Monotone Ones Research Articles

Non-monotonic auto-regulation in single gene circuits.

We theoretically study the effects of non-monotonic response curves in genetic auto-regulation by exploring the possible dynamical behaviors for such systems. Our motivation is twofold: we aim at conceiving the simplest genetic circuits for synthetic biology and at understanding the natural auto-regulation of the LrpB protein of the Sulfolobus solfataricus archaeon which exhibits non-monotonicity. We analyzed three toy models, based on mass-action kinetics, with increasing complexity and sought for oscillations and (fast) bistable switching. We performed large parameter scans and sensitivity analyses, and quantified the quality of the oscillators and switches by computing relative volumes in parameter space reproducing the sought dynamical behavior. All single gene systems need finely tuned parameters in order to oscillate, but bistable switches are more robust against parameter changes. We expected non-monotonic switches to be faster than monotonic ones, however solutions combining both auto-activation and repression in the physiological range to obtain fast switches are scarce. Our analysis shows that the Ss-LrpB system can not provide a bistable switch and that robust oscillations are unlikely. Gillespie simulations suggest that the function of the natural Ss-LrpB system is sensing via a spiking behavior, which is in line with the fact that this protein has a metabolic regulatory function and binds to a ligand.

Single-electron pumping in single-common-gate quadruple-dot devices with asymmetric gate capacitances

Single-common-gate quadruple-dot single-electron devices with asymmetric gate capacitances (Cg) can transfer a single electron to a negative-biased electrode by alternating only one gate voltage. The pumping is possible for non-monotonic Cg distributions such as saw-toothed and various random Cg distributions, though the Cg distributions of the previously reported common-gate triple-dot pumping devices are limited to monotonic ones. The maximum absolute value of negative-biasing voltage against which a single electron can be transferred is 0.2181·e/Cj, where e is the elementary charge and Cj is the junction capacitance. This is 2.7 times larger than the largest one in common-gate triple-dot pumping devices with a monotonic Cg distribution.

Juxtaposing Catalan Permutation Classes with Monotone Ones

This paper enumerates all juxtaposition classes of the form "$\mathrm{Av}(abc)$ next to $\mathrm{Av}(xy)$", where $abc$ is a permutation of length three and $xy$ is a permutation of length two. We use Dyck paths decorated by sequences of points to represent elements from such a juxtaposition class. Context free grammars are then used to enumerate these decorated Dyck paths.

Natural Deduction for Four-Valued both Regular and Monotonic Logics

The development of recursion theory motivated Kleene to create regular three-valued logics. Remove it taking his inspiration from the computer science, Fitting later continued to investigate regular three-valued logics and defined them as monotonic ones. Afterwards, Komendantskaya proved that there are four regular three-valued logics and in the three-valued case the set of regular logics coincides with the set of monotonic logics. Next, Tomova showed that in the four-valued case regularity and monotonicity do not coincide. She counted that there are 6400 four-valued regular logics, but only six of them are monotonic. The purpose of this paper is to create natural deduction systems for them. We also describe some functional properties of these logics.

Dose-response meta-analysis of differences in means.

BackgroundMeta-analytical methods are frequently used to combine dose-response findings expressed in terms of relative risks. However, no methodology has been established when results are summarized in terms of differences in means of quantitative outcomes.MethodsWe proposed a two-stage approach. A flexible dose-response model is estimated within each study (first stage) taking into account the covariance of the data points (mean differences, standardized mean differences). Parameters describing the study-specific curves are then combined using a multivariate random-effects model (second stage) to address heterogeneity across studies.ResultsThe method is fairly general and can accommodate a variety of parametric functions. Compared to traditional non-linear models (e.g. Emax, logistic), spline models do not assume any pre-specified dose-response curve. Spline models allow inclusion of studies with a small number of dose levels, and almost any shape, even non monotonic ones, can be estimated using only two parameters. We illustrated the method using dose-response data arising from five clinical trials on an antipsychotic drug, aripiprazole, and improvement in symptoms in shizoaffective patients. Using the Positive and Negative Syndrome Scale (PANSS), pooled results indicated a non-linear association with the maximum change in mean PANSS score equal to 10.40 (95 % confidence interval 7.48, 13.30) observed for 19.32 mg/day of aripiprazole. No substantial change in PANSS score was observed above this value. An estimated dose of 10.43 mg/day was found to produce 80 % of the maximum predicted response.ConclusionThe described approach should be adopted to combine correlated differences in means of quantitative outcomes arising from multiple studies. Sensitivity analysis can be a useful tool to assess the robustness of the overall dose-response curve to different modelling strategies. A user-friendly R package has been developed to facilitate applications by practitioners.

Non-monotone traveling waves and entire solutions for a delayed nonlocal dispersal equation

This paper is concerned with the traveling waves and entire solutions for a delayed nonlocal dispersal equation with convolution- type crossing-monostable nonlinearity. We first establish the existence of non-monotone traveling waves. By Ikehara’s Tauberian theorem, we further prove the asymptotic behavior of traveling waves, including monotone and non-monotone ones. Then, based on the obtained asymptotic behavior, the uniqueness of the traveling waves is proved. Finally, the entire solutions are considered. By introducing two auxiliary monostable equations and establishing some comparison arguments for the three equations, some new types of entire solutions are constructed via the traveling wavefronts and spatially independent solutions of the auxiliary equations.

The nonadiabatic dust charge variation on dust acoustic solitary and shock waves in strongly coupled dusty plasmas

The combined effects of nonadiabatic dust charge fluctuation and strongly coupled dust particles on the nonlinear propagation of dust acoustic (DA) waves in dusty plasma consisting of nonthermal electrons and trapped ions with vortex-like distribution are presented here. We use generalized viscoelastic hydrodynamic model for dust particles. In the weak nonlinearity limit, a modified Korteweg–de Vries (KdV) equation with a damping term and a KdV–Burger equation have been derived in the kinetic regime and hydrodynamic regime, respectively. The approximate analytical solitary solution of modified KdV equation is derived in the weak nonadiabatic dust charge variation limit, which shows that the amplitude of DA solitary waves decreases with time. The presence of viscosity due to strong coupling stands for the formation of DA shock waves in the hydrodynamic regime. The results show that the DA shock waves will be oscillating one for weak viscosity and will become monotonic ones for large viscosity.

Numerical study and theoretical modelling of void growth in porous ductile materials subjected to cyclic loadings

Experiments have shown that in porous ductile materials, cyclic loadings lead to lower fracture strains than monotone ones. The effect has been tentatively ascribed to a continued increase of the mean porosity during each cycle with the number of cycles ( ratcheting of the porosity ). In this work, we first perform finite-element-based micromechanical simulations of elementary hollow cells. These cells are initially spherical, contain an initially spherical void and are loaded cyclically through conditions of homogeneous boundary strain rate; the triaxiality is held constant throughout in absolute value. These simulations fully confirm the interpretation of the reduced fracture strains under cyclic loadings just mentioned. The modelling of the ratcheting of the porosity is then discussed. Gurson (1977)'s classical model is shown not to be able to predict such an effect, the evolution of the porosity being stabilized right from the first semi-cycle. The so-called LPD model due to Leblond et al. (1995), an improved variant of Gurson (1977)'s model with a more refined description of strain hardening, makes a better job but fails to accurately reproduce the results of the micromechanical simulations. One explanation of the discrepancy is the assumption of positively proportional straining made in this model, which is basically inadequate for cyclic loadings. An improved version of the LPD model is introduced; this version discards this assumption, at the expense of introduction and radial discretization of an underlying spherical microcell at each material point. It is not significantly more com-putationally expensive than the old one and permits a satisfactory reproduction of the results of the micromechanical simulations. This paves the way to simulations of ductile rupture under cyclic loadings within the framework of Gurson-like models.

The exclusive interpretation of plural nominals in quantificational environments

In some contexts, plural nominals have inclusive interpretation, allowing atoms in their reference domain; in others, they are exclusive, allowing only sums. Selecting between the two interpretations has been shown to be sensitive to both world-knowledge pressures (Farkas & de Swart 2010) and contextual relevance (Grimm 2010). The principal semantic factor claimed to be involved is monotonicity direction (Sauerland, Anderssen & Yatsushiro 2005; Spector 2007; Zweig 2009; Farkas & de Swart 2010): upward monotone environments tend to select exclusive readings; downward monotone ones, inclusive readings. In four image verification experiments, we tested this claim and found support for the generalization. The effect of monotonicity direction, however, is small. Moreover we find that varying whether a plural is in the scope of a quantified description has a much larger effect on the prevalence of the exclusive interpretation. This suggests that monotonicity, though involved, is not a decisive factor in plural interpretation.

Tree projections and structural decomposition methods: Minimality and game-theoretic characterization

Tree projections provide a mathematical framework that encompasses all the various (purely) structural decomposition methods that have been proposed in the literature to single out classes of nearly-acyclic (hyper)graphs, such as the tree decomposition method, which is the most powerful decomposition method on graphs, and the (generalized) hypertree decomposition method, which is its natural counterpart on arbitrary hypergraphs.The paper analyzes this framework, by focusing in particular on “minimal” tree projections, that is, on tree projections without useless redundancies. First, it is shown that minimal tree projections enjoy a number of properties that are usually required for normal form decompositions in various structural decomposition methods. In particular, they enjoy the same kind of connection properties as (minimal) tree decompositions of graphs, with the result being tight in the light of the negative answer that is provided to the open question about whether they enjoy a slightly stronger notion of connection property, defined to speed-up the computation of hypertree decompositions. Second, it is shown that tree projections admit a natural game-theoretic characterization in terms of the Robber and Captain game. In this game, as for the Robber and Cops game characterizing tree decompositions, the existence of winning strategies implies the existence of monotone ones. As a special case, the Robber and Captain game can be used to characterize the generalized hypertree decomposition method, where such a game-theoretic characterization was missing and asked for. Besides their theoretical interest, these results have immediate algorithmic applications both for the general setting and for structural decomposition methods that can be recast in terms of tree projections.

Proportional and non-proportional hardening behavior of dual-phase steels

The elastic–plastic response of sheet materials during non-proportional paths is seldom incorporated in constitutive equations used for routine sheet forming simulation, but can have a significant effect on formability and springback. Monotonic tension and compression, coaxial tension–compression (T–C), coaxial compression–tension (C–T), and two-stage/non-coaxial tensile tests were performed for three grades of dual phase steels: DP590, DP780, and DP980. The reverse flow curves have three characteristics: reduced yield stress (Bauschinger effect), rapid transient strain hardening over a few percent strain, and long-term or “permanent” softening. The departure of the reverse hardening curves from monotonic ones is larger than with other typical sheet forming alloys, presumably because of the effects of large second-phase martensite particles in dual-phase steels.A Modified Chaboche type model was applied in this paper to simulate the elastic–plastic behavior of DP steels. In addition to one or more standard nonlinear components of the back stress, a linear term was added to represent the “permanent” offset of hardening following a stress reversal. The parameters for the model were fit using the monotonic and reverse tensile test results only, and the model predictions were then compared with large-strain balanced biaxial bulge test, non-coaxial, two-stage tensile tests, and draw-bend springback tests. The Modified Chaboche model captured the response following a path change much better than isotropic hardening models, but there is a fundamental difference between large-strain hardening after a path change that occurs between path reversals and changes of principal strain axis. The Chaboche model can reproduce either behaviors, but not both simultaneously.

Ductility of 304 stainless steel under pulsed uniaxial loading

The enhanced ductility that 304 stainless steel is exhibiting under pulsed loading (Zhang and Yuan, 2009) is investigated here using a combination of experiments and analysis. The simplest loading case, i.e., uniaxial tension, was selected to avoid the complicating effects of multiaxial stress states and/or contact and friction with a rigid die. Three types of tensile tests were performed: monotonic, pulsed and hold. For a range of strain rates, the pulsed and the hold tests exhibited different elongation-to-fracture from the monotonic tests. Digital image correlation and infrared thermography were employed to further probe this behavior. It was discovered that since the pulsed tests lasted longer than the corresponding monotonic ones (i.e., those with the same loading speed) but the total plastic work expended was comparable, milder deformation-induced heating developed in the pulsed tests. Since the resulting temperature gradients act as imperfections that trigger the localization of deformation, the enhanced elongation-to-fracture in the pulsed tests was attributed to the milder gradients that developed. Subsequently, a special isothermal tension test was used to de-couple the mechanical from the thermal behavior of the material and was repeated at various strain rates and temperatures. The material properties determined from this test were used as input to coupled, thermomechanical finite element simulations of the experiments. Despite numerous simplifications, such as constant thermal properties with temperature, the simulations captured the essential physics of the problem and yielded very close predictions of the elongation-to-fracture observed in the experiments.

Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints

In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general linearly constrained quasiconvex minimization problems. For this method, we prove global convergence when the regularization parameters go to zero. The latter assumption can be dropped when the function is assumed to be pseudoconvex. We also obtain convergence results for quasimonotone variational inequalities, which are more general than monotone ones.

Generating spherical multiquadrangulations by restricted vertex splittings and the reducibility of equilibrium classes

A quadrangulation is a graph embedded on the sphere such that each face is bounded by a walk of length 4, parallel edges allowed. All quadrangulations can be generated by a sequence of graph operations called vertex splitting, starting from the path P_2 of length 2. We define the degree D of a splitting S and consider restricted splittings S_{i,j} with i <= D <= j. It is known that S_{2,3} generate all simple quadrangulations. Here we investigate the cases S_{1,2}, S_{1,3}, S_{1,1}, S_{2,2}, S_{3,3}. First we show that the splittings S_{1,2} are exactly the monotone ones in the sense that the resulting graph contains the original as a subgraph. Then we show that they define a set of nontrivial ancestors beyond P_2 and each quadrangulation has a unique ancestor. Our results have a direct geometric interpretation in the context of mechanical equilibria of convex bodies. The topology of the equilibria corresponds to a 2-coloured quadrangulation with independent set sizes s, u. The numbers s, u identify the primary equilibrium class associated with the body by V\'arkonyi and Domokos. We show that both S_{1,1} and S_{2,2} generate all primary classes from a finite set of ancestors which is closely related to their geometric results. If, beyond s and u, the full topology of the quadrangulation is considered, we arrive at the more refined secondary equilibrium classes. As Domokos, L\'angi and Szab\'o showed recently, one can create the geometric counterparts of unrestricted splittings to generate all secondary classes. Our results show that S_{1,2} can only generate a limited range of secondary classes from the same ancestor. The geometric interpretation of the additional ancestors defined by monotone splittings shows that minimal polyhedra play a key role in this process. We also present computational results on the number of secondary classes and multiquadrangulations.

The construction and characterization of egalitarian solutions for multi-choice NTU games

In this article we construct a procedure to define the egalitarian solutions in the context of multi-choice non-transferable utility (NTU) games. Also, we show that in the presence of other weak axioms the egalitarian solutions are the only monotonic ones.

The exclusive interpretation of plural nominals in quantificational environments

In some contexts, plural nominals have inclusive interpretation, allowing atoms in their reference domain; in others, they are exclusive, allowing only sums. Selecting between the two interpretations has been shown to be sensitive to both world-knowledge pressures (Farkas &amp; de Swart 2010) and contextual relevance (Grimm 2010). The principal semantic factor claimed to be involved is monotonicity direction (Sauerland, Anderssen &amp; Yatsushiro 2005; Spector 2007; Zweig 2009; Farkas &amp; de Swart 2010): upward monotone environments tend to select exclusive readings; downward monotone ones, inclusive readings. In four image verification experiments, we tested this claim and found support for the generalization. The effect of monotonicity direction, however, is small. Moreover we find that varying whether a plural is in the scope of a quantified description has a much larger effect on the prevalence of the exclusive interpretation. This suggests that monotonicity, though involved, is not a decisive factor in plural interpretation.

Upper bounds on the number of eigenvalues of stationary Schrödinger operators

In this article we provide several upper bounds on the number of eigenvalues, respectively, for Schrödinger operators of one-dimensional case, central potential case, and the case with point-interactions. Compared with Bargman’s and Calogero’s results, the new bounds can give finite estimates when the potential function has a heavy tail. Besides, a generalization of Calogero’s bound is given, which can be applied to bell shaped potential functions rather than merely monotonous ones. With respect to Schrödinger operators containing Dirac functions, some bounds are also established.

Experimetal study on the FRP-concrete bond behavior under repeated loadings

In this study, the effects of repeated loads on the FRP-concrete bond strength were investigated experimentally by direct pull out tests according to CSA S806-02. A conventional reinforcing steel bar and two types of glass-fiber-reinforced plastic (GFRP) bars were embedded in concrete and tested under four different loading patterns. The bond strength–slip curves of the bars were obtained and analyzed. The results showed that the maximum bond strengths under the repeated loads differed from those obtained under monotonic ones. In addition, noticeable differences in degradation of the bond strength with respect to the magnitude of slip were observed between the different bar types tested. On the basis of an image analysis of failure surfaces, they were attributed to the different bond failure mechanisms associated with the steel and GFRP bars.

Theoretical Estimation to the Cyclic Strength Coefficient and the Cyclic Strain-Hardening Exponent for Metallic Materials: Preliminary Study

The ultimate purpose of the present article is to theoretically estimate the cyclic strength coefficient and the cyclic strain-hardening exponent. For this purpose, the performance parameters of 22 alloys were examined and equations that relate the cyclic strength coefficient and the cyclic strain-hardening exponent to the monotonic tensile ones were developed. Then, by using formulas that express the strength coefficient and the strain-hardening exponent through the four conventional tensile performance parameters, i.e., the yield strength, the ultimate tensile strength, the fracture strength, and the fracture ductility, expressions that describe the cyclic strength coefficient and the cyclic strain-hardening exponent are established. By means of cyclic stress-strain curve, the limitations of the traditional methods of estimating the cyclic strength coefficient and the cyclic strain-hardening exponent are pointed out, and the ability of the new equations at describing the process are established. From the equations the cyclic strength coefficient and the cyclic strain-hardening exponent can be theoretically estimated using the monotonic ones. Furthermore, in the absence of the strength coefficient and the strain-hardening exponent, the cyclic ones can still be obtained from the expressions using the four conventional tensile performance parameters.

Mining constraint-based patterns using automatic relaxation

Constraint-based mining is an active field of research which is a necessary step to achieve interactive and successful KDD processes. The limitations of the task lies in languages being limited to describe the mined patterns and the ability to express varied constraints. In practice, current approaches focus on a language and the most generic frameworks mine individually or simultaneously a monotone and an anti-monotone constraints. In this paper, we propose a generic framework dealing with any partially ordered language and a large set of constraints. We prove that this set of constraints called primitive-based constraints not only is a superclass of both kinds of monotone ones and their boolean combinations but also other classes such as convertible and succinct constraints. We show that the primitive-based constraints can be efficiently mined thanks to a relaxation method based on virtual patterns which summarize the specificities of the search space. Indeed, this approach automatically deduces pruning conditions having suitable monotone properties and thus these conditions can be pushed into usual constraint mining algorithms. We study the optimal relaxations. Finally, we provide an experimental illustration of the efficiency of our proposal by experimenting it on several contexts.