representations of a given integer to the joint spectral radius of a certain set of matrices.

Range Quickselect, a simple modification of the well-known Quickselect algorithm for selection, can be used to efficiently find an element with rank k in a given range [i..j], out of n given elements. We study basic cost measures of Range Quickselect by computing exact and asymptotic results for the expected number of passes, comparisons and data moves during the execution of this algorithm.The key element appearing in the analysis of Range Quickselect is a trivariate recurrence that we solve in full generality. The general solution of the recurrence proves to be very useful, as it allows us to tackle several related problems, besides the analysis that originally motivated us.In particular, we have been able to carry out a precise analysis of the expected number of moves of the pth element when selecting the jth smallest element with standard Quickselect, where we are able to give both exact and asymptotic results.Moreover, we can apply our general results to obtain exact and asymptotic results for several parameters in binary search trees, namely the expected number of common ancestors of the nodes with rank i and j, the expected size of the subtree rooted at the least common ancestor of the nodes with rank i and j, and the expected distance between the nodes of ranks i and j.