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Martin Nilsson

Publications and source records attributed to Martin Nilsson.

11 recordsLinked to original sources

A Programmer's Guide to Cascaded Adaptive Combiners: Online Learning by Biologically Accurate Models of Multilayer Neuron Networks

Learning in biological multilayer neuronal networks offers insights that extend beyond the classical weighted-sum neuron model commonly used in artificial neural networks. This article presents an accessible guide to a mechanistic neuronal network model that more accurately captures aspects of biological computation while enabling a simple yet powerful mechanism for learning in multilayer neural networks. The proposed approach supports efficient online streamed learning and provides a practical alternative to backpropagation. We demonstrate its potential in an image classification task, achieving competitive classification performance. The approach's simplicity, biological grounding, and broad applicability highlight a promising path toward algorithms that unify mechanistic neuron models and machine learning.

cs.NE

LuMaMi28: Real-Time Millimeter-Wave Massive MIMO Systems with Antenna Selection

This paper presents LuMaMi28, a real-time 28 GHz massive multiple-input multiple-output (MIMO) testbed. In this testbed, the base station has 16 transceiver chains with a fully-digital beamforming architecture (with different pre-coding algorithms) and simultaneously supports multiple user equipments (UEs) with spatial multiplexing. The UEs are equipped with a beam-switchable antenna array for real-time antenna selection where the one with the highest channel magnitude, out of four pre-defined beams, is selected. For the beam-switchable antenna array, we consider two kinds of UE antennas, with different beam-width and different peak-gain. Based on this testbed, we provide measurement results for millimeter-wave (mmWave) massive MIMO performance in different real-life scenarios with static and mobile UEs. We explore the potential benefit of the mmWave massive MIMO systems with antenna selection based on measured channel data, and discuss the performance results through real-time measurements.

eess.SP

Millimeter-Wave Massive MIMO Testbed with Hybrid Beamforming

Massive multiple-input multiple-out (MIMO) technology is vital in millimeter-wave (mmWave) bands to obtain large array gains. However, there are practical challenges, such as high hardware cost and power consumption in such systems. A promising solution to these problems is to adopt a hybrid beamforming architecture. This architecture has a much lower number of transceiver (TRx) chains than the total antenna number, resulting in cost- and energy-efficient systems. In this paper, we present a real-time mmWave (28 GHz) massive MIMO testbed with hybrid beamforming. This testbed has a 64-antenna/16-TRx unit for beam-selection, which can be expanded to larger array sizes in a modular way. For testing everything from baseband processing algorithms to scheduling and beam-selection in real propagation environments, we extend the capability of an existing 100-antenna/100-TRx massive MIMO testbed (below 6 GHz), built upon software-defined radio technology, to a flexible mmWave massive MIMO system.

eess.SP

On the transition of Charlier polynomials to the Hermite function

It has been known for over 70 years that there is an asymptotic transition of Charlier polynomials to Hermite polynomials. This transition, which is still presented in its classical form in modern reference works, is valid if and only if a certain parameter is integer. In this light, it is surprising that a much more powerful transition exists from Charlier polynomials to the Hermite function, valid for any real value of the parameter. This greatly strengthens the asymptotic connections between Charlier polynomials and special functions, with applications for instance in queueing theory. It is shown in this paper that the convergence is uniform in bounded intervals, and a sharp rate bound is proved. It is also shown that there is a transition of derivatives of Charlier polynomials to the derivative of the Hermite function, again with a sharp rate bound. Finally, it is proved that zeros of Charlier polynomials converge to zeros of the Hermite function. While rigorous, the proofs use only elementary techniques.

math.CA

Generalized Singular Spectrum Time Series Analysis

This paper is a study of continuous time Singular Spectrum Analysis (SSA). We show that the principal eigenfunctions are solutions to a set of linear ODEs with constant coefficients. We also introduce a natural generalization of SSA, constructed using local (Lie-) transformation groups. The time translations used in standard SSA is a special case. The eigenfunctions then satisfy a simple type of linear ODE with time dependent coefficient, determined by the infinitesimal generator of the transformation group. Finally, more general one parameter mappings are considered.

physics.data-an

Quasispecies evolution on a fitness landscape with a fluctuating peak

A quasispecies evolving on a fitness landscape with a single peak of fluctuating height is studied. In the approximation that back mutations can be ignored, the rate equations can be solved analytically. It is shown that the error threshold on this class of dynamic landscapes is defined by the time average of the selection pressure. In the case of a periodically fluctuating fitness peak we also study the phase-shift and response amplitude of the previously documented low-pass filter effect. The special case of a small harmonic fluctuation is treated analytically.

physics.bio-ph

Optimal Mutation Rates in Dynamic Environments

In this paper we study the evolution of the mutation rate for simple organisms in dynamic environments. A model with multiple fitness coding loci tracking a moving fitness peak is developed and an analytical expression for the optimal mutation rate is derived. Surprisingly it turns out that the optimal mutation rate per genome is approximately independent of genome length, something that also has been observed in nature. Simulations confirm the theoretical predictions. We also suggest an explanation for the difference in mutation frequency between RNA and DNA based organisms.

physics.bio-ph

Error Thresholds on Dynamic Fittness-Landscapes

In this paper we investigate error-thresholds on dynamics fitness-landscapes. We show that there exists both lower and an upper threshold, representing limits to the copying fidelity of simple replicators. The lower bound can be expressed as a correction term to the error-threshold present on a static landscape. The upper error-threshold is a new limit that only exists on dynamic fitness-landscapes. We also show that for long genomes on highly dynamic fitness-landscapes there exists a lower bound on the selection pressure needed to enable effective selection of genomes with superior fitness independent of mutation rates, i.e., there are distinct limits to the evolutionary parameters in dynamic environments.

physics.bio-ph

The Computational Complexity of Sandpiles

Given an initial distribution of sand in an Abelian sandpile, what final state does it relax to after all possible avalanches have taken place? In d >= 3, we show that this problem is P-complete, so that explicit simulation of the system is almost certainly necessary. We also show that the problem of determining whether a sandpile state is recurrent is P-complete in d >= 3. In d=1, we give two algorithms for predicting the sandpile on a lattice of size n, both faster than explicit simulation: a serial one that runs in time O(n log n), and a parallel one that runs in time O(log^3 n), i.e. in the class NC^3. The latter is based on a more general problem we call Additive Ranked Generability. This leaves the two-dimensional case as an interesting open problem.

cond-mat

Parallel Quantum Computation and Quantum Codes

We propose a definition of QNC, the quantum analog of the efficient parallel class NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding and decoding standard quantum error-correcting codes, or more generally any circuit consisting of controlled-not gates, controlled pi-shifts, and Hadamard gates. Finally, while we note the Quantum Fourier Transform can be parallelized to linear depth, we conjecture that an even simpler `staircase' circuit cannot be parallelized to less than linear depth, and might be used to prove that QNC < QP.

quant-ph

Some Notes on Parallel Quantum Computation

We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth, while circuits composed of both cannot. Finally, while we note the Quantum Fourier Transform can be parallelized to linear depth, we exhibit a simple quantum circuit related to it that we believe cannot be parallelized to less than linear depth, and therefore might be used to prove that QNC < QP.

quant-ph