arXiv subjects

Thomas Martinetz

Publications and source records attributed to Thomas Martinetz.

31 records · Page 2Linked to original sources

arXiv2017

Recursive Autoconvolution for Unsupervised Learning of Convolutional Neural Networks

In visual recognition tasks, such as image classification, unsupervised learning exploits cheap unlabeled data and can help to solve these tasks more efficiently. We show that the recursive autoconvolution operator, adopted from physics, boosts existing unsupervised methods by learning more discriminative filters. We take well established convolutional neural networks and train their filters layer-wise. In addition, based on previous works we design a network which extracts more than 600k features per sample, but with the total number of trainable parameters greatly reduced by introducing shared filters in higher layers. We evaluate our networks on the MNIST, CIFAR-10, CIFAR-100 and STL-10 image classification benchmarks and report several state of the art results among other unsupervised methods.

cs.CV↗

arXiv2014

Committees of deep feedforward networks trained with few data

Deep convolutional neural networks are known to give good results on image classification tasks. In this paper we present a method to improve the classification result by combining multiple such networks in a committee. We adopt the STL-10 dataset which has very few training examples and show that our method can achieve results that are better than the state of the art. The networks are trained layer-wise and no backpropagation is used. We also explore the effects of dataset augmentation by mirroring, rotation, and scaling.

cs.CV↗

arXiv2013

The phase response of the cortical slow oscillation

Cortical slow oscillations occur in the mammalian brain during deep sleep and have been shown to contribute to memory consolidation, an effect that can be enhanced by electrical stimulation. As the precise underlying working mechanisms are not known it is desired to develop and analyze computational models of slow oscillations and to study the response to electrical stimuli. In this paper we employ the conductance based model of Compte et al. [J Neurophysiol 89, 2707] to study the effect of electrical stimulation. The population response to electrical stimulation depends on the timing of the stimulus with respect to the state of the slow oscillation. First, we reproduce the experimental results of electrical stimulation in ferret brain slices by Shu et al. [Nature 423, 288] from the conductance based model. We then numerically obtain the phase response curve for the conductance based network model to quantify the network's response to weak stimuli. Our results agree with experiments in vivo and in vitro that show that sensitivity to stimulation is weaker in the up than in the down state. However, we also find that within the up state stimulation leads to a shortening of the up state, or phase advance, whereas during the up-down transition a prolongation of up states is possible, resulting in a phase delay. Finally, we compute the phase response curve for the simple mean-field model by Ngo et al. [Europhys Lett 89, 68002] and find that the qualitative shape of the PRC is preserved, despite its different mechanism for the generation of slow oscillations.

q-bio.NC↗

arXiv2012

The physics of business cycles and inflation

We analyse four consecutive cycles observed in the USA for employment and inflation. They are driven by three oil price shocks and an intended interest rate shock. Non-linear coupling between the rate equations for consumer products as prey and consumers as predators provides the required instability, but its natural damping is too high for spontaneous cycles. Extending the Lotka-Volterra equations with a small term for collective anticipation yields a second analytic solution without damping. It predicts the base period, phase shifts, and the sensitivity to shocks for all six cyclic variables correctly.

q-fin.GN↗

arXiv2012

Predicting economic growth with classical physics and human biology

We collect and analyze the data for working time, life expectancy, and the pair output and infrastructure of industrializing nations. During S-functional recovery from disaster the pair's time shifts yield 25 years for the infrastructure's physical lifetime. At G7 level the per capita outputs converge and the time shifts identify a heritable quantity with a reaction time of 62 years. It seems to control demand and the spare time required for enjoying G7 affluence. The sum of spare and working time is fixed by the universal flow of time. This yields analytic solutions for equilibrium, recovery, and long-term evolution for all six variables with biologically stabilized parameters.

q-fin.GN↗

arXiv2012

A physical theory of economic growth

Economic growth is unpredictable unless demand is quantified. We solve this problem by introducing the demand for unpaid spare time and a user quantity named human capacity. It organizes and amplifies spare time required for enjoying affluence like physical capital, the technical infrastructure for production, organizes and amplifies working time for supply. The sum of annual spare and working time is fixed by the universal flow of time. This yields the first macroeconomic equilibrium condition. Both storable quantities form stabilizing feedback loops. They are driven with the general and technical knowledge embodied with parts of the supply by education and construction. Linear amplification yields S-functions as only analytic solutions. Destructible physical capital controls medium-term recoveries from disaster. Indestructible human capacity controls the collective long-term industrial evolution. It is immune even to world wars and runs from 1800 to date parallel to the unisex life expectancy in the pioneering nations. This is the first quantitative information on long-term demand. The theory is self-consistent. It reproduces all peaceful data from 1800 to date without adjustable parameter. It has full forecasting power since the decisive parameters are constants of the human species. They predict an asymptotic maximum for the economic level per capita. Long-term economic growth appears as a part of natural science.

q-fin.GN↗

arXiv2010

On the boundedness of an iteration involving points on the hypersphere

For a finite set of points $X$ on the unit hypersphere in $\mathbb{R}^d$ we consider the iteration $u_{i+1}=u_i+χ_i$, where $χ_i$ is the point of $X$ farthest from $u_i$. Restricting to the case where the origin is contained in the convex hull of $X$ we study the maximal length of $u_i$. We give sharp upper bounds for the length of $u_i$ independently of $X$. Precisely, this upper bound is infinity for $d\ge 3$ and $\sqrt2$ for $d=2$.

cs.CG↗

arXiv2000

Dynamic Fitness Landscapes in Molecular Evolution

We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environment's resource composition lead to both non-constant replication and decay rates of the molecules. In general, therefore, molecular evolution takes place in a dynamic rather than a static fitness landscape. We incorporate dynamic replication and decay rates into the standard quasispecies theory of molecular evolution, and show that for periodic time-dependencies, a system of evolving molecules enters a limit cycle for $t\to\infty$. For fast periodic changes, we show that molecules adapt to the time-averaged fitness landscape, whereas for slow changes they track the variations in the landscape arbitrarily closely. We derive a general approximation method that allows us to calculate the attractor of time-periodic landscapes, and demonstrate using several examples that the results of the approximation and the limiting cases of very slow and very fast changes are in perfect agreement. We also discuss landscapes with arbitrary time dependencies, and show that very fast changes again lead to a system that adapts to the time-averaged landscape. Finally, we analyze the dynamics of a finite population of molecules in a dynamic landscape, and discuss its relation to the infinite population limit.

physics.bio-ph↗

arXiv1999

Molecular Evolution in Time Dependent Environments

The quasispecies theory is studied for dynamic replication landscapes. A meaningful asymptotic quasispecies is defined for periodic time dependencies. The quasispecies' composition is constantly changing over the oscillation period. The error threshold moves towards the position of the time averaged landscape for high oscillation frequencies and follows the landscape closely for low oscillation frequencies.

physics.bio-ph↗

arXiv1999

Genetic Algorithms in Time-Dependent Environments

The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize the asymptotic states in dependence on the mutation rate and the time scale of changes. Furthermore, the notion of regular changes is raised for which the population can be shown to converge towards a generalized quasispecies. Based on this, error thresholds and an optimal mutation rate are approximately calculated for a generational genetic algorithm with a moving needle-in-the-haystack landscape. The so found phase diagram is fully consistent with our general considerations.

physics.bio-ph↗

arXiv1999

Adaptive walks on time-dependent fitness landscapes

The idea of adaptive walks on fitness landscapes as a means of studying evolutionary processes on large time scales is extended to fitness landscapes that are slowly changing over time. The influence of ruggedness and of the amount of static fitness contributions are investigated for model landscapes derived from Kauffman's $NK$ landscapes. Depending on the amount of static fitness contributions in the landscape, the evolutionary dynamics can be divided into a percolating and a non-percolating phase. In the percolating phase, the walker performs a random walk over the regions of the landscape with high fitness.

physics.bio-ph↗

arXiv1998

Lifetimes of agents under external stress

An exact formula for the distribution of lifetimes in coherent-noise models and related models is derived. For certain stress distributions, this formula can be analytically evaluated and yields simple closed expressions. For those types of stress for which a closed expression is not available, a numerical evaluation can be done in a straightforward way. All results obtained are in perfect agreement with numerical experiments. The implications for the coherent-noise models' application to macroevolution are discussed.

physics.data-an↗

arXiv1998

Hierarchical noise in large systems of independent agents

A generalization of the coherent-noise models [M. E. J. Newman and K. Sneppen, Phys. Rev. E{\bf54}, 6226 (1996)] is presented where the agents in the model are subjected to a multitude of stresses, generated in a hierarchy of different contexts. The hierarchy is realized as a Cayley-tree. Two different ways of stress propagation in the tree are considered. In both cases, coherence arises in large subsystems of the tree. Clear similarities between the behavior of the tree model and of the coherent-noise model can be observed. For one of the two methods of stress propagation, the behavior of the tree model can be approximated very well by an ensemble of coherent-noise models, where the sizes $k$ of the systems in the ensemble scale as $k^{-2}$. The results are found to be independent of the tree's structure for a large class of reasonable choices. Additionally, it is found that power-law distributed lifetimes of agents arise even under the complete absence of correlations between the stresses the agents feel.

physics.data-an↗