Sequential Composition Research Articles

Sunklodas’ Approach to Normal Approximation for Time-Dependent Dynamical Systems

We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general normalizing sequence $b(N)$ of invertible square matrices, are approximated by a normal distribution with respect to a metric of regular test functions. Depending on the metric and the normalizing sequence $b(N)$, the conditions imply that the error in the approximation decays either at the rate $O(N^{-1/2})$ or the rate $O(N^{-1/2} \log N)$, under the additional assumption that $\Vert b(N)^{-1} \Vert \lesssim N^{-1/2}$. The error comes with a multiplicative constant whose exact value can be computed directly from the conditions. The proof is based on an observation due to Sunklodas regarding Stein's method of normal approximation. We give applications to one-dimensional random piecewise expanding maps and to sequential, random, and quasistatic intermittent systems.

Tracelets and Tracelet Analysis Of Compositional Rewriting Systems

Taking advantage of a recently discovered associativity property of rule compositions, we extend the classical concurrency theory for rewriting systems over adhesive categories. We introduce the notion of tracelets, which are defined as minimal derivation traces that universally encode sequential compositions of rewriting rules. Tracelets are compositional, capture the causality of equivalence classes of traditional derivation traces, and intrinsically suggest a clean mathematical framework for the definition of various notions of abstractions of traces. We illustrate these features by introducing a first prototype for a framework of tracelet analysis, which as a key application permits to formulate a first-of-its-kind algorithm for the static generation of minimal derivation traces with prescribed terminal events.

Quantum Materials Exploration by Sequential Screening Technique of Heteroatomicity

Subnanoparticles (SNPs) exhibit unique properties and functions due to their extremely small particle sizes which extend into the quantum scale. Although the synthesis of SNPs requiring precise control of atomicity and composition has not been accomplished, we recently developed an atom-hybridization method (AHM) that realizes such atomic-level control using a macromolecular template. As a next step in the quest for innovative quantum materials, the practical creation of functional subnanomaterials will become a central subject. In this study, we established a new screening technique for functional SNPs by focusing on the simple indium-tin binary system with sequential compositions using the latest AHM. As a result, it was revealed that a thermodynamically unstable indium species was produced only at a certain composition leading to a durable luminescent function. Such a phenomenon in subnanosized substances will play an important role in the development of the as-yet-unknown field of quantum materials.

On the axiomatisability of priority III: Priority strikes again

Aceto et al., proved that, over the process algebra BCCSP with the priority operator of Baeten, Bergstra and Klop, the equational theory of order-insensitive bisimilarity is not finitely based. However, it was noticed that by substituting the action prefixing operator of BCCSP with BPA's sequential composition, the infinite family of equations used to show that non-finite axiomatisability result could be proved by a finite collection of sound equations. That observation left as an open question the existence of a finite axiomatisation for order-insensitive bisimilarity over BPA with the priority operator. In this paper we provide a negative answer to this question. We prove that, in the presence of at least two actions, order-insensitive bisimilarity is not finitely based over BPA with priority.

Composition of Resource-Service Chain Based on Evolutionary Algorithm in Distributed Cloud Manufacturing Systems

In distributed cloud manufacturing (CMfg) systems, multi-resource service can complete more complex manufacturing tasks than single resource service. Especially in business process, all the resource services are invoked in a certain sequence, which is called the Resource-Service Chain (RSC). The RSC, as a sequential composition of resource services, expresses the scheduling and the flow of servicing to a distributed business process. A perfect composition can improve utilization ratio and efficient matching availability of resource services greatly. However, most of the existing methods for resource service composition paid no attention to the temporal relationship between resource services. Moreover, the methods strongly depend on relevant element to be considered. Inspired by biological evolution, a Resource-Service Chain Composition Evolutionary (RSCCE) algorithm is proposed. Specifically, RSCCE tries to find multiple optimal solutions, namely all RSCs in a workflow with given constraints. To begin, initial sets of composite resource service are resolved by calculating the degree of dependency between resource services, so as to obtain initial RSCs by workflow. Then, RSCCE algorithm applies genetic algorithm to search for the extended of each initial RSC, a longer chain composing of it, to improve the reuse of RSC. Under this approach, gene and chromosome represent resource service and the entire RSC respectively. If the propagated chromosomes violate the sequence of resource service, as constraint in RSCCE algorithm, they will be repaired to obtain a valid solution. Finally, we take a multi-enterprise collaborative business process as an example to simulate our approach. Experimental results confirm the effectiveness of the approach.

Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time

The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected sensitivity. A previous approach develops a relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded. In this work, we consider probabilistic while loops where the number of iterations is not fixed, but randomized and depends on the initial input values. We present a sound approach for proving expected sensitivity of such programs. Our sound approach is martingale-based and can be automated through existing martingale-synthesis algorithms. Furthermore, our approach is compositional for sequential composition of while loops under a mild side condition. We demonstrate the effectiveness of our approach on several classical examples from Gambler's Ruin, stochastic hybrid systems and stochastic gradient descent. We also present experimental results showing that our automated approach can handle various probabilistic programs in the literature.

A Parametrized Analysis of Algorithms on Hierarchical Graphs

Hierarchical graphs are used in order to describe systems with a sequential composition of sub-systems. A hierarchical graph consists of a vector of subgraphs. Vertices in a subgraph may “call” other subgraphs. The reuse of subgraphs, possibly in a nested way, causes hierarchical graphs to be exponentially more succinct than equivalent flat graphs. Early research on hierarchical graphs and the computational price of their succinctness suggests that there is no strong correlation between the complexity of problems when applied to flat graphs and their complexity in the hierarchical setting. That is, the complexity in the hierarchical setting is higher, but all “jumps” in complexity up to an exponential one are exhibited, including no jumps in some problems. We continue the study of the complexity of algorithms for hierarchical graphs, with the following contributions: (1) In many applications, the subgraphs have a small, often a constant, number of exit vertices, namely vertices from which control returns to the calling subgraph. We offer a parameterized analysis of the complexity and point to problems where the complexity becomes lower when the number of exit vertices is bounded by a constant. (2) We describe a general methodology for algorithms on hierarchical graphs. The methodology is based on an iterative compression of subgraphs in a way that maintains the solution to the problems and results in subgraphs whose size depends only on the number of exit vertices, and (3) we handle labeled hierarchical graphs, where edges are labeled by letters from some alphabet, and the problems refer to the languages of the graphs.

An expressive and tractable rule-based description language

ABSTRACT is a rule language introduced by Nguyen, Nguyen, and Szałas for the Semantic Web. It has a PTime data complexity and is more expressive than Horn- . These rule languages, however, do not allow PDL-like role constructors (i.e., union, sequential composition, the reflexive-transitive closure and the test operator). Using the transitive closure of a role is not the same as using a transitive role that is a superrole of . Furthermore, the test operator together with the other PDL-like role constructors would allow users to express sophisticated concepts. In this paper, we extend with PDL-like role constructors to obtain the rule language . We modify the algorithm given by Nguyen, Nguyen, and Szałas (2015) to obtain another one that checks satisfiability of a knowledge base in instead of . The resulting algorithm also has a PTime data complexity and is therefore tractable.

A paraconsistent approach to actions in informationally complex environments

Contemporary systems situated in real-world open environments frequently have to cope with incomplete and inconsistent information that typically increases complexity of reasoning and decision processes. Realistic modeling of such informationally complex environments calls for nuanced tools. In particular, incomplete and inconsistent information should neither trivialize nor stop both reasoning or planning. The paper introduces ACTLOG, a rule-based four-valued language designed to specify actions in a paraconsistent and paracomplete manner. ACTLOG is an extension of 4QLBel, a language for reasoning with paraconsistent belief bases. Each belief base stores multiple world representations. In this context, ACTLOG’s action may be seen as a belief bases’ transformer. In contrast to other approaches, ACTLOG actions can be executed even when the underlying belief base contents is inconsistent and/or partial. ACTLOG provides a nuanced action specification tools, allowing for subtle interplay among various forms of nonmonotonic, paraconsistent, paracomplete and doxastic reasoning methods applicable in informationally complex environments. Despite its rich modeling possibilities, it remains tractable. ACTLOG permits for composite actions by using sequential and parallel compositions as well as conditional specifications. The framework is illustrated on a decontamination case study known from the literature.

Autonomous Stairwell Ascent

SummaryThis paper documents autonomous multi-floor stairwell ascent by a legged robot. This is made possible through empirically deployed sequential composition of several reactive controllers, with perceptually triggered transitions. This composition relies on simplified assumptions regarding the robot’s sensory capabilities, its level of mobility, and the environment it operates in. The discrepancies between these assumptions and the physical reality are capably handled by the intrinsic motor competence of the robot. This behavior is implemented on the legged RHex platform and experiments spanning 10 different stairwells with various challenges are conducted.

Privacy Loss Classes: The Central Limit Theorem in Differential Privacy

Abstract Quantifying the privacy loss of a privacy-preserving mechanism on potentially sensitive data is a complex and well-researched topic; the de-facto standard for privacy measures are ε-differential privacy (DP) and its versatile relaxation (ε, δ)-approximate differential privacy (ADP). Recently, novel variants of (A)DP focused on giving tighter privacy bounds under continual observation. In this paper we unify many previous works via the privacy loss distribution (PLD) of a mechanism. We show that for non-adaptive mechanisms, the privacy loss under sequential composition undergoes a convolution and will converge to a Gauss distribution (the central limit theorem for DP). We derive several relevant insights: we can now characterize mechanisms by their privacy loss class, i.e., by the Gauss distribution to which their PLD converges, which allows us to give novel ADP bounds for mechanisms based on their privacy loss class; we derive exact analytical guarantees for the approximate randomized response mechanism and an exact analytical and closed formula for the Gauss mechanism, that, given ε, calculates δ, s.t., the mechanism is (ε, δ)-ADP (not an over-approximating bound).

Context-Free Session Type Inference

Some interesting communication protocols can be precisely described only by context-free session types, an extension of conventional session types supporting a general form of sequential composition. The complex metatheory of context-free session types, however, hinders the definition of corresponding checking and inference algorithms. In this work, we study a new syntax-directed type system for context-free session types that is easy to embed into a host programming language. We also detail 2 OCaml embeddings that allow us to piggyback on OCaml’s type system to check and infer context-free session types.

A Phase-Invariant Linear Torque-Angle-Velocity Relation Hidden in Human Walking Data.

Human walking is a sequential composition of gait cycles. Each gait cycle can be divided into four motion phases separated by heel strike and toe off. A classical conjecture in the control of lower limb assistive devices, state-of-the-art prostheses, and exoskeletons, is that each motion phase requires a different controller, such that adequate control of locomotion requires at least four distinct controllers. In this paper, we show that the joint torque versus joint angle and velocity relation hidden in the normal human walking data can be remarkably well represented with a single linear controller. In particular, based on the analysis of seven healthy subjects, we show that a one phase 20±5% sparse linear relation between the joint torques, angles and velocities explains 96.1±0.4% (mean±sem) of the normal human walking data (sparsity defines the percentage of zero control parameters). This result is comparable to what can be achieved using a significantly more complex four-phase non-sparse linear controller which explains 98.7±0.2% of the walking data, and is significantly better than a one-phase fully sparsified linear controller that could only explain 11.9±0.2% of the same data. Based on these results, we posit that the proposed phase-invariant sparse linear controller provides one of the simplest representations that can adequately explain the joint torque, angle and velocity relation present in the human walking data. The resulting control structure may be useful in developing simple yet competent phase-invariant controllers for next-generation prostheses and exoskeleton devices used for human assistance and augmentation.

Feedback motion planning of unmanned surface vehicles via random sequential composition

In this paper, we propose a new motion planning method that aims to robustly and computationally efficiently solve path planning and navigation problems for unmanned surface vehicles (USVs). Our approach is based on synthesizing two different existing methodologies: sequential composition of dynamic behaviours and rapidly exploring random trees (RRT). The main motivation of this integrated solution is to develop a robust feedback-based and yet computationally feasible motion planning algorithm for USVs. In order to illustrate the main approach and show the feasibility of the method, we performed simulations and tested the overall performance and applicability for future experimental applications. We also tested the robustness of the method under relatively extreme environmental uncertainty. Simulation results indicate that our method can produce robust and computationally feasible solutions for a broad class of USVs.

Training Normal Bayes Classifier on Distributed Data

The paper describes an approach to parallelization of Normal Bayes classifier training algorithm for distributed data. In the process of distributed data analysis and the algorithm performance, the results fail to join properly. Due to this, the algorithm is to be performed in a distributed manner. For this purpose, we use representation of the algorithm as a sequential composition of functions. The algorithm is parallelized to work with data distributed horizontally and vertically. This allows placing parallel functions of the algorithm at data nodes. Experiments show that transfer of computations to sources allow to decrease training time and network traffic. We implement the algorithm variants as an extension of the industrial-strength Java-based library Xelopes.

Efficient Parallel Self-Assembly Under Uniform Control Inputs

We prove that by successively combining subassemblies, we can achieve sublinear construction times for “staged” assembly of microscale objects from a large number of tiny particles, for vast classes of shapes; this is a significant advance in the context of programmable matter and self-assembly for building high-yield microfactories. The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles bond when forced together with a compatible particle. Previous work considered sequential composition of objects, resulting in construction time that is linear in the number $N$ of particles, which is inefficient for large $N$ . Our progress implies critical speedup for constructible shapes; for convex polyominoes, even a constant construction time is possible. We also show that our construction process can be used for pipelining, resulting in an amortized constant production time.

Service composition and optimal selection in cloud manufacturing: landscape analysis and optimization by a hybrid imperialist competitive and local search algorithm

Cloud manufacturing as an emerging service-oriented manufacturing paradigm integrates and manages geographically distributed manufacturing resources such that complex and highly customized manufacturing tasks can be performed cooperatively. The service composition and optimal selection (SCOS) problem, in which manufacturing cloud services are optimally selected for performing subtasks, is one of the key issues for implementing a cloud manufacturing system. In this paper, we propose a new mixed-integer programming model for solving the SCOS problem with sequential composition structure. Unlike the majority of previous research on the problem, in the proposed model, the transportation between distributed resources and its effects on quality of services are considered. Although a wide variety of metaheuristics have been tailored for solving the SCOS problem, no consistent and comprehensive conclusion has been reached so far on the superiority of a specific algorithm. Therefore, for the first time, solution space landscape of the problem was analyzed through several statistical criteria which demonstrated that the landscape is rugged and local optima are clustered in a small region of the search space. Therefore, to find good solutions, a metaheuristic algorithm needs to perform both proper exploitation and exploration of the search space. According to the landscape analysis, the basic imperialist competitive algorithm (ICA) was hybridized with a local search (LS) algorithm resulting in the hybrid ICA (HICA). To examine the performance of the proposed HICA, an example of online motorcycle production in the USA as well as four randomly generated large-scale instances, were solved through the LS, ICA, and HICA. Computational results showed that transportation consideration is indispensable for obtaining more realistic solutions in cloud manufacturing. The results also revealed that the HICA outperformed the LS and basic ICA in terms of the value of cost objective function, the stability of solutions and convergence speed. Hence, not only statistically but also analytically, it was proved that algorithms incorporating both exploitation and exploration are able to solve the SCOS problem more efficiently.

Jo-DPMF: Differentially private matrix factorization learning through joint optimization

Stochastic gradient descent (SGD) is a widely-used technique to implement matrix factorization. SGD-based matrix factorization involves many iterative computations. Therefore, according to the sequential composition theory of differential privacy, conventional implementation strategies of differentially private matrix factorization may lead to significant error accumulation, no matter whether the Laplace noise is added to the original matrix or to the factorized matrices. In fact, the implementation of differentially private matrix factorization is so challenging that results proposed to date have the problem of inefficient privacy and data utility. In this paper, we employ the objective perturbation method to address the challenge; this method dramatically alleviates error accumulation by perturbing the objective function instead of perturbing the results. Our method outperforms the state-of-the-art methods since it only requires a scalar noise rather than a vector noise to achieve the same magnitude of privacy. Furthermore, our method may learn the resulted matrices by joint optimization, which follows the conventional learning procedure of SGD and optimizes its convergence speed and accuracy as much as possible. In addition to the differential privacy guarantee, we also empirically show the way that the novel model works together with k-coRating, a k-anonymity-like privacy preserving model, to enhance data utility.

A formally based parallelization of data mining algorithms for multi-core systems

We describe a novel, systematic approach to efficiently parallelizing data mining algorithms: starting with the representation of an algorithm as a sequential composition of functions, we formally transform it into a parallel form using higher-order functions for specifying parallelism. We implement the approach as an extension of the industrial-strength Java-based library Xelopes, and we illustrate its use by developing a multi-threaded Java program for the popular naive Bayes classification algorithm. In comparison with the popular MapReduce programming model, our resulting programs enable not only data-parallel, but also task-parallel implementation and a combination of both. Our experiments demonstrate an efficient parallelization and good scalability on multi-core processors.

On Algebras of Algorithms and Specifications over Uninterpreted Data

Summary This paper continues formalization in Mizar [2, 1] of basic notions of the composition-nominative approach to program semantics [13] which was started in [8, 11]. The composition-nominative approach studies mathematical models of computer programs and data on various levels of abstraction and generality and provides tools for reasoning about their properties. Besides formalization of semantics of programs, certain elements of the composition-nominative approach were applied to abstract systems in a mathematical systems theory [4, 6, 7, 5, 3]. In the paper we introduce a definition of the notion of a binominative function over a set D understood as a partial function which maps elements of D to D. The sets of binominative functions and nominative predicates [11] over given sets form the carrier of the generalized Glushkov algorithmic algebra [14]. This algebra can be used to formalize algorithms which operate on various data structures (such as multidimensional arrays, lists, etc.) and reason about their properties. We formalize the operations of this algebra (also called compositions) which are valid over uninterpretated data and which include among others the sequential composition, the prediction composition, the branching composition, the monotone Floyd-Hoare composition, and the cycle composition. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [10, 12, 9].