arXiv subjects

Stefan Reimann

Publications and source records attributed to Stefan Reimann.

12 recordsLinked to original sources

arXiv2025

'Memory States' from Almost Nothing: Representing and Computing in a Non-associative Algebra

This note presents a non-associative algebraic framework for the representation and computation of information items in high-dimensional space. This framework is consistent with the principles of spatial computing and with the empirical findings in cognitive science about memory. Computations are performed through a process of multiplication-like binding and non-associative interference-like bundling. Models that rely on associative bundling typically lose order information, which necessitates the use of auxiliary order structures, such as position markers, to represent sequential information that is important for cognitive tasks. In contrast, the non-associative bundling proposed allows the construction of sparse representations of arbitrarily long sequences that maintain their temporal structure across arbitrary lengths. In this operation, noise is a constituent element of the representation of order information, rather than a means of obscuring it. The non-associative nature of the proposed framework results in the representation of a single sequence by two distinct states. The L-state, generated through left-associative bundling, continuously updates and emphasises a recency effect, while the R-state, formed through right-associative bundling, encodes finite sequences or chunks, capturing a primacy effect. The construction of these states may be associated with activity in the prefrontal cortex in relation to short-term memory and hippocampal encoding in long-term memory, respectively. The accuracy of retrieval is contingent upon a decision-making process that is based on the mutual information between the memory states and the cue. The model is able to replicate the Serial Position Curve, which reflects the empirical recency and primacy effects observed in cognitive experiments.

cs.AI↗

arXiv2024

Items or Relations -- what do Artificial Neural Networks learn?

What has an Artificial Neural Network (ANN) learned after being successfully trained to solve a task - the set of training items or the relations between them? This question is difficult to answer for modern applied ANNs because of their enormous size and complexity. Therefore, here we consider a low-dimensional network and a simple task, i.e., the network has to reproduce a set of training items identically. We construct the family of solutions analytically and use standard learning algorithms to obtain numerical solutions. These numerical solutions differ depending on the optimization algorithm and the weight initialization and are shown to be particular members of the family of analytical solutions. In this simple setting, we observe that the general structure of the network weights represents the training set's symmetry group, i.e., the relations between training items. As a consequence, linear networks generalize, i.e., reproduce items that were not part of the training set but are consistent with the symmetry of the training set. In contrast, non-linear networks tend to learn individual training items and show associative memory. At the same time, their ability to generalize is limited. A higher degree of generalization is obtained for networks whose activation function contains a linear regime, such as tanh. Our results suggest ANN's ability to generalize - instead of learning items - could be improved by generating a sufficiently big set of elementary operations to represent relations and strongly depends on the applied non-linearity.

cs.LG↗

arXiv2022

A novel HD Computing Algebra: Non-associative superposition of states creating sparse bundles representing order information

Information inflow into a computational system is by a sequence of information items. Cognitive computing, i.e. performing transformations along that sequence, requires to represent item information as well as sequential information. Among the most elementary operations is bundling, i.e. adding items, leading to 'memory states', i.e. bundles, from which information can be retrieved. If the bundling operation used is associative, e.g. ordinary vector-addition, sequential information can not be represented without imposing additional algebraic structure. A simple stochastic binary bundling rule inspired by the stochastic summation of neuronal activities allows the resulting memory state to represent both, item information as well as sequential information as long as it is non-associative. The memory state resulting from bundling together an arbitrary number of items is non-homogeneous and has a degree of sparseness, which is controlled by the activation threshold in summation. The bundling operation proposed allows to build a filter in the temporal as well as in the items' domain, which can be used to navigate the continuous inflow of information.

cs.NE↗

arXiv2021

Automated fragment identification for electron ionisation mass spectrometry: application to atmospheric measurements of halocarbons

Non-target screening consists in searching a sample for all present substances, suspected or unknown, with very little prior knowledge about the sample. This approach has been introduced more than a decade ago in the field of water analysis, together with dedicated compound identification tools, but is still very scarce for indoor and atmospheric trace gas measurements, despite the clear need for a better understanding of the atmospheric trace gas composition.For a systematic detection of emerging trace gases in the atmosphere, a new and powerful analytical method is gas chromatography (GC) of preconcentrated samples, followed by electron ionisation, high resolution mass spectrometry (EI-HRMS). In this work, we present data analysis tools to enable automated fragment formula annotation for unknown compounds measured by GC-EI-HRMS. Based on co-eluting mass/charge fragments, we developed an innovative data analysis method to reliably reconstruct the chemical formulae of the fragments, using efficient combinatorics and graph theory. The method does not require the presence of the molecular ion, which is absent in ~40% of EI spectra. Our method has been trained and validated on \textgreater50 halocarbons and hydrocarbons, with 3 to 20 atoms and molar masses of 30 to 330 g mol-1, measured with a mass resolution of approx.~3500. For 90% of the compounds, more than 90% of the annotated fragment formulae are correct. Cases of wrong identification can be attributed to the scarcity of detected fragments per compound or the lack of isotopic constraint (no minor isotopocule detected).Our method enables to reconstruct most probable chemical formulae independently from spectral databases. Therefore, it demonstrates the suitability of EI-HRMS data for non-target analysis and paves the way for the identification of substances for which no EI mass spectrum is registered in databases. We illustrate the performances of our method for atmospheric trace gases and suggest that it may be well suited for many other types of samples. The L-GPL licenced Python code is released under the name ALPINAC for ALgorithmic Process for Identification of Non-targeted Atmospheric Compounds.

physics.comp-ph↗

arXiv2021

Computing with Cognitive States

Basic experimental findings about human working memory can be described by an algebra built on high-dimensional binary states, representing information items, and two operations: multiplication for binding and addition for bundling. In contrast to common VSA algebras, bundling is not associative. Consequently bundling a sequence of items preserves their sequential ordering. The cognitive states representing a memorised list exhibit a primacy as well as a recency gradient. The typical concave-up and asymmetrically shaped serial position curve is derived as a linear combination of those gradients. Quantitative implications of the algebra are shown to agree well with empirical data from basic cognitive tasks including storage and retrieval of information in human working memory.

q-bio.NC↗

arXiv2012

The class of nonlinear stochastic models as a background for the bursty behavior in financial markets

We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results we derive PDF of burst duration for the proposed model. We confirm analytical expressions by numerical evaluation and discuss bursty behavior of return in financial markets in the framework of modeling by nonlinear SDE.

q-fin.ST↗

arXiv2010

The Financial Bubble Experiment: Advanced Diagnostics and Forecasts of Bubble Terminations Volume II-Master Document

This is the second installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 7 bubbles in 7 different global assets; for 4 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that document of the original analysis on 1 November 2010.

q-fin.ST↗

arXiv2010

The Financial Bubble Experiment: advanced diagnostics and forecasts of bubble terminations

On 2 November 2009, the Financial Bubble Experiment was launched within the Financial Crisis Observatory (FCO) at ETH Zurich (\url{http://www.er.ethz.ch/fco/}). In that initial report, we diagnosed and announced three bubbles on three different assets. In this latest release of 23 December 2009 in this ongoing experiment, we add a diagnostic of a new bubble developing on a fourth asset.

q-fin.ST↗

arXiv2010

Dynamics on/in financial markets: dynamical decoupling and stylized facts

Stylized facts can be regarded as constraints for any modeling attempt of price dynamics on a financial market, in that an empirically reasonable model has to reproduce these stylized facts at least qualitatively. The dynamics of market prices is modeled on a macro-level as the result of the dynamic coupling of two dynamical components. The degree of their dynamical decoupling is shown to have a significant impact on the stochastic properties of return trials such as the return distribution, volatility clustering, and the multifractal behavior of time scales of asset returns. Particularly we observe a cross over in the return distribution from a Gaussian-like to a Levy-like shape when the degree of decoupling increases. In parallel, the larger the degree of decoupling is the more pronounced is volatility clustering. These findings suggest that the considerations of time in an economic system, in general, and the coupling of constituting processes is essential for understanding the behavior of a financial market.

q-fin.CP↗

arXiv2010

On the effect of multiplicative noise in a supercritical pitchfork bifurcation

The most important characteristic of {\em multiplicative noise} is that its effects of system's dynamics depends on the recent system's state. Consideration of multiplicative noise on self-referential systems including biological and economical systems therefore is of importance. In this note we study an elementary example. While in a deterministic super critical pitchfork bifurcation with positive bifurcation parameter $λ$ the positive branch $\sqrtλ$ is stable, multiplicative white noise $λ_t =λ + σζ_t$ on the unique parameter reduces stability in that the system's state tends to 0 almost surely, even for $λ>0$, while for 'small' noise $σ< \sqrt{2 λ}$ the point $\sqrt{λ-σ^2/2}$ is a meta-stable state. In this case, correspondingly, the system will 'die out', i.e. $X_t \to 0$ within finite time.

nlin.CD↗

arXiv2006

The Process of price formation and the skewness of asset returns

Distributions of assets returns exhibit a slight skewness. In this note we show that our model of endogenous price formation \cite{Reimann2006} creates an asymmetric return distribution if the price dynamics are a process in which consecutive trading periods are dependent from each other in the sense that opening prices equal closing prices of the former trading period. The corresponding parameter $α$ is estimated from daily prices from 01/01/1999 - 12/31/2004 for 9 large indices. For the S&P 500, the skewness distribution of all its constituting assets is also calculated. The skewness distribution due to our model is compared with the distribution of the empirical skewness values of the ingle assets.

physics.soc-ph↗

arXiv2006

An elementary model of price dynamics in a financial market: Distribution, Multiscaling & Entropy

Stylized facts of empirical assets log-returns $Z$ include the existence of (semi) heavy tailed distributions $f_Z(z)$ and a non-linear spectrum of Hurst exponents $τ(β)$. Empirical data considered are daily prices of 10 large indices from 01/01/1990 to 12/31/2004. We propose a stylized model of price dynamics which is driven by expectations. The model is a multiplicative random process with a stochastic, state-dependent growth rate which establishes a negative feedback component in the price dynamics. This 0-order model implies that the distribution of log-returns is Laplacian $f_Z(z) \sim \exp(-\frac{|z|}α)$, whose single parameter $α$ can be regarded as a measure for the long-time averaged liquidity in the respective market. A comparison with the (more general) Weibull distribution shows that empirical daily log returns are close to being Laplacian distributed. The spectra of Hurst exponents of both, empirical data $τ_{emp}$ and simulated data due to our model $τ_{theor}$, are compared. Due to the finding of non-linear Hurst spectra, the Renyi entropy (RE) $R_β(f_Z)$is considered. An explicit functional form of the RE for an exponential distribution is derived. Theoretical REs of simulated asset return trails are in good agreement with the RE estimated from empirical returns.

physics.soc-ph↗