Confidence and the Stock Market: An Agent-Based Approach

Using a behavioral finance approach we study the impact of behavioral bias. We construct an artificial market consisting of fundamentalists and chartists to model the decision-making process of various agents. The agents differ in their strategies for evaluating stock prices, and exhibit differing memory lengths and confidence levels. When we increase the heterogeneity of the strategies used by the agents, in particular the memory lengths, we observe excess volatility and kurtosis, in agreement with real market fluctuations—indicating that agents in real-world financial markets exhibit widely differing memory lengths. We incorporate the behavioral traits of adaptive confidence and observe a positive correlation between average confidence and return rate, indicating that market sentiment is an important driver in price fluctuations. The introduction of market confidence increases price volatility, reflecting the negative effect of irrationality in market behavior.     

Impact of Stock Market Structure on Intertrade Time and Price Dynamics

We analyse times between consecutive transactions for a diverse group of stocks registered on the NYSE and NASDAQ markets, and we relate the dynamical properties of the intertrade times with those of the corresponding price fluctuations. We report that market structure strongly impacts the scale-invariant temporal organisation in the transaction timing of stocks, which we have observed to have long-range power-law correlations. Specifically, we find that, compared to NYSE stocks, stocks registered on the NASDAQ exhibit significantly stronger correlations in their transaction timing on scales within a trading day. Further, we find that companies that transfer from the NASDAQ to the NYSE show a reduction in the correlation strength of transaction timing on scales within a trading day, indicating influences of market structure. We also report a persistent decrease in correlation strength of intertrade times with increasing average intertrade time and with corresponding decrease in companies'' market capitalization–a trend which is less pronounced for NASDAQ stocks. Surprisingly, we observe that stronger power-law correlations in intertrade times are coupled with stronger power-law correlations in absolute price returns and higher price volatility, suggesting a strong link between the dynamical properties of intertrade times and the corresponding price fluctuations over a broad range of time scales. Comparing the NYSE and NASDAQ markets, we demonstrate that the stronger correlations we find in intertrade times for NASDAQ stocks are associated with stronger correlations in absolute price returns and with higher volatility, suggesting that market structure may affect price behavior through information contained in transaction timing. These findings do not support the hypothesis of universal scaling behavior in stock dynamics that is independent of company characteristics and stock market structure. Further, our results have implications for utilising transaction timing patterns in price prediction and risk management optimization on different stock markets.     

Adaptive and nonadaptive plasticity in changing environments: Implications for sexual species with different life history strategies

Populations adapt to novel environmental conditions by genetic changes or phenotypic plasticity. Plastic responses are generally faster and can buffer fitness losses under variable conditions. Plasticity is typically modeled as random noise and linear reaction norms that assume simple one‐to‐one genotype–phenotype maps and no limits to the phenotypic response. Most studies on plasticity have focused on its effect on population viability. However, it is not clear, whether the advantage of plasticity depends solely on environmental fluctuations or also on the genetic and demographic properties (life histories) of populations. Here we present an individual‐based model and study the relative importance of adaptive and nonadaptive plasticity for populations of sexual species with different life histories experiencing directional stochastic climate change. Environmental fluctuations were simulated using differentially autocorrelated climatic stochasticity or noise color, and scenarios of directional climate change. Nonadaptive plasticity was simulated as a random environmental effect on trait development, while adaptive plasticity as a linear, saturating, or sinusoidal reaction norm. The last two imposed limits to the plastic response and emphasized flexible interactions of the genotype with the environment. Interestingly, this assumption led to (a) smaller phenotypic than genotypic variance in the population (many‐to‐one genotype–phenotype map) and the coexistence of polymorphisms, and (b) the maintenance of higher genetic variation—compared to linear reaction norms and genetic determinism—even when the population was exposed to a constant environment for several generations. Limits to plasticity led to genetic accommodation, when costs were negligible, and to the appearance of cryptic variation when limits were exceeded. We found that adaptive plasticity promoted population persistence under red environmental noise and was particularly important for life histories with low fecundity. Populations producing more offspring could cope with environmental fluctuations solely by genetic changes or random plasticity, unless environmental change was too fast.     

A single heat-stress bout induces rapid and prolonged heat acclimation in the California mussel,Mytilus californianus

Climate change is not only causing steady increases in average global temperatures but also increasing the frequency with which extreme heating events occur. These extreme events may be pivotal in determining the ability of organisms to persist in their current habitats. Thus, it is important to understand how quickly an organism''s heat tolerance can be gained and lost relative to the frequency with which extreme heating events occur in the field. We show that the California mussel, Mytilus californianus—a sessile intertidal species that experiences extreme temperature fluctuations and cannot behaviourally thermoregulate—can quickly (in 24–48 h) acquire improved heat tolerance after exposure to a single sublethal heat-stress bout (2 h at 30 or 35°C) and then maintain this improved tolerance for up to three weeks without further exposure to elevated temperatures. This adaptive response improved survival rates by approximately 75% under extreme heat-stress bouts (2 h at 40°C). To interpret these laboratory findings in an ecological context, we evaluated 4 years of mussel body temperatures recorded in the field. The majority (approx. 64%) of consecutive heat-stress bouts were separated by 24–48 h, but several consecutive heat bouts were separated by as much as 22 days. Thus, the ability of M. californianus to maintain improved heat tolerance for up to three weeks after a single sublethal heat-stress bout significantly improves their probability of survival, as approximately 33% of consecutive heat events are separated by 3–22 days. As a sessile animal, mussels likely evolved the capability to rapidly gain and slowly lose heat tolerance to survive the intermittent, and often unpredictable, heat events in the intertidal zone. This adaptive strategy will likely prove beneficial under the extreme heat events predicted with climate change.     

Intraday Seasonalities and Nonstationarity of Trading Volume in Financial Markets: Individual and Cross-Sectional Features

We study the intraday behaviour of the statistical moments of the trading volume of the blue chip equities that composed the Dow Jones Industrial Average index between 2003 and 2014. By splitting that time interval into semesters, we provide a quantitative account of the nonstationary nature of the intraday statistical properties as well. Explicitly, we prove the well-known ∪-shape exhibited by the average trading volume—as well as the volatility of the price fluctuations—experienced a significant change from 2008 (the year of the “subprime” financial crisis) onwards. That has resulted in a faster relaxation after the market opening and relates to a consistent decrease in the convexity of the average trading volume intraday profile. Simultaneously, the last part of the session has become steeper as well, a modification that is likely to have been triggered by the new short-selling rules that were introduced in 2007 by the Securities and Exchange Commission. The combination of both results reveals that the ∪ has been turning into a ⊔. Additionally, the analysis of higher-order cumulants—namely the skewness and the kurtosis—shows that the morning and the afternoon parts of the trading session are each clearly associated with different statistical features and hence dynamical rules. Concretely, we claim that the large initial trading volume is due to wayward stocks whereas the large volume during the last part of the session hinges on a cohesive increase of the trading volume. That dissimilarity between the two parts of the trading session is stressed in periods of higher uproar in the market.     

Fluctuation Analysis of Centrosomes Reveals a Cortical Function of Kinesin-1

The actin and microtubule networks form the dynamic cytoskeleton. Network dynamics is driven by molecular motors applying force onto the networks and the interactions between the networks. Here we assay the dynamics of centrosomes in the scale of seconds as a proxy for the movement of microtubule asters. With this assay we want to detect the role of specific motors and of network interaction. During interphase of syncytial embryos of Drosophila, cortical actin and the microtubule network depend on each other. Centrosomes induce cortical actin to form caps, whereas F-actin anchors microtubules to the cortex. In addition, lateral interactions between microtubule asters are assumed to be important for regular spatial organization of the syncytial embryo. The functional interaction between the microtubule asters and cortical actin has been largely analyzed in a static manner, so far. We recorded the movement of centrosomes at 1 Hz and analyzed their fluctuations for two processes—pair separation and individual movement. We found that F-actin is required for directional movements during initial centrosome pair separation, because separation proceeds in a diffusive manner in latrunculin-injected embryos. For assaying individual movement, we established a fluctuation parameter as the deviation from temporally and spatially slowly varying drift movements. By analysis of mutant and drug-injected embryos, we found that the fluctuations were suppressed by both cortical actin and microtubules. Surprisingly, the microtubule motor Kinesin-1 also suppressed fluctuations to a similar degree as F-actin. Kinesin-1 may mediate linkage of the microtubule (+)-ends to the actin cortex. Consistent with this model is our finding that Kinesin-1-GFP accumulates at the cortical actin caps.     

Chromatin Hydrodynamics

Following recent observations of large scale correlated motion of chromatin inside the nuclei of live differentiated cells, we present a hydrodynamic theory—the two-fluid model—in which the content of a nucleus is described as a chromatin solution with the nucleoplasm playing the role of the solvent and the chromatin fiber that of a solute. This system is subject to both passive thermal fluctuations and active scalar and vector events that are associated with free energy consumption, such as ATP hydrolysis. Scalar events drive the longitudinal viscoelastic modes (where the chromatin fiber moves relative to the solvent) while vector events generate the transverse modes (where the chromatin fiber moves together with the solvent). Using linear response methods, we derive explicit expressions for the response functions that connect the chromatin density and velocity correlation functions to the corresponding correlation functions of the active sources and the complex viscoelastic moduli of the chromatin solution. We then derive general expressions for the flow spectral density of the chromatin velocity field. We use the theory to analyze experimental results recently obtained by one of the present authors and her co-workers. We find that the time dependence of the experimental data for both native and ATP-depleted chromatin can be well-fitted using a simple model—the Maxwell fluid—for the complex modulus, although there is some discrepancy in terms of the wavevector dependence. Thermal fluctuations of ATP-depleted cells are predominantly longitudinal. ATP-active cells exhibit intense transverse long wavelength velocity fluctuations driven by force dipoles. Fluctuations with wavenumbers larger than a few inverse microns are dominated by concentration fluctuations with the same spectrum as thermal fluctuations but with increased intensity.     

High Quality Topic Extraction from Business News Explains Abnormal Financial Market Volatility

Understanding the mutual relationships between information flows and social activity in society today is one of the cornerstones of the social sciences. In financial economics, the key issue in this regard is understanding and quantifying how news of all possible types (geopolitical, environmental, social, financial, economic, etc.) affects trading and the pricing of firms in organized stock markets. In this article, we seek to address this issue by performing an analysis of more than 24 million news records provided by Thompson Reuters and of their relationship with trading activity for 206 major stocks in the S&P US stock index. We show that the whole landscape of news that affects stock price movements can be automatically summarized via simple regularized regressions between trading activity and news information pieces decomposed, with the help of simple topic modeling techniques, into their “thematic” features. Using these methods, we are able to estimate and quantify the impacts of news on trading. We introduce network-based visualization techniques to represent the whole landscape of news information associated with a basket of stocks. The examination of the words that are representative of the topic distributions confirms that our method is able to extract the significant pieces of information influencing the stock market. Our results show that one of the most puzzling stylized facts in financial economies, namely that at certain times trading volumes appear to be “abnormally large,” can be partially explained by the flow of news. In this sense, our results prove that there is no “excess trading,” when restricting to times when news is genuinely novel and provides relevant financial information.     

What Would Jaws Do? The Tyranny of Film and the Relationship between Gaze and Higher-Level Narrative Film Comprehension

What is the relationship between film viewers’ eye movements and their film comprehension? Typical Hollywood movies induce strong attentional synchrony—most viewers look at the same things at the same time. Thus, we asked whether film viewers’ eye movements would differ based on their understanding—the mental model hypothesis—or whether any such differences would be overwhelmed by viewers’ attentional synchrony—the tyranny of film hypothesis. To investigate this question, we manipulated the presence/absence of prior film context and measured resulting differences in film comprehension and eye movements. Viewers watched a 12-second James Bond movie clip, ending just as a critical predictive inference should be drawn that Bond’s nemesis, “Jaws,” would fall from the sky onto a circus tent. The No-context condition saw only the 12-second clip, but the Context condition also saw the preceding 2.5 minutes of the movie before seeing the critical 12-second portion. Importantly, the Context condition viewers were more likely to draw the critical inference and were more likely to perceive coherence across the entire 6 shot sequence (as shown by event segmentation), indicating greater comprehension. Viewers’ eye movements showed strong attentional synchrony in both conditions as compared to a chance level baseline, but smaller differences between conditions. Specifically, the Context condition viewers showed slightly, but significantly, greater attentional synchrony and lower cognitive load (as shown by fixation probability) during the critical first circus tent shot. Thus, overall, the results were more consistent with the tyranny of film hypothesis than the mental model hypothesis. These results suggest the need for a theory that encompasses processes from the perception to the comprehension of film.     

A Financial Market Model Incorporating Herd Behaviour

Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents’ accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents’ accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option.     

Wall Street's assessment of plastic surgery--related technology: a clinical and financial analysis

Many plastic surgeons develop technologies that are manufactured by Wall Street-financed companies. Others participate in the stock market as investors. This study examines the bioengineered skin industry to determine whether it integrates clinical and financial information as Wall Street tenets would predict, and to see whether the financial performance of these companies provides any lessons for practicing plastic surgeons. In efficient markets, the assumptions on which independent financial analysts base their company sales and earnings projections are clinically reasonable, the volatility of a company's stock price does not irrationally differ from that of its industry sector, and the buy/sell recommendations of analysts are roughly congruent. For the companies in this study, these key financial parameters were compared with a benchmark index of 69 biotech companies of similar age and annual revenues (Student's t test). Five bioengineered skin companies were included in the study. Analysts estimated that each company would sell its product to between 24 and 45 percent of its target clinical population. The average stock price volatility was significantly higher for study companies than for those in the benchmark index (p < 0.05). Similarly, buy/sell recommendations of analysts for the study companies were significantly less congruent than those for the benchmark companies (p < 0.05). These results indicate clinically unrealistic projections for market penetration, significantly high price volatility, and significantly high discordance among professional analysts. In all cases, the market is inefficient-an unusual finding on Wall Street. A likely explanation for this market failure is a cycle of poor clinical correlation when assigning sales projections, which in turn leads to price volatility and discordance of buy/sell recommendations. This study's findings have implications for plastic surgeons who develop new technology or who participate in the equities markets as investors. Plastic surgeons who develop new medical devices or technology cannot universally depend on the market to drive clinically reasonable financial performance. Although inflated sales estimates have benefits in the short term, failure to meet projections exacts severe financial penalties. Plastic surgeons who invest in the stock market, because of their unique clinical experience, may sometimes be in the position to evaluate new technologies and companies better than Wall Street experts. Well-timed trades that use this expertise can result in opportunities for profit.     

A first-principles model of early evolution: emergence of gene families, species, and preferred protein folds

In this work we develop a microscopic physical model of early evolution where phenotype—organism life expectancy—is directly related to genotype—the stability of its proteins in their native conformations—which can be determined exactly in the model. Simulating the model on a computer, we consistently observe the “Big Bang” scenario whereby exponential population growth ensues as soon as favorable sequence–structure combinations (precursors of stable proteins) are discovered. Upon that, random diversity of the structural space abruptly collapses into a small set of preferred proteins. We observe that protein folds remain stable and abundant in the population at timescales much greater than mutation or organism lifetime, and the distribution of the lifetimes of dominant folds in a population approximately follows a power law. The separation of evolutionary timescales between discovery of new folds and generation of new sequences gives rise to emergence of protein families and superfamilies whose sizes are power-law distributed, closely matching the same distributions for real proteins. On the population level we observe emergence of species—subpopulations that carry similar genomes. Further, we present a simple theory that relates stability of evolving proteins to the sizes of emerging genomes. Together, these results provide a microscopic first-principles picture of how first-gene families developed in the course of early evolution.     

Study on Market Stability and Price Limit of Chinese Stock Index Futures Market: An Agent-Based Modeling Perspective

This paper explores a method of managing the risk of the stock index futures market and the cross-market through analyzing the effectiveness of price limits on the Chinese Stock Index 300 futures market. We adopt a cross-market artificial financial market (include the stock market and the stock index futures market) as a platform on which to simulate the operation of the CSI 300 futures market by changing the settings of price limits. After comparing the market stability under different price limits by appropriate liquidity and volatility indicators, we find that enhancing price limits or removing price limits both play a negative impact on market stability. In contrast, a positive impact exists on market stability if the existing price limit is maintained (increase of limit by10%, down by 10%) or it is broadened to a proper extent. Our study provides reasonable advice for a price limit setting and risk management for CSI 300 futures.     

Beat gestures influence which speech sounds you hear

Beat gestures—spontaneously produced biphasic movements of the hand—are among the most frequently encountered co-speech gestures in human communication. They are closely temporally aligned to the prosodic characteristics of the speech signal, typically occurring on lexically stressed syllables. Despite their prevalence across speakers of the world''s languages, how beat gestures impact spoken word recognition is unclear. Can these simple ‘flicks of the hand'' influence speech perception? Across a range of experiments, we demonstrate that beat gestures influence the explicit and implicit perception of lexical stress (e.g. distinguishing OBject from obJECT), and in turn can influence what vowels listeners hear. Thus, we provide converging evidence for a manual McGurk effect: relatively simple and widely occurring hand movements influence which speech sounds we hear.     

Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks

The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs) are responsible for their emergence. Comparing two different models of network topology—random networks of Erdős-Rényi type and networks with highly interconnected hubs—we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations.     

Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons

The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter—describing somatic integration—and the spike-history filter—accounting for spike-frequency adaptation—dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na⁺-channel inactivation regulate the sensitivity to rapid input fluctuations.     

Motor-related signals support localization invariance for stable visual perception

Our ability to perceive a stable visual world in the presence of continuous movements of the body, head, and eyes has puzzled researchers in the neuroscience field for a long time. We reformulated this problem in the context of hierarchical convolutional neural networks (CNNs)—whose architectures have been inspired by the hierarchical signal processing of the mammalian visual system—and examined perceptual stability as an optimization process that identifies image-defining features for accurate image classification in the presence of movements. Movement signals, multiplexed with visual inputs along overlapping convolutional layers, aided classification invariance of shifted images by making the classification faster to learn and more robust relative to input noise. Classification invariance was reflected in activity manifolds associated with image categories emerging in late CNN layers and with network units acquiring movement-associated activity modulations as observed experimentally during saccadic eye movements. Our findings provide a computational framework that unifies a multitude of biological observations on perceptual stability under optimality principles for image classification in artificial neural networks.     

Stochastic Simulation of Biomolecular Networks in Dynamic Environments

Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate—using decision-making by a large population of quorum sensing bacteria—that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits.     

Meiosis in Male DROSOPHILA MELANOGASTER. II. Nonrandom Segregation of Compound-Second Chromosomes

The segregation of compound-second chromosomes in males from two different stocks has been examined. Segregation is random in males from the C(2L)RM4, dp; C(2R)RM4, px stock. Gametes containing only one of the two compound chromosomes comprise 50% of the gametes, and gametes containing either both elements or neither element make up the other 50% of the gametes.——In males from the C(2L)RM, b; C(2R)RM, cn stock, gametes containing either C(2L)RM, b or C(2R)RM, cn make up the majority of the gametes. Gametes containing both chromosomes or neither chromosome account for only 2-3% of the gametes. The nonrandom segregation is due to the C(2R)RM, cn chromosome.——Viability is reduced in flies carrying the C(2R)RM, cn chromosome. This includes larval lethality, delayed development and premature adult lethality. Cytologically, this chromosome contains a large duplication of 2L material, which includes material proximal to region 38 or 39. It is suggested that the viability and segregational properties associated with this chromosome are due to the duplicated 2L material.     

What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations—e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being “suboptimal”. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the “neural code”. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise—via stochastic resonance or otherwise—than if it did. We also challenge neuroscientists and biologists, both computational and experimental, to embrace a very broad definition of stochastic resonance in terms of signal-processing “noise benefits”, and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.