Sigmoidal Response Function Research Articles

Parameter Estimation of KST-IRT Model under Local Dependence

A mantra often repeated in the introductory material to psychometrics and Item Response Theory (IRT) is that a Rasch model is a probabilistic version of a Guttman scale. The idea comes from the observation that a sigmoidal item response function provides a probabilistic version of the characteristic function that models an item response in the Guttman scale. It appears, however, more difficult to reconcile the assumption of local independence, which traditionally accompanies the Rasch model, with the item dependence existing in a Guttman scale. In recent work, an alternative probabilistic version of a Guttman scale was proposed, combining Knowledge Space Theory (KST) with IRT modeling, here referred to as KST-IRT. The present work has, therefore, a two-fold aim. Firstly, the estimation of the parameters involved in KST-IRT models is discussed. More in detail, two estimation methods based on the Expectation Maximization (EM) procedure are suggested, i.e., Marginal Maximum Likelihood (MML) and Gibbs sampling, and are compared on the basis of simulation studies. Secondly, for a Guttman scale, the estimates of the KST-IRT models are compared with those of the traditional combination of the Rasch model plus local independence under the interchange of the data generation processes. Results show that the KST-IRT approach might be more effective in capturing local dependence as it appears to be more robust under misspecification of the data generation process, but it comes with the price of an increased number of parameters.

Saturating Nonlinearities of Contrast Response in Human Visual Cortex.

Response nonlinearities are ubiquitous throughout the brain, especially within sensory cortices where changes in stimulus intensity typically produce compressed responses. Although this relationship is well established in electrophysiological measurements, it remains controversial whether the same nonlinearities hold for population-based measurements obtained with human fMRI. We propose that these purported disparities are not contingent on measurement type and are instead largely dependent on the visual system state at the time of interrogation. We show that deploying a contrast adaptation paradigm permits reliable measurements of saturating sigmoidal contrast response functions (10 participants, 7 female). When not controlling the adaptation state, our results coincide with previous fMRI studies, yielding nonsaturating, largely linear contrast responses. These findings highlight the important role of adaptation in manifesting measurable nonlinear responses within human visual cortex, reconciling discrepancies reported in vision neuroscience, re-establishing the qualitative relationship between stimulus intensity and response across different neural measures and the concerted study of cortical gain control.SIGNIFICANCE STATEMENT Nonlinear stimulus-response relationships govern many essential brain functions, ranging from the sensory to cognitive level. Certain core response properties previously shown to be nonlinear with nonhuman electrophysiology recordings have yet to be reliably measured with human neuroimaging, prompting uncertainty and reconsideration. The results of this study stand to reconcile these incongruencies in the vision neurosciences, demonstrating the profound impact adaptation can have on brain activation throughout the early visual cortex. Moving forward, these findings facilitate the study of modulatory influences on sensory processing (i.e., arousal and attention) and help establish a closer link between neural recordings in animals and hemodynamic measurements from human fMRI, resuming a concerted effort to understand operations in the mammalian cortex.

Uncertainty quantification of the soil moisture response functions for microbial dormancy and resuscitation

Abiotic factors influence ecosystem functioning mainly through the biological mechanisms such as the shifts in microbial community structure and/or physiology. Sigmoidal shape soil moisture response functions (SMRFs) have been widely used to modify the dormancy and resuscitation rates in microbially explicit soil biogeochemical models. However, these SMRFs and their effects on microbial dormancy have not been well quantified with experimental data. Using observations from a three-year field experiment in subtropical forests, we conducted a comprehensive parameterization of typical sigmoidal SMRFs. We quantified uncertainties in the three parameters of these SMRFs: (i) the critical soil water potential (SWP) for microbes entering dormancy, φA2D=−0.46±0.03MPa (mean ± standard deviation); (ii) the ratio of the critical SWP for resuscitation to φA2D, τ=0.39±0.16; and (iii) the exponent in the SMRFs, ω=3.38±0.54. Our results show much higher uncertainty in the SMRF for microbial resuscitation than microbial dormancy, due to the parameter τ being included in microbial reactivation with larger uncertainty than that of φA2D and ω. In addition, the active microbes, rather than the total living microbes, were overwhelmingly controlled by soil moisture, leading to the stronger dependency of microbial respiration on soil moisture in the dry season than in the wet season. The SMRFs and their parameter values/uncertainties derived in this study could be directly incorporated into or used as a priori in ecosystem and Earth system models that account for microbial dormancy and resuscitation.

Abstract 3975: Target engagement, thrombocytopenia, and efficacy induced by the dual Bcl2/xL inhibitor AZD4320 are quantitatively linked by a PK/PD model in leukemia xenografts

Abstract The proteins Bcl2 and Bcl-xL are often up-regulated in cancer, and hold in check the apoptosis that would normally be initiated by accumulation of the BH3-only proteins Bax and Bak in response to genomic dysregulation. AZD4320 potently disrupts that interaction, initiating the apoptotic cascade in Bcl-2 or Bcl-xL-dependent tumors. Because platelets are known to be dependent on Bcl-xL, thrombocytopenia is an expected on-target effect. AZD4320 was administered at dose levels 0.5-10 mg/kg, both intravenously and extravascularly, to immune-compromised mice inoculated subcutaneously with the RS4;11 model of acute lymphocytic leukemia (ALL). Drug concentrations were measured by liquid chromatography-mass spectrometry (LC-MS) in plasma and tumor. A cleaved-caspase-3 ELISA was used to assess apoptotic activity in the tumor. Parallel efficacy studies, were used to assess tumor growth compared to vehicle, following tumors from initial regression at tolerated doses to regrowth. Tumors were measured using calipers, and tumor volumes computed using an ellipsoid approximation. We present a mini-physiologically based pharmacokinetic/pharmacodynamic (mPBPK/PD) model that links drug concentrations in plasma and tumor to observed caspase activity and efficacy in an integrated manner, across multiple dose levels and schedules. The tumor is modeled as a pool of sensitive cells which can be triggered rapidly by AZD4320 to apoptose, from which point they transition gradually to death, reducing tumor volume. Cleaved caspase-3 is used as a marker of apoptosis, and modeled using a sigmoidal response function with steep slope parameter. In this way, we effectively capture the transient nature of the response, despite AZD4320's long residence in the tumor. Thrombocytopenia is described not as an effect on the megakaryocyte precursors, but as a linear concentration-dependent effect on circulating platelets. Feedback from the circulation to megakaryocytes drives increased production to fill the deficit. Parameters are well-estimated throughout. Together, these components provide a comprehensive means to investigate the effects of dose and schedule with a dual Bcl2/BCL-xL inhibitor. Citation Format: Francis D. Gibbons, Ammar Adam, Marie-Eve Beaudoin, Eric Gangl, Paul Secrist. Target engagement, thrombocytopenia, and efficacy induced by the dual Bcl2/xL inhibitor AZD4320 are quantitatively linked by a PK/PD model in leukemia xenografts [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 3975.

Interval timing under a behavioral microscope: Dissociating motivational and timing processes in fixed-interval performance.

The distribution of latencies and interresponse times (IRTs) of rats was compared between two fixed-interval (FI) schedules of food reinforcement (FI 30s and FI 90s), and between two levels of food deprivation. Computational modeling revealed that latencies and IRTs were well described by mixture probability distributions embodying two-state Markov chains. Analysis of these models revealed that only a subset of latencies is sensitive to the periodicity of reinforcement, and prefeeding only reduces the size of this subset. The distribution of IRTs suggests that behavior in FI schedules is organized in bouts that lengthen and ramp up in frequency with proximity to reinforcement. Prefeeding slowed down the lengthening of bouts and increased the time between bouts. When concatenated, latency and IRT models adequately reproduced sigmoidal FI response functions. These findings suggest that behavior in FI schedules fluctuates in and out of schedule control; an account of such fluctuation suggests that timing and motivation are dissociable components of FI performance. These mixture-distribution models also provide novel insights on the motivational, associative, and timing processes expressed in FI performance. These processes may be obscured, however, when performance in timing tasks is analyzed in terms of mean response rates.

Sparseness, antisparseness and anything in between: the operating point of a neuron determines its computational repertoire.

A recent model of intrinsic plasticity coupled to Hebbian synaptic plasticity proposes that adaptation of a neuron's threshold and gain in a sigmoidal response function to achieve a sparse, exponential output firing rate distribution facilitates the discovery of heavy-tailed or super- gaussian sources in the neuron's inputs. We show that the exponential output distribution is irrelevant to these dynamics and that, furthermore, while sparseness is sufficient, it is not necessary. The intrinsic plasticity mechanism drives the neuron's threshold large and positive, and we prove that in such a regime, the neuron will find supergaussian sources; equally, however, if the threshold is large and negative (an antisparse regime), it will also find supergaussian sources. Away from such extremes, the neuron can also discover subgaussian sources. By examining a neuron with a fixed sigmoidal nonlinearity and considering the synaptic strength fixed-point structure in the two-dimensional parameter space defined by the neuron's threshold and gain, we show that this space is carved up into sub- and supergaussian-input-finding regimes, possibly with regimes of simultaneous stability of sub- and supergaussian sources or regimes of instability of all sources; a single gaussian source may also be stabilized by the presence of a nongaussian source. A neuron's operating point (essentially its threshold and gain coupled with its input statistics) therefore critically determines its computational repertoire. Intrinsic plasticity mechanisms induce trajectories in this parameter space but do not fundamentally modify it. Unless the trajectories cross critical boundaries in this space, intrinsic plasticity is irrelevant and the neuron's nonlinearity may be frozen with identical receptive field refinement dynamics.

Memoryless nonlinear response: A simple mechanism for the 1/f noise

Discovering the mechanism underlying the ubiquity of “” noise has been a long-standing problem. The wide range of systems in which the fluctuations show the implied long-time correlations suggests the existence of some simple and general mechanism that is independent of the details of any specific system. We argue here that a memoryless nonlinear response suffices to explain the observed nontrivial values of α: a random input noisy signal S(t) with a power spectrum varying as , when fed to an element with such a response function R, gives an output that can have a power spectrum with . As an illustrative example, we show that an input Brownian noise acting on a device with a sigmoidal response function , with x < 1, produces an output with , for . Our discussion is easily extended to more general types of input noise as well as more general response functions.

Characterization of Phase Transition in the Thalamocortical System during Anesthesia-Induced Loss of Consciousness

The thalamocortical system plays a key role in the breakdown or emergence of consciousness, providing bottom-up information delivery from sensory afferents and integrating top-down intracortical and thalamocortical reciprocal signaling. A fundamental and so far unanswered question for cognitive neuroscience remains whether the thalamocortical switch for consciousness works in a discontinuous manner or not. To unveil the nature of thalamocortical system phase transition in conjunction with consciousness transition, ketamine/xylazine was administered unobtrusively to ten mice under a forced working test with motion tracker, and field potentials in the sensory and motor-related cortex and thalamic nuclei were concomitantly collected. Sensory and motor-related thalamocortical networks were found to behave continuously at anesthesia induction and emergence, as evidenced by a sigmoidal response function with respect to anesthetic concentration. Hyperpolarizing and depolarizing susceptibility diverged, and a non-discrete change of transitional probability occurred at transitional regimes, which are hallmarks of continuous phase transition. The hyperpolarization curve as a function of anesthetic concentration demonstrated a hysteresis loop, with a significantly higher anesthetic level for transition to the down state compared to transition to the up state. Together, our findings concerning the nature of phase transition in the thalamocortical system during consciousness transition further elucidate the underlying basis for the ambiguous borderlines between conscious and unconscious brains. Moreover, our novel analysis method can be applied to systematic and quantitative handling of subjective concepts in cognitive neuroscience.

Traveling Wave Solutions for a Predator–Prey System With Sigmoidal Response Function

We study the existence of traveling wave solutions for a diffusive predator-prey system. The system considered in this paper is governed by a Sigmoidal response function which is more general than those studied previously. Our method is an improvement to the original method introduced in the work of Dunbar \cite{Dunbar1,Dunbar2}. A bounded Wazewski set is used in this work while unbounded Wazewski sets were used in \cite{Dunbar1,Dunbar2}. The existence of traveling wave solutions connecting two equilibria is established by using the original Wazewski's theorem which is much simpler than the extended version in Dunbar's work.

Stable and transient periodic oscillations in a mathematical model for CTL response to HTLV-I infection

The cytotoxic T lymphocyte (CTL) response to the infection of CD4+ T cells by human T cell leukemia virus type I (HTLV-I) has previously been modelled using standard response functions, with relatively simple dynamical outcomes. In this paper, we investigate the consequences of a more general CTL response and show that a sigmoidal response function gives rise to complex behaviours previously unobserved. Multiple equilibria are shown to exist and none of the equilibria is a global attractor during the chronic infection phase. Coexistence of local attractors with their own basin of attractions is the norm. In addition, both stable and unstable periodic oscillations can be created through Hopf bifurcations. We show that transient periodic oscillations occur when a saddle-type periodic solution exists. As a consequence, transient periodic oscillations can be robust and observable. Implications of our findings to the dynamics of CTL response to HTLV-I infections in vivo and pathogenesis of HAM/TSP are discussed.

Multi-ion detection by one-shot optical sensors using a colour digital photographic camera

The feasibility and performance of a procedure to evaluate previously developed one-shot optical sensors as single and selective analyte sensors for potassium, magnesium and hardness are presented. The procedure uses a conventional colour digital photographic camera as the detection system for simultaneous multianalyte detection. A 6.0 megapixel camera was used, and the procedure describes how it is possible to quantify potassium, magnesium and hardness simultaneously from the images captured, using multianalyte one-shot sensors based on ionophore-chromoionophore chemistry, employing the colour information computed from a defined region of interest on the sensing membrane. One of the colour channels in the red, green, blue (RGB) colour space is used to build the analytical parameter, the effective degree of protonation (1-α(eff)), in good agreement with the theoretical model. The linearization of the sigmoidal response function increases the limit of detection (LOD) and analytical range in all cases studied. The increases were from 5.4 × 10(-6) to 2.7 × 10(-7) M for potassium, from 1.4 × 10(-4) to 2.0 × 10(-6) M for magnesium and from 1.7 to 2.0 × 10(-2) mg L(-1) of CaCO(3) for hardness. The method's precision was determined in terms of the relative standard deviation (RSD%) which was from 2.4 to 7.6 for potassium, from 6.8 to 7.8 for magnesium and from 4.3 to 7.8 for hardness. The procedure was applied to the simultaneous determination of potassium, magnesium and hardness using multianalyte one-shot sensors in different types of waters and beverages in order to cover the entire application range, statistically validating the results against atomic absorption spectrometry as the reference procedure. Accordingly, this paper is an attempt to demonstrate the possibility of using a conventional digital camera as an analytical device to measure this type of one-shot sensor based on ionophore-chromoionophore chemistry instead of using conventional lab instrumentation.

Dynamics of actively regulated gene networks

A popular way of modelling gene regulatory networks is to design the models as if the genes were acting directly on each other. Genes are activated or inhibited by transcription factors which are direct gene products. The action of a transcription factor on a gene is modelled as a binary on–off dose-response function or a sigmoid around a certain threshold concentration. A transcription factor may act on several genes with equal or different thresholds. The combined effect of several transcription factors on a gene is generally assumed to obey Boolean-like composition rules. A mathematical challenge related to such network models is to analyse the behaviour in the narrow domains in phase space where at least one variable is close to one of its thresholds, called switching domains. In the present paper we analyse the motion in switching domains for models with steep sigmoidal response functions under the assumption that each transcription factor only regulates one gene at each of its thresholds. This biologically reasonable assumption allows us to establish rules that determine the passage through any switching domain and the sequence of domains through which the system passes. The rules can be effectively implemented in a sound automated analyser for such networks. The assumption simplifies certain mathematical and computational issues, but unfortunately may be at variance with one of the necessary conditions for the singular perturbation theory which our derivations are based on. We give sufficient conditions ensuring that, despite this, the difficulties raised by our assumption can be evaded and singular perturbation approximation safely applied.

Colourimetric characterisation of disposable optical sensors from spectroradiometric measurements

Spectroradiometric measurements of reflectance and CIELAB hue-angle, were tested for K(I) determination using disposable optical sensors based on ion exchange mechanism. The linearisation of the sigmoidal response function, using a logistic regression, increases the linear range noticeably to 7.65 x 10(-8)-1.5 M and 1.22 x 10(-7)-1.5 M for CIELAB hue-angle and reflectance, respectively. The trueness of both procedures was demonstrated comparing it with results obtained by a DAD spectrophotometer used as a reference measurement procedure. The usefulness of the procedure was checked by analysing K(I) in different types of waters and beverages. Additionally, we studied the possible visual discrimination for the whole potassium range tested, obtaining the possibility of discriminating twelve groups of concentrations.

Threshold-dominated regulation hides genetic variation in gene expression networks

BackgroundIn dynamical models with feedback and sigmoidal response functions, some or all variables have thresholds around which they regulate themselves or other variables. A mathematical analysis has shown that when the dose-response functions approach binary or on/off responses, any variable with an equilibrium value close to one of its thresholds is very robust to parameter perturbations of a homeostatic state. We denote this threshold robustness. To check the empirical relevance of this phenomenon with response function steepnesses ranging from a near on/off response down to Michaelis-Menten conditions, we have performed a simulation study to investigate the degree of threshold robustness in models for a three-gene system with one downstream gene, using several logical input gates, but excluding models with positive feedback to avoid multistationarity. Varying parameter values representing functional genetic variation, we have analysed the coefficient of variation (CV) of the gene product concentrations in the stable state for the regulating genes in absolute terms and compared to the CV for the unregulating downstream gene. The sigmoidal or binary dose-response functions in these models can be considered as phenomenological models of the aggregated effects on protein or mRNA expression rates of all cellular reactions involved in gene expression.ResultsFor all the models, threshold robustness increases with increasing response steepness. The CVs of the regulating genes are significantly smaller than for the unregulating gene, in particular for steep responses. The effect becomes less prominent as steepnesses approach Michaelis-Menten conditions. If the parameter perturbation shifts the equilibrium value too far away from threshold, the gene product is no longer an effective regulator and robustness is lost. Threshold robustness arises when a variable is an active regulator around its threshold, and this function is maintained by the feedback loop that the regulator necessarily takes part in and also is regulated by. In the present study all feedback loops are negative, and our results suggest that threshold robustness is maintained by negative feedback which necessarily exists in the homeostatic state.ConclusionThreshold robustness of a variable can be seen as its ability to maintain an active regulation around its threshold in a homeostatic state despite external perturbations. The feedback loop that the system necessarily possesses in this state, ensures that the robust variable is itself regulated and kept close to its threshold. Our results suggest that threshold regulation is a generic phenomenon in feedback-regulated networks with sigmoidal response functions, at least when there is no positive feedback. Threshold robustness in gene regulatory networks illustrates that hidden genetic variation can be explained by systemic properties of the genotype-phenotype map.

Contrast Gain Control Is Drift-Rate Dependent: An Informational Analysis

Neurons in the visual cortex code relative changes in illumination (contrast) and adapt their sensitivities to the visual scene by centering the steepest regions of their sigmoidal contrast response functions (CRFs: spike rate as a function of contrast) on the prevailing contrast. The influence of this contrast gain control has not been reported at nonoptimal drift rates. We calculated the Fisher information contained in the CRFs of halothane-anesthetized cats. Fisher information gives a measure of the accuracy of contrast representations based on the ratio of the square of the steepness of the CRF and the spike-rate dependency of the spiking variance. Variance increases with spike rate, so Fisher information is maximal where the CRF is steep and spike rates are low. Here, we show that the contrast at which the maximal Fisher information (C(MFI)) occurs for each adapting drift rate is at a fixed level above the adapting contrast. For adapting contrasts of 0 to 0.32 the relationship between C(MFI) and adapting contrast is well described by a straight line with a slope close to 1. The intercept of this line on the C(MFI)-axis is drift-rate dependent, although the slope is not. At high drift rates relative to each cell's peak the C(MFI) offset is higher than that for low drift rates. The results show that the contrast coding strategy in visual cortex maximizes accuracy for contrasts above the prevailing contrast in the environment for all drift rates. We argue that tuning the system for accuracy at contrasts above the prevailing value is optimal for viewing natural scenes.

The Influence of Cosolvent Polarity on the Flow Properties of Hydroalcoholic Gels. Empirical Models

The aim of this study was to investigate the influence of cosolvent polarity on the rheological flow properties of aqueous and hydroalcoholic gels obtained from the Carbopol Ultrez 10 base and used for topical applications. Specifically, we have examined the effect of pH (range 4.0--7.0) on the consistency and flow properties of dispersed systems in water and mixtures--15 : 85% v/v of methanol : water, ethanol : water, n-propanol : water and n-butanol : water--at a constant polymer concentration of 0.3% w/w. The gels, which had decreasing polarity values in the jellifying medium, showed qualitatively similar flow behavior, characteristic of pseudoplastic systems, and all of the flow curves were adjusted to the Ostwald model. Sigmoidal dose response functions were calculated to describe the flow and consistency indexes as a function of pH. As a result, the influence of alcohol polarity on the polymer network has been assessed meaningfully using the empirical parameters obtained: maximum consistency index value (k(max)), pH value required for 50% development of polymer network (pH(50)), and asymptotic flow index value (n(min)) for the fully structured gels.

Systematic study of the flow behaviour and mechanical properties of Carbopol ® Ultrez™ 10 hydroalcoholic gels

Flow behaviour and mechanical properties of 0:100, 15:85, and 30:70 v/v gelled ethanol:water mixtures are studied as a function of pH (4.0–7.0) and Carbopol ® Ultrez™ 10 concentration (0.1–0.5%). As previously reported individually for 30% v/v alcoholic Ultrez™ 10 gels, flow curves were adjusted to the Ostwald's model, and similar sigmoidal dose response functions were obtained to describe the pH dependence of consistency index and mechanical properties of the systems. The concentration dependence of flow indexes was also best adjusted to one-phase exponential decay functions. As a result, the influence of ethanol content on polymer network is meaningfully assessed by means of the obtained empirical parameters: bottom value of each variable ( Y max), pH value required for a 50% polymer network development (pH 50), and asymptotic flow index value for the fully structured gels ( n min). Also, it is assessed the influence of cosolvent on the above-mentioned empirical variables, by studying pH-dependence of gelation in methanol:water, 1-propanol:water and 1-butanol:water 15:85% v/v mixtures. As a result, the alcohol induced variations in consistency and mechanical properties of hydroalcoholic gels were well correlated to modifications in the solubility parameter (δ T).

CHAOS IN A THREE-DIMENSIONAL GENERAL MODEL OF NEURAL NETWORK

The dynamics of a network of three neurons with all possible connections is studied here. The equations of control are given by three differential equations with nonlinear, positive and bounded sigmoidal response function of the neurons. The system passes from stable to periodic and then to chaotic regimes and returns to stationary regime with change in parameter values of synaptic weights and decay rates. We have developed programs and used Locbif package to study phase portraits, bifurcation diagrams which confirm the result. Lyapunov Exponents have been calculated to confirm chaos.

Rheological characterization of hydroalcoholic gels — 15% ethanol — of Carbopol® Ultrez™ 10

The rheological behaviour of Carbopol® Ultrez™ 10 ethanolic (15%) gels was studied as a function of two main variables: pH (4.0–7.0) and the polymer concentration (0.1–0.5%). Flow curves of all hydroalcoholic gels were adjusted to the Ostwald model. Sigmoidal dose response functions were obtained to describe the pH dependence of consistency index of the systems. The concentration dependence of flow indexes was best adjusted to one-phase exponential decay functions. Finally, by substituting in the power law expression, an empirical model is given to estimate viscosities of gels for any value of pH and polymer concentration in the ranges evaluated. As a result, the influence of the variables on polymer network is meaningfully assessed by means of the obtained empirical parameters: bottom value ( Y max), pH value required for a 50% polymer network development (pH 50), and asymptotic flow index value for the fully structured gels ( n min).

Neural Networks for Localized Approximation

We prove that feedforward artificial neural networks with a single hidden layer and an ideal sigmoidal response function cannot provide localized approximation in a Euclidean space of dimension higher than one. We also show that networks with two hidden layers can be designed to provide localized approximation. Since wavelet bases are most effective for local approximation, we give a discussion of the implementation of spline wavelets using multilayered networks where the response function is a sigmoidal function of order at least two.