Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility

Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant strings that equate the left and right hand sides of the equation. While the problem of solving word equations is decidable, the decidability of the problem of solving a word equation with a length constraint (i.e., a constraint relating the lengths of words in the word equation) has remained a long-standing open problem. In this paper, we focus on the subclass of quadratic word equations, i.e., in which each variable occurs at most twice. We first show that the length abstractions of solutions to quadratic word equations are in general not Presburger-definable. We then describe a class of counter systems with Presburger transition relations which capture the length abstraction of a quadratic word equation with regular constraints. We provide an encoding of the effect of a simple loop of the counter systems in the theory of existential Presburger Arithmetic with divisibility (PAD). Since PAD is decidable, we get a decision procedure for quadratic words equations with length constraints for which the associated counter system is \emph{flat} (i.e., all nodes belong to at most one cycle). We show a decidability result (in fact, also an NP algorithm with a PAD oracle) for a recently proposed NP-complete fragment of word equations called regular-oriented word equations, together with length constraints. Decidability holds when the constraints are additionally extended with regular constraints with a 1-weak control structure.Comment: 18 page

Genetic Instability : the dark side of the hypoxic response

Under low oxygen tension, the activated transcription factor HIF-1? upregulates an array of hypoxia-inducible genes via heterodimerization with ARNT and binding to the hypoxia-responsive element in the promoter. Alternatively, HIF-1? regulates hypoxia-responsive genes by functionally antagonizing the oncoprotein Myc via protein-protein interactions. This so-called HIF-1?–Myc mechanism apparently not only accounts for the gene up-regulation, but also for the gene down-regulation during hypoxia, depending upon the active and repressive nature of Myc in gene expression. Indeed, our recent study demonstrated that both mismatch repair genes, MSH2 and MSH6, are inhibited by this mechanism in a p53-dependent manner. In particular, the constitutively bound transcription factor Sp1 serves as a molecular switch by recruiting HIF-1? in hypoxia to displace the transcription activator Myc from the promoter. Therefore, our findings shed light on the mechanisms underlying hypoxia-induced genetic instability, an “adverse” effect of the hypoxic response, and yet a germane process to tumor survival and progression

To immerse or not? Experimenting with two virtual retail environments

Purpose: The aim of this paper is to examine the determinants of users’ simulated experience in a virtual store and to show the subsequent impact of that experience on engagement. The outcome of that engagement is examined in relation to enjoyment, satisfaction and purchase intentions. Design/methodology/approach: The method comprised an experiment comparing users’ perceptions of a standard 2D online clothing store with an enhanced, immersive one that aimed to provide shopping value approaching that of a traditional store by using a 3D experience where participants wore special glasses and a data glove. Findings: Results demonstrate the major role of telepresence components in simulated experience and the critical role of that experience, along with hedonic and utilitarian values, in engagement. Purchase intention is influenced by satisfaction, which is in turn influenced by enjoyment and engagement. Engagement in turn is influenced by utilitarian and hedonic value and the experience of product simulation or telepresence, which is composed of control, colour and graphics vividness, and 3D authenticity. In the immersive, 3D environment experience is more associated with engagement and enjoyment, leading to greater purchase intention. The immersive, 3D environment thus has the potential to rival traditional shopping in terms of experience, resulting in higher sales for retailers and satisfaction for consumers. Originality: This work has evaluated a robust model of purchase intention and demonstrated it to hold not only in a 3D environment on a conventional computer platform, but also in an immersive one, where participants wear special glasses and a data glove

Imaging stress and magnetism at high pressures using a nanoscale quantum sensor.

Pressure alters the physical, chemical, and electronic properties of matter. The diamond anvil cell enables tabletop experiments to investigate a diverse landscape of high-pressure phenomena. Here, we introduce and use a nanoscale sensing platform that integrates nitrogen-vacancy (NV) color centers directly into the culet of diamond anvils. We demonstrate the versatility of this platform by performing diffraction-limited imaging of both stress fields and magnetism as a function of pressure and temperature. We quantify all normal and shear stress components and demonstrate vector magnetic field imaging, enabling measurement of the pressure-driven [Formula: see text] phase transition in iron and the complex pressure-temperature phase diagram of gadolinium. A complementary NV-sensing modality using noise spectroscopy enables the characterization of phase transitions even in the absence of static magnetic signatures

Selection of reliable reference genes for the normalisation of gene expression levels following time course LPS stimulation of murine bone marrow derived macrophages

© 2017 The Author(s). Background: Macrophages are key players in the initiation, perpetuation and regulation of both innate and adaptive immune responses. They largely perform these roles through modulation of the expression of genes, especially those encoding cytokines. Murine bone marrow derived macrophages (BMDMs) are commonly used as a model macrophage population for the study of immune responses to pro-inflammatory stimuli, notably lipopolysaccharide (LPS), which may be pertinent to the human situation. Evaluation of the temporal responses of LPS stimulated macrophages is widely conducted via the measurement of gene expression levels by RT-qPCR. While providing a robust and sensitive measure of gene expression levels, RT-qPCR relies on the normalisation of gene expression data to a stably expressed reference gene. Generally, a normalisation gene(s) is selected from a list of "traditional" reference genes without validation of expression stability under the specific experimental conditions of the study. In the absence of such validation, and given that many studies use only a single reference gene, the reliability of data is questionable. Results: The stability of expression levels of eight commonly used reference genes was assessed during the peak (6 h) and resolution (24 h) phases of the BMDM response to LPS. Further, this study identified two additional genes, which have not previously been described as reference genes, and the stability of their expression levels during the same phases of the inflammatory response were validated. Importantly, this study demonstrates that certain "traditional" reference genes are in fact regulated by LPS exposure, and, therefore, are not reliable candidates as their inclusion may compromise the accuracy of data interpretation. Testament to this, this study shows that the normalisation of gene expression data using an unstable reference gene greatly affects the experimental data obtained, and, therefore, the ultimate biological conclusions drawn. Conclusion: This study reaffirms the importance of validating reference gene stability for individual experimental conditions. Given that gene expression levels in LPS stimulated macrophages is routinely used to infer biological phenomena that are of relevance to human conditions, verification of reference gene expression stability is crucial

The role of payoff parameters for cooperation in the one-shot Prisoner\u27s Dilemma

The Prisoner\u27s Dilemma is arguably the most important model of social dilemmas, but our knowledge about how its material payoff structure affects cooperation is incomplete. We investigate the effect of variation in material payoffs on cooperation in one-shot Prisoner\u27s Dilemma games. We report results from three experiments (N = 1,993): in a preliminary experiment, we vary the payoffs over a large range. In our first main experiment (Study 1), we present a novel design that varies payoffs orthogonally in a within-subjects design. Our second main experiment, Study 2, investigates the orthogonal variation of payoffs in a between-subjects design. In a complementary analysis we also study the closely related payoff indices of normalized loss and gain, and the K-index. A robust finding of our experiments is that cooperation increases with the gains of mutual cooperation over mutual defection