arXiv subjects

P. Kozlowski

Publications and source records attributed to P. Kozlowski.

8 recordsLinked to original sources

arXiv2024

Optimizing Charge Transport Simulation for Hybrid Pixel Detectors

To enhance the spatial resolution of the M\"ONCH 25 \textmu m pitch hybrid pixel detector, deep learning models have been trained using both simulation and measurement data. Challenges arise when comparing simulation-based deep learning models to measurement-based models for electrons, as the spatial resolution achieved through simulations is notably inferior to that from measurements. Discrepancies are also observed when directly comparing X-ray simulations with measurements, particularly in the spectral output of single pixels. These observations collectively suggest that current simulations require optimization. To address this, the dynamics of charge carriers within the silicon sensor have been studied using Monte Carlo simulations, aiming to refine the charge transport modeling. The simulation encompasses the initial generation of the charge cloud, charge cloud drift, charge diffusion and repulsion, and electronic noise. The simulation results were validated with measurements from the M\"ONCH detector for X-rays, and the agreement between measurements and simulations was significantly improved by accounting for the charge repulsion.

physics.ins-det↗

arXiv2003

Statistical mechanics of the majority game

The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a particular Hopfield like hamiltonian. On the basis of a replica symmetric calculations, we draw the phase diagram, which contains the analog of a retrieval phase. The number of metastable states is estimated using the annealed approximation. The results are confronted with extensive numerical simulations.

cond-mat.stat-mech↗

arXiv2001

On-line learning and generalisation in coupled perceptrons

We study supervised learning and generalisation in coupled perceptrons trained on-line using two learning scenarios. In the first scenario the teacher and the student are independent networks and both are represented by an Ashkin-Teller perceptron. In the second scenario the student and the teacher are simple perceptrons but are coupled by an Ashkin-Teller type four-neuron interaction term. Expressions for the generalisation error and the learning curves are derived for various learning algorithms. The analytic results find excellent confirmation in numerical simulations.

cond-mat.dis-nn↗

arXiv2001

On the equivalence of the Ashkin-Teller and the four-state Potts-glass models of neural networks

We show that for a particular choice of the coupling parameters the Ashkin-Teller spin-glass neural network model with the Hebb learning rule and one condensed pattern yields the same thermodynamic properties as the four-state anisotropic Potts-glass neural network model. This equivalence is not seen at the level of the Hamiltonians.

cond-mat.dis-nn↗

arXiv2000

Optimal coloured perceptrons

Ashkin-Teller type perceptron models are introduced. Their maximal capacity per number of couplings is calculated within a first-step replica-symmetry-breaking Gardner approach. The results are compared with extensive numerical simulations using several algorithms.

cond-mat.dis-nn↗

arXiv2000

The Ashkin-Teller neural network near saturation

The thermodynamic and retrieval properties of the Ashkin-Teller neural network model storing an infinite number of patterns are examined in the replica-symmetric mean-field approximation. In particular, for linked patterns temperature-capacity phase diagrams are derived for different values of the two-neuron and four-neuron coupling strengths. This model can be considered as a particular non-trivial generalisation of the Hopfield model and exhibits a number of interesting new features. Some aspects of replica-symmetry breaking are discussed.

cond-mat.dis-nn↗

arXiv1998

Statics and dynamics of an Ashkin-Teller neural network with low loading

An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns built from the two types of neurons, with different degrees of (in)dependence is studied. In particular, thermodynamic properties including the existence and stability of Mattis states are discussed. Furthermore, the dynamic behaviour is examined by deriving flow equations for the macroscopic overlap. It is found that for linked patterns the model shows better retrieval properties than a corresponding Hopfield model.

cond-mat.dis-nn↗

arXiv1998

The critical Ising lines of the d=2 Ashkin-Teller model

The universal critical point ratio $Q$ is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in the presence of a non-vanishing thermal field is found from finite-size scaling and the corresponding expression is fitted to the accurate perturbative transfer-matrix data calculations for the $L\times L$ square clusters with $L\leq 9$.

cond-mat.stat-mech↗