Here, for the first time, development studies encounters the set of ideas popularly known as 'Chaos Theory'. Samir Rihani applies to the processes of economic development, ideas from complex adaptive systems like uncertainty, complexity, and unpredictability. Rihani examines various aspects of the development process - including the World Bank, debt, and the struggle against poverty - and demonstrates the limitations of fundamentally linear thinking in an essentially non-linear world.

Harmonic Grammar (HG) is a model of linguistic constraint interaction in which well-formedness is calculated as the sum of weighted constraint violations. We show how linear programming algorithms can be used to determine whether there is a weighting for a set of constraints that fits a set of linguistic data. The associated software package OT-Help provides a practical tool for studying large and complex linguistic systems in the HG framework and comparing the results with those of OT. We describe (...) the translation from Harmonic Grammars to systems solvable by linear programming, and we illustrate the usefulness of OT-Help with a set of studies of the predictions HG makes for phonological typology. (shrink)

Linear Logic is a versatile framework with diverse applications in computer science and mathematics. One intriguing fragment of Linear Logic is Multiplicative-Additive Linear Logic (MALL), which forms the exponential-free component of the larger framework. Modifying MALL, researchers have explored weaker logics such as Noncommutative MALL (Bilinear Logic, BL) and Cyclic MALL (CyMALL) to investigate variations in commutativity. In this paper, we focus on Cyclic Nonassociative Bilinear Logic (CyNBL), a variant that combines noncommutativity and nonassociativity. We introduce a (...) sequent system for CyNBL, which includes an auxiliary system for incorporating nonlogical axioms. Notably, we establish the cut elimination property for CyNBL. Moreover, we establish the strong conservativeness of CyNBL over Full Nonassociative Lambek Calculus (FNL) without additive constants. The paper highlights that all proofs are constructed using syntactic methods, ensuring their constructive nature. We provide insights into constructing cut-free proofs and establishing a logical relationship between CyNBL and FNL. (shrink)

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer's rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

In this article we investigate whether the following conjecture is true or not: does the addition-free theta functions form a canonical notation system for the linear versions of Friedman’s well-partial-orders with the so-called gap-condition over a finite set of n labels. Rather surprisingly, we can show this is the case for two labels, but not for more than two labels. To this end, we determine the order type of the notation systems for addition-free theta functions in terms of (...) ordinals less than ε0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _0$$\end{document}. We further show that the maximal order type of the Friedman ordering can be obtained by a certain ordinal notation system which is based on specific binary theta functions. (shrink)

The main result of this paper is a normalizing system of natural deduction for the full language of intuitionistic linear logic. No explicit weakening or contraction rules for -formulas are needed. By the systematic use of general elimination rules a correspondence between normal derivations and cut-free derivations in sequent calculus is obtained. Normalization and the subformula property for normal derivations follow through translation to sequent calculus and cut-elimination.

For linear discrete-time systems with randomly variable input trail length, a proportional- type iterative learning control law is proposed. To tackle the randomly variable input trail length, a modified control input at the desirable trail length is introduced in the proposed ILC law. Under the assumption that the initial state fluctuates around the desired initial state with zero mean, the designed ILC scheme can drive the ILC tracking errors to zero at the desirable trail length in expectation sense. The (...) designed ILC algorithm allows the trail length of control input which is different from system state and output at a specific iteration. In addition, the identical initial condition widely used in conventional ILC design is also mitigated. An example manifests the validity of the proposed ILC algorithm. (shrink)

Let F be a signature and R a strictly orthogonal rewrite system on ground terms of F . We give an effective proof of a bounding condition for R , based on a detailed analysis of how terms are transformed during the rewrite process, which allows us to give recursive bounds on the derivation lengths of terms. We give a syntactic characterisation of the Grzegorczyk hierarchy and a rewriting schema for calculating its functions. As a consequence of this, using (...) results of Elias Tahhan–Bittar, it can be shown that, for n⩾3 , the derivation length functions for functions in Grzegorczyk class E n belong to Grzegorczyk class E n+1 . We also give recursive bounds for the derivation lengths of functions defined by parameter recursion. (shrink)

The paper is devoted to the concise description of some Natural Deduction System (ND for short) for Linear Temporal Logic. The system's distinctive feature is that it is labelled and analytical. Labels convey necessary semantic information connected with the rules for temporal functors while the analytical character of the rules lets the system work as a decision procedure. It makes it more similar to Labelled Tableau Systems than to standard Natural Deduction. In fact, our solution of (...) linearity representation is rather independent of the underlying proof method, provided that some form of (analytic) cut is admissible. We will also discuss some generalisations of the system and compare it with other formalizations of linearity. (shrink)

This paper investigates the bipartite consensus of linear discrete-time multiagent systems with exogenous disturbances. A discrete-time disturbance-observer- based technology is involved for attenuating the exogenous disturbances. And both the state feedback and observer-based output feedback bipartite consensus protocols are proposed by using the DTDO method. It turned out that bipartite consensus can be realized under the given protocols if the topology is connected and structurally balanced. Finally, numerical simulations are presented to illustrate the theoretical findings.

Due to the complex behavior of a multiscroll chaotic system, it is a good candidate for the secure communications. In this paper, by adding an additional variable to the modified Lorenz-type system, a new chaotic system that includes only linear and piecewise items but can generate 4n + 4 scroll chaotic attractors via choosing the various values of natural number n is proposed. Its dynamics including bifurcation, multistability, and symmetric coexisting attractors, as well as various chaotic (...) and periodic behaviors, are analyzed by means of attraction basin, bifurcation diagram, dynamic map, phase portrait, Lyapunov exponent spectrum, and C0 complexity in detail. The mechanism of the occurrence for generating multiscroll chaotic attractors is presented. Finally, this multiscroll chaotic system is implemented by using the Altera Cyclone IV EP4CE10F17C8 FPGA. It is found that this FPGA-based design has an advantage of requiring less resources for 0% of the embedded multipliers and 0% of the PLLs of this FPGA are occupied. (shrink)

The logic FBCI given by linearly ordered BCI-matrices is known not to be an axiomatic extension of the well-known BCI logic. In this paper we axiomatize FBCI by adding a recursively enumerable set of schemes of inference rules to BCI and show that there is no finite axiomatization for FBCI.

Anderson and Belnap presented indexed Fitch-style natural deduction systems for the relevant logics R, E, and T. This work was extended by Brady to cover a range of relevant logics. In this paper I present indexed tree natural deduction systems for the Anderson–Belnap–Brady systems and show how to translate proofs in one format into proofs in the other, which establishes the adequacy of the tree systems.

Order picking, which is collecting a set of products from different locations in a warehouse, has repeatedly been described as one of the most laborious and time-consuming internal logistic processes. Each order is issued to pick some products located at given locations in the warehouse. In this paper, we consider an order picking problem, in which a number of orders with different delivery due dates are going to be retrieved by a limited number of order pickers in multiperiods such that (...) the total tardiness is minimized. The aim is to determine a retrieval plan in terms of order batching and order picker multitrip routing as decision variables. Besides, products are arrived and replenished at the predetermined locations at different periods. Therefore, products sitting in those locations should be delivered soon to provide empty rooms for replenishment. A mixed integer linear programming formulation is proposed for this new problem. The model is optimally solved for small-size problems. For larger instances, grouping metaheuristic algorithms are proposed based on particle swarm optimization and the league championship algorithm that use group-based operators to generate reasonable batches of orders. Improvement heuristics are designed as well. The performance of the MILP formulation and metaheuristic algorithms is analyzed for different problem instances whose designs are based on real data gathered from an auto parts warehouse. Results indicate that our algorithms can stably solve large instances of the problem in a reasonable time. (shrink)

We introduce the notion of τ-like partial order, where τ is one of the linear order types ω, ω*, ω + ω*, and ζ. For example, being ω-like means that every element has finitely many predecessors, while being ζ-like means that every interval is finite. We consider statements of the form “any τ-like partial order has a τ-like linear extension” and “any τ-like partial order is embeddable into τ” . Working in the framework of reverse mathematics, we show (...) that these statements are equivalent either to equation image or to equation image over the usual base system equation image. (shrink)

It is well known that infinite minimal sets for continuous functions on the interval are Cantor sets; that is, compact zero dimensional metrizable sets without isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat Chaos 13:1665–1671, 2003) that infinite minimal sets for continuous functions on connected linearly ordered spaces enjoy the same properties as Cantor sets except that they can fail to be metrizable. However, no examples of such subsets have been known. In this note (...) we construct, in ZFC, ${2^{\mathfrak{c}}}$ non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces. (shrink)

In an unpublished note Reddy introduced an extended intuitionistic linear calculus, called LLMS (for Linear Logic Model of State), to model state manipulation via the notions of sequential composition and ‘regenerative values’. His calculus introduces the connective ‘before’ ▹ and an associated modality †, for the storage of objects sequentially reusable. Earlier and independently de Paiva introduced a (collection of) dialectica categorical models for (classical and intuitionistic) Linear Logic, the categories Dial2Set. These categories contain, apart from the (...) structure needed to model linear logic, an extra tensor product functor and an extra comonad structure corresponding to a modality related to the extra tensor product. It is surprising that these works arising from completely different motivations can be related in a meaningful way. In this article, following joint work with Corrêa and Haeusler, we first adapt Reddy's system LLMS providing a commutative version of the connective ‘before’ and its associated modality and then construct a dialectica category on Sets , which we show is a sound model for the modified version of Reddy's the system LLMSc. Moreover, following the work of Tucker, we provide another variant of the Dialectica categories with a non-commutative tensor and its associated modality, which models soundlyLLMS itself. We conclude with some speculation on future applications. (shrink)

Neuroethological investigations of mammalian and avian auditory systems have documented species-specific specializations for processing complex acoustic signals that could, if viewed in abstract terms, have an intriguing and striking relevance for human speech sound categorization and representation. Each species forms biologically relevant categories based on combinatorial analysis of information-bearing parameters within the complex input signal. This target article uses known neural models from the mustached bat and barn owl to develop, by analogy, a conceptualization of human processing of consonant plus (...) vowel sequences that offers a partial solution to the noninvariance dilemma the locus equations orderly output constraint”) is hypothesized based on the notion of an evolutionarily conserved auditory-processing strategy. High correlation and linearity between critical parameters in the speech signal that help to cue place of articulation categories might have evolved to satisfy a preadaptation by mammalian auditory systems for representing tightly correlated, linearly related components of acoustic signals. (shrink)

This paper is concerned with the event-based state and fault estimation problem for a class of linear discrete systems with randomly occurring faults and missing measurements. Different from the static event-based transmission mechanism with a constant threshold, a dynamic event-based mechanism is exploited here to regulate the threshold parameter, thus further reducing the amount of data transmission. Some mutually independent Bernoulli random variables are used to characterize the phenomena of ROFs and missing measurements. In order to simultaneously estimate the (...) system state and the fault signals, the main attention of this paper is paid to the design of recursive filter; for example, for all DETM, ROFs, and missing measurements, an upper bound for the estimation error covariance is ensured and the relevant filter gain matrix is designed by minimizing the obtained upper bound. Moreover, the rigorous mathematical analysis is carried out for the exponential boundedness of the estimation error. It is clear that the developed algorithms are dependent on the threshold parameters and the upper bound together with the probabilities of missing measurements and ROFs. Finally, a numerical example is provided to indicate the effectiveness of the presented estimation schemes. (shrink)

This paper introduce a new variant of the Genetic Algorithm whichis developed to handle multivariable, multi-objective and very high search space optimization problems like the solving system of non-linear equations. It is an integer coded Genetic Algorithm with conventional cross over and mutation but with Inverse algorithm is varying its search space by varying its digit length on every cycle and it does a fine search followed by a coarse search. And its solution to the optimization problem will (...) converge to precise value over the cycles. Every equation of the system is considered as a single minimization objective function. Multiple objectives are converted to a single fitness function by summing their absolute values. Some difficult test functions for optimization and applications are used to evaluate this algorithm. The results prove that this algorithm is capable to produce promising and precise results. (shrink)

This paper presents decomposition of the fourth-order Euler-type linear time-varying system as a commutative pair of two second-order Euler-type systems. All necessary and sufficient conditions for the decomposition are deployed to investigate the commutativity, sensitivity, and the effect of disturbance on the fourth-order LTVS. Some systems are commutative, and some are not commutative, while some are commutative under certain conditions. Based on this fact, the commutativity of fourth-order Euler-type LTVS is investigated by introducing the commutative requirements, theories, and (...) conditions. The fourth-order Euler-type LTVSs are investigated into commutative pairs of twice Euler-type second-order linear time-varying systems. The decomposition theories and conditions are derived, proved, and solved to simplify the use of commutativity for practical and industrial uses. Some fourth-order systems are sensitive toward change in initial conditions or parameters while others are not, and the effect due to disturbance also varies within systems. Furthermore, the stability and robustness of systems have so many issues. But we consider fourth-order Euler-type LTVS to observe, investigate, and tackle these issues. Lastly, the realization of fourth-order LTVS from cascaded two second-order systems can be laboratory experimented which is an open problem for future engineers to investigate. However, the theoretical results show a good agreement with the simulation results is considered in this work. Perhaps it might have unlimited physical applications in science and engineering as well as theoretical contribution. But beyond any reasonable doubt, the novelty is guaranteed because this study is the first of its kind that introduces the decomposition of the fourth-order Euler-type linear time-varying system as a commutative pair of two second-order Euler-type systems. Illustrative examples are presented to support the results. (shrink)

This article describes the emergence of formal methods in theory of partial differential equations in the French school of mathematics through Janet’s work in the period 1913–1930. In his thesis and in a series of articles published during this period, Janet introduced an original formal approach to deal with the solvability of the problem of initial conditions for finite linear PDE systems. His constructions implicitly used an interpretation of a monomial PDE system as a generating family of a (...) multiplicative set of monomials. He introduced an algorithmic method on multiplicative sets to compute compatibility conditions, and to study the problem of the existence and the uniqueness of a solution to a linear PDE system with given initial conditions. The compatibility conditions are formulated using a refinement of the division operation on monomials defined with respect to a partition of the set of variables into multiplicative and non-multiplicative variables. Janet was a pioneer in the development of these algorithmic methods, and the completion procedure that he introduced on polynomials was the first one in a long and rich series of works on completion methods which appeared independently throughout the twentieth-century in various algebraic contexts. (shrink)

A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating (...) values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behavior is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper. (shrink)

We present an overview of linear-time temporal logics with Presburger constraints whose models are sequences of tuples of integers. Such formal specification languages are well-designed to specify and verify systems that can be modelled with counter systems. The paper recalls the general framework of LTL over concrete domains and presents the main decidability and complexity results related to fragments of Presburger LTL. Related formalisms are also briefly presented.