Boolean Components Research Articles

Linear cuts in Boolean networks

Boolean networks are popular tools for the exploration of qualitative dynamical properties of biological systems. Several dynamical interpretations have been proposed based on the same logical structure that captures the interactions between Boolean components. They reproduce, in different degrees, the behaviours emerging in more quantitative models. In particular, regulatory conflicts can prevent the standard asynchronous dynamics from reproducing some trajectories that might be expected upon inspection of more detailed models. We introduce and study the class of networks with linear cuts, where linear components—intermediates with a single regulator and a single target—eliminate the aforementioned regulatory conflicts. The interaction graph of a Boolean network admits a linear cut when a linear component occurs in each cycle and in each path from components with multiple targets to components with multiple regulators. Under this structural condition the attractors are in one-to-one correspondence with the minimal trap spaces, and the reachability of attractors can also be easily characterized. Linear cuts provide the base for a new interpretation of the Boolean semantics that captures all behaviours of multi-valued refinements with regulatory thresholds that are uniquely defined for each interaction, and contribute a new approach for the investigation of behaviour of logical models.

P200 Characterisation of remission in patients with rheumatoid arthritis treated with upadacitinib or comparators

Abstract Background Across all phase 3 studies, treatment with upadacitinib (UPA), a JAK1-selective inhibitor, was associated with significantly higher remission (REM) rates, compared to placebo (PBO) or active comparators, in RA patients who were methotrexate (MTX)-naive, had inadequate response to conventional synthetic (csDMARD-IR) or had inadequate response or intolerance to biologic DMARDs (bDMARD-IR). Methods REM definitions are based on composite scores of various individual assessments of disease activity. To determine the response to UPA on REM and component assessments, we assessed the proportions of patients achieving REM using multiple REM definitions, and the improvement in their respective individual components, compared to PBO or active comparators, in 3 different RA patient populations spanning a range of RA patient populations. Methods: Three phase 3 studies included patients who were MTX naïve (SELECT EARLY, n = 945), MTX-IR (SELECT COMPARE, n = 1629) and bDMARD-IR (SELECT BEYOND, n = 498). The proportion of patients achieving REM at Week 12 by 4 definitions (DAS28-CRP<2.6; CDAI <2.8; SDAI <3.3 and Boolean, defined as < 1 for TJC, SJC, patient’s global assessment of disease activity [PtGA], and CRP <1 mg/L) were determined. For each definition of REM, the mean change in each of the respective component scores was also assessed. Binary endpoints are based on Non-responder imputation (NRI), and continuous endpoints on mixed-effect model repeat measurement (MMRM). Comparisons were made between UPA-treated groups vs respective control arms (MTX, adalimumab [ADA] or PBO). Results Patient demographics and disease characteristics have been previously reported. 1-3 At 12 weeks, in EARLY and COMPARE, a significantly greater proportion of patients receiving UPA 15 mg or 30 mg QD achieved REM by all 4 definitions vs MTX, PBO or ADA (Table). In BEYOND, (a refractory population many of whom had inadequate response to multiple bDMARDs), a significantly greater proportion of patients receiving UPA 30mg achieved all REM definitions vs PBO within the first 12 weeks, with significantly greater proportions on UPA 15mg achieving DAS28-CRP<2.6 and Boolean REM. Rates of REM in BEYOND further increased through Wk 24 for both dose groups. Compared to respective control groups, patients receiving UPA 15 or 30 mg QD had significantly greater improvements in each REM disease component (except for PhGA vs ADA in COMPARE). Significantly more patients receiving UPA also achieved the required cutoffs on the individual components of Boolean REM compared to respective controls. Conclusion Significantly greater proportions of patients receiving UPA 15 or 30mg achieved REM by multiple definitions at 12 weeks compared to PBO, MTX or ADA. All disease activity components of each REM definition were significantly improved in patients receiving UPA compared to MTX or PBO, and all Boolean components were significantly improved in patients receiving UPA 15mg compared to ADA. Disclosures S. Hall: Grants/research support; AbbVie, BMS, Lilly, Janssen, Pfizer, UCB, Novartis. T. Takeuchi: Honoraria; Mitsubishi-Tanabe Pharma Corp, Janssen Pharma KK, Chugai Pharma, Astellas Pharma Inc., AbbVie GK, Eisai Co., Ltd, BMS, Daiichi Sankyo Company Ltd, Eli Lilly Japan KK, Pfizer Japan Inc. Grants/research support; Pfizer Japan Inc., Eisai Co., Ltd, Astellas Pharma Inc., AbbVie GK, Asahi Kasei Pharma Corp, Nippon Kayaku Co., Ltd, Taisho Toyama Pharma, Takeda Pharma, AYUMI Pharma, Takahashi Industrial. G. Thomson: Consultancies; Amgen. Grants/research support; AbbVie. P. Emery: Grants/research support; Research grants and consulting fees from Pfizer, MSD, AbbVie, Bristol-Myers Squibb, UCB, Roche, Novartis, Samsung, Sandoz and Lilly. B. Combe: Grants/research support; Consultancy fees from Abbvie, BMS, Jansen, Lilly, MSD, Pfizer, Roche Chugai, UCB. A. Everding: None. K. Pavelka: Honoraria; Honoraria for lectures and consultations from companies: Pfizer, MSD, BMS, UCB, Amgen, Egis, Roche, AbbVie. Y. Song: Corporate appointments; Employee of AbbVie. T. Shaw: Corporate appointments; Employee of AbbVie. A. Friedman: Corporate appointments; Employee of AbbVie. I. Song: Corporate appointments; Employee of AbbVie. E. Mysler: Grants/research support; Research grants and consulting fees from AbbVie, Lilly, Pfizer, Roche, BMS, Sandoz.

Formal Verification of Hardware Components in Critical Systems

Hardware components, such as memory and arithmetic units, are integral part of every computer-controlled system, for example, Unmanned Aerial Vehicles (UAVs). The fundamental requirement of these hardware components is that they must behave as desired; otherwise, the whole system built upon them may fail. To determine whether or not a component is behaving adequately, the desired behaviour of the component is often specified in the Boolean algebra. Boolean algebra is one of the most widely used mathematical tools to analyse hardware components represented at gate level using Boolean functions. To ensure reliable computer-controlled system design, simulation and testing methods are commonly used to detect faults; however, such methods do not ensure absence of faults. In critical systems’ design, such as UAVs, the simulation-based techniques are often augmented with mathematical tools and techniques to prove stronger properties, for example, absence of faults, in the early stages of the system design. In this paper, we define a lightweight mathematical framework in computer-based theorem prover Coq for describing and reasoning about Boolean algebra and hardware components (logic circuits) modelled as Boolean functions. To demonstrate the usefulness of the framework, we (1) define and prove the correctness of principle of duality mechanically using a computer tool and all basic theorems of Boolean algebra, (2) formally define the algebraic manipulation (step-by-step procedure of proving functional equivalence of functions) used in Boolean function simplification, and (3) verify functional correctness and reliability properties of two hardware components. The major advantage of using mechanical theorem provers is that the correctness of all definitions and proofs can be checked mechanically using the type checker and proof checker facilities of the proof assistant Coq.

Landscape Boolean functions

In this paper we define a class of generalized Boolean functions defined on $ {\mathbb F}_2^n $ with values in $ {\mathbb Z}_q $ (we consider $ q = 2^k $, $ k\geq 1 $, here), which we call landscape functions (whose class contains generalized bent, semibent, and plateaued) and find their complete characterization in terms of their Boolean components. In particular, we show that the previously published characterizations of generalized plateaued Boolean functions (which includes generalized bent and semibent) are in fact particular cases of this more general setting. Furthermore, we provide an inductive construction of landscape functions, having any number of nonzero Walsh-Hadamard coefficients. We also completely characterize generalized plateaued functions in terms of the second derivatives and fourth moments.

Considering nearest neighbor constraints of quantum circuits at the reversible circuit level

Since many underlying quantum algorithms include a Boolean component, synthesis of the respective circuits is often conducted by a two-stage procedure: First, a reversible circuit realizing the Boolean component is generated. Afterwards, this circuit is mapped into a respective quantum gate cascade. In addition, recent physical accomplishments have led to further issues to be considered, e.g. nearest neighbor constraints. However, due to the lack of proper metrics, these constraints usually have been addressed at the quantum circuit level only. In this paper, we present an approach that allows the consideration of nearest neighbor constraints already at the reversible circuit level. For this purpose, a recently introduced gate library is assumed for which a proper metric is proposed. By means of an optimization approach, the applicability of the proposed scheme is illustrated.

Combination etanercept and methotrexate provides better disease control in very early (≤4 months) versus early rheumatoid arthritis (>4 months and

ObjectiveThe objective of this post hoc analysis was to test the benefits of treating very early rheumatoid arthritis (VERA; ≤4 months) using COMET trial data. Treatment response in VERA and...

Mental models of Boolean concepts

Negation, conjunction, and disjunction are major building blocks in the formation of concepts. This article presents a new model-based theory of these Boolean components. It predicts that individuals simplify the models of instances of concepts. Evidence corroborates the theory and challenges alternative accounts, such as those based on minimal descriptions, algebraic complexity, or structural invariance. A computer program implementing the theory yields more accurate predictions than these rival accounts. Two experiments showed that the numbers of models of a Boolean concept predict the difficulty of formulating a description of it. As mental models may also underlie deductive reasoning, the present theory integrates two hitherto separate areas of investigation.

Effects of topology on network evolution

The ubiquity of scale-free topology in nature raises the question of whether this particular network design confers an evolutionary advantage1. A series of studies has identified key principles controlling the growth and the dynamics of scale-free networks2,3,4. Here, we use neuron-based networks of boolean components as a framework for modelling a large class of dynamical behaviours in both natural and artificial systems5,6,7. Applying a training algorithm, we characterize how networks with distinct topologies evolve towards a pre-established target function through a process of random mutations and selection8,9,10. We find that homogeneous random networks and scale-free networks exhibit drastically different evolutionary paths. Whereas homogeneous random networks accumulate neutral mutations and evolve by sparse punctuated steps11,12, scale-free networks evolve rapidly and continuously. Remarkably, this latter property is robust to variations of the degree exponent. In contrast, homogeneous random networks require a specific tuning of their connectivity to optimize their ability to evolve. These results highlight an organizing principle that governs the evolution of complex networks and that can improve the design of engineered systems.

Redundancy removal and test generation for circuits with non-Boolean primitives

Production VLSI circuits typically consist of primitives like tristate buffers, bidirectional buffers, and bus configurations that assume non-Boolean values like the high-impedance state. We describe a systematic methodology for extending test generation algorithms that work on combinational circuits with only Boolean primitives to full-scan production circuits. Key features of the methodology are illustrated using the energy minimization based test generation algorithm for combinational circuits. The main features of our methodology that make the test generation algorithm practical for large production circuits are: (1) only one Boolean variable is used to represent the value on a signal and all signals assume only Boolean values during the test generation procedure; (2) the function of non-Boolean primitives is separated into Boolean and non-Boolean components with energy functions required only for the Boolean component; and (3) non-Boolean components are implicitly considered in the energy minimization procedure. In this process, no new energy functions other than the normal Boolean gate energy functions are needed. We give a method for identifying and removing redundancies in production circuits using energy minimization. The formulation is also applicable to Boolean satisfactorily and BDD methods. We first use the test generation algorithm for identifying undetectable faults and then relax specific constraints in the original test generation problem by ignoring the non-Boolean components. We show that undetectability in the relaxed formulation implies redundancy. We report redundancy removal results for production VLSI circuits, ISCAS 85, and full-scan versions of the ISCAS 89 benchmark circuits.

A study of probabilistic information retrieval systems in the case of inconsistent expert judgments

The maximum entropy principle may be applied to the design of probabilistic retrieval systems. When there are inconsistent expert judgments, the resulting optimization problem cannot be solved. The inconsistency of the expert judgments can be revealed by solving a linear programming formulation. In the case of inconsistent judgment, four plausible schemes are proposed in order to find revised judgments which are consistent with the true data structure but still reflect the original expert judgment. These schemes are the Interactive, Minimum Distance, Minimum Cross-Entropy, and Path methods. Background and Purpose of the Study The maximum entropy principle (MEP) based on Shannon’s measure (Shannon, 1928) has been used with great success in many areas. Cooper and Huizinga (1982) and Cooper (1983) have applied the MEP to the design of probabilistic information retrieval systems. Specifically, we consider a collection of documents which are categorized into Boolean components by attributes. The MEP estimates the probability of “relevance” of each Boolean component by integrating expert judgments about the “relevance” of attributes with the observed distribution of the Boolean components. The MEP retrieval system, in response to a user’s request, provides an ordering of the Boolean components using this estimated probability of “relevance.” Cooper (1983) has noted the potential of the MEP retrieval system as follows

On the lattice structure of quantum logic

A weak logical structure is defined as a set of boolean propositional logics in which one can define common operations of negation and implication. The set union of the boolean components of a weak logical structure is a logic of propositions which is an orthocomplemented poset, where orthocomplementation is interpreted as negation and the partial order as implication. It is shown that if one can define on this logic an operation of logical conjunction which has certain plausible properties, then the logic has the structure of an orthomodular lattice. Conversely, if the logic is an orthomodular lattice then the conjunction operation may be defined on it.