Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach

Noise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

Trends in Winter Warm Spells in the Central England Temperature Record

An important impact of climate change on agriculture and the sustainability of ecosystems is the increase of extended warm spells during winter. We apply crossing theory to the central England temperature time series of winter daily maximum temperatures to quantify how increased occurrence of higher temperatures translates into more frequent, longer-lasting, and more intense winter warm spells. We find since the late 1800s an overall two- to threefold increase in the frequency and duration of winter warm spells. A winter warm spell of 5 days in duration with daytime maxima above 13°C has a return period that was often over 5 years but now is consistently below 4 years. Weeklong warm intervals that return on average every 5 years now consistently exceed ~13°C. The observed changes in the temporal pattern of environmental variability will affect the phenology of ecological processes and the structure and functioning of ecosystems.

Evaluating Probabilistic Traffic Load Effects on Large Bridges Using Long-Term Traffic Monitoring Data

With the steadily growing of global transportation market, the traffic load has increased dramatically over the past decades, which may develop into a risk source for existing bridges. The simultaneous presence of heavy trucks that are random in nature governs the serviceability limit for large bridges. This study investigated probabilistic traffic load effects on large bridges under actual heavy traffic load. Initially, critical stochastic traffic loading scenarios were simulated based on millions of traffic monitoring data in a highway bridge in China. A methodology of extrapolating maximum traffic load effects was presented based on the level-crossing theory. The effectiveness of the proposed method was demonstrated by probabilistic deflection investigation of a suspension bridge. Influence of traffic density variation and overloading control on the maximum deflection was investigated as recommendations for designers and managers. The numerical results show that the congested traffic mostly governs the critical traffic load effects on large bridges. Traffic growth results in higher maximum deformations and probabilities of failure of the bridge in its lifetime. Since the critical loading scenario contains multi-types of overloaded trucks, an effective overloading control measure has a remarkable influence on the lifetime maximum deflection. The stochastic traffic model and corresponding computational framework is expected to be developed to more types of bridges.

The neural pathway midline crossing theory: a historical analysis of Santiago Rámon y Cajal’s contribution on cerebral localization and on contralateral forebrain organization

Throughout history, many scientists have wondered about the reason for neural pathway decussation in the CNS resulting in contralateral forebrain organization. Hitherto, one of the most accepted theories is the one described by the renowned Spanish physician, Santiago Rámon y Cajal at the end of the 19th century. This Nobel Prize winner, among his many contributions to science, gave us the answer to this question: the key lies in the optic chiasm. Based on the fact that the ocular lenses invert the image formed in the retina, Cajal explained how the decussation of the fibers in the optic chiasm is necessary to obtain a continuous image of the outside in the brain. The crossing of the tactile and motor pathways occurred posteriorly as a compensatory mechanism to allow the cortical integration of the sensory, motor, and visual functions. This theory had a great influence on the scientific community of his time, and maintains its importance today, in which none of the theories formulated to date has managed to entirely refute Cajal’s. In addition, the decussation of neural pathways plays a significant role in different diseases, especially in the recovery process after a hemispheric lesion and in several congenital pathologies. The advantages of cerebral lateralization have also recently been published, although the evolutionary connection between fiber decussation and cortical function lateralization remains a mystery to be solved. A better understanding of the molecular and genetic substrates of the midline crossing processes might result in significant clinical advances in brain plasticity and repair.

Towards a Rubric for Stimulating and Evaluating Sustainable Learning

Preparing students for dealing with sustainability issues is a challenge in the field of education. This is a challenge because we don’t know exactly what we are educating for, as there are no defined answers or outcomes to the issues; the future is unpredictable. Dealing with these issues requires crossing boundaries between people coming from different ‘practices’, e.g., disciplines, cultures, academia versus society, thereby making the learning and working process a challenging but critical learning experience in itself. We argue that education for sustainability should not primarily focus on student content knowledge or development of certain products or answers. It should focus on stimulating students to go through boundary-crossing learning processes critical for getting a grip on the unpredictable future. This allows students to learn to work with ‘others’ around the boundaries, and thereby to develop the ability to co-create new knowledge and work towards innovation or transformation for sustainable practice. Building on the boundary crossing theory and using mixed methods and interventions, this design-based study iteratively develops a boundary crossing rubric as an instrument to operationalise student learning in transdisciplinary projects into concrete student behaviour. This rubric in turn can explicate, stimulate and assess student learning and development in transdisciplinary sustainability projects.

PROBABILITY MODEL AND RELIABILITY ANALYSIS OF CABLE STRESS FOR CABLE-STAYED BRIDGE

The aim of this paper is to investigate the time-varying effect of stay cable of long-span cable-stayed bridges subject to vehicle load. The analysis has been carried out on the Su-Tong cable-stayed bridge in Jiangsu, China that has the second-longest span among the completed composite-deck cable-stayed bridges in the world currently. Probability models of vehicle load in each lane (fast lane, middle lane and slow lane) and cable stress under random vehicle load were developed based on the stochastic process theory. The results show the gross vehicle weight follows lognormal distribution or multi-peak distribution, and the time-interval of the vehicle follows a lognormal distribution. Then, the probability function of maximum cable stress was determined using up-crossing theory. Finally, the reliability of stay cable under random vehicle load was analysed. The reliability index ranges from 9.59 to 10.82 that satisfies the target reliability index of highway bridge structure of finished dead state.

Ordnung und Abweichung. Jurij M. Lotmans Grenzüberschreitungstheorie aus modallogischer Perspektive

In the 1970s and 1980s, literary theorists, particularly in the German-speaking world, showed increasing interest in appropriating the distinctive methodologies of both the positivist social sciences and the natural sciences. Alongside empirical (e. g. Groeben 1982) and analytical approaches to literature (e. g. Fink/Schmidt 1984), the structuralist school shaped by Lotman’s narrative theory attempted a scientific turn in literary theory (cf. Köppe/Winko 2010), aiming for an exact science, or at least one more exact than the traditional ›art of interpretation‹ admitted by Staiger (1955). We trace the structuralist approach, or more precisely, the central aspect of structuralist narratology, the theory of boundary-crossing, first in Lotman (1979), and then criticise Renner’s remodelling based on formal logic (1983), and finally remodel boundary-crossing theory by means of modal logic. By doing this, we hope to demonstrate the potential of a methodologically self-aware, terminologically precise text analysis that is therefore capable of intersubjectivity.At the beginning of the 1970s, the Estonian literary scholar and cultural semiotician Jurij M. Lotman took as his starting point the strong human affinity for the replication of abstract systems (The most influential formulation of Lotman’s boundary-crossing theory – at least in the German speaking world – was that of Karl N. Renner in the early 1980s. Renner understood events to be disruptions of order, and disruptions of order in turn as logical contradictions. In addition to the formal logic representation of disruptions of order, Lotman and Renner differ in that Renner presupposes that the ›eventful situation‹ arisesThe consequences of the principle of non-contradiction do not occur to Renner. While Renner is, in fact, dissatisfied with his model, for him the problem lies in a different circumstance: his ordering statements lack the characteristics of postulates. It can be deduced from his writings that he wishes his ordering statements to be understood as normative statements. However, non-modal sentences, and these are precisely what Renner uses, do not describe, even in the case of subjunctions/implications, what should be, but merely whatThis problem, addressed but not explored by Renner, can be solved with the help of normative reasoning/deontic modal logic. Instead of an operator of necessity, here an operator of obligation is used. Using this operator, we can produce contradiction-free statements about how something should be, which can be placed in relation to selective statements about how things are. Our aim, however, is not exclusively or primarily to criticise Renner, but rather to develop the particular benefits which these consideration of formal logic bring to cross-boundary theory – namely the connection between the quality of the ordering statements, and the durative and non-durative aspect of events.We demonstrate this using Pierre Boulles’ 1963 novel