Matematiska vetenskaper // Mathematical Sciences

Använd denna länk för att länka till samlingen:

https://odr.chalmers.se/handle/20.500.12380/17

Studerar matematikens strukturer och utvecklar dem för att bättre förstå vår värld, och till nytta för forskning och teknisk utveckling.
De matematiska vetenskaperna utforskar tankens grundläggande begrepp och lagar. De är oumbärliga för modern naturvetenskap och teknik. Även inom andra vetenskaper spelar matematisk och statistisk metodik en alltmer framträdande roll. Matematik är också en vetenskap i sig själv och grundforskning i matematik är en förutsättning för dess många tillämpningar. Institutionen är gemensam för Chalmers tekniska högskola och Göteborgs universitet.

Läs mer om våra utbildningar

För forskning och forskningspublikationer, se https://research.chalmers.se/organisation/matematiska-vetenskaper/

Studies mathematical structures, developing them to better understand our world and to benefit from research and technological development.
The mathematical sciences are fundamental and indispensable to a large part of modern science and engineering. Progress in other disciplines is often linked to an increased use of mathematics. Mathematics is also a subject in itself, and fundamental research is a necessary condition for its many applications. The Department is joint for the Chalmers University of Technology and University of Gothenburg.

Studying at the Department of Mathematical Sciences at Chalmers

For research and research output, please visit https://research.chalmers.se/en/organization/mathematical-sciences/

Browse

Visar 1 - 20 av 545

A column generation approach to the flexible job-shop problem with ordering requirements on operations
(2018) Jonsson, Niclas; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
A Deep Learning Method for Nonlinear Stochastic Filtering: Energy-Based Deep Splitting for Fast and Accurate Estimation of Filtering Densities
(2024) Rydin, Filip; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Larsson, Stig; Andersson, Adam; Bågmark, Kasper
In filtering the problem is to find the conditional distribution of a dynamically evolving state given noisy measurements. Critically, designing accurate filters for nonlinear problems that scale well with the state dimension is exceedingly difficult. In this thesis, a novel filtering method based on deep learning solutions to the Fokker–Planck partial differential equation is treated. Training can be performed offline, which results in a computationally efficient algorithm online, even in high dimensions. This is promising for applications which require good real-time performance, such as target-tracking. The filtering method, referred to as Energy-Based Deep Splitting (EBDS), is presented in detail and implemented. The performance of EBDS on different example problems is then investigated and compared to benchmark filters, such as variants of the Kalman filter and particle filters. In one dimension EBDS seems to perform superbly, especially considering how fast the filter is at evaluation. In higher dimensions the method performs worse in comparison to the benchmarks, although it still yields sensible density estimates in most cases. Additionally, convergence for EBDS in the number of prediction steps is investigated empirically for two of the example problems. The results in both examples indicate strong convergence of order 1/2. Lastly, a neural network architecture based on Long Short-Term Memory (LSTM) encoders is proposed for EBDS. This architecture yields reduced errors compared to standard fully-connected networks. In summary, the results indicate that the method is promising and should be examined further. This thesis can be viewed as a reference for future works that aim to apply EBDS in more specific settings or that aim to improve the method further.
A Dispatching Algorithm with Application to Fleets of Shared Autonomous Vehicles
(2017) Hellsten, Erik; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
Fleets of shared autonomous vehicles have been predicted to dominate the transport sector within a near future. For this to work efficiently—including the handling of spontaneous requests—the associated routing problems need to be modelled dynamically and solved efficiently. We formulate and model the problem of routing a fleet of shared autonomous vehicles over a period of time. For each vehicle and each moment in time, it must be decided which customers to serve and which routes to take. The resulting model is solved using a rolling horizon optimisation methodology together with an insertion heuristic for new requests. The optimisation problems resulting from the rolling horizon methodology are solved using column generation, where the subproblems, being elementary shortest path problems with side constraints, are solved using both a local-search heuristic and a dynamic programming algorithm. Our computational experiments show that real-world sized problem instances can be solved to near-optimality within a reasonable computing time.
A generalized vehicle routing problem with spatial and temporal synchronization. Mathematical modelling and solution.
(2016) Mustedanaganic, Amir; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
A genetic programming approach to finding discrepancies in log files
(2021) Gulliksson, Martin; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Raum, Martin; Helgegren, Elin
An evolutionary algorithm is used to find discrepancies in log files. From a set of error-free reference logs, a set of regular expression patterns describing the logs’ general structure is generated using genetic programming. The patterns can then be checked against logs containing errors, with the goal being that added, removed and reordered lines are detected. Using a regex-oriented approach allows for grouping lines together even though the contents are not exactly the same in every instance. The approach works well so long as the log files provided do not contain too much noise.
A machine learning approach for predicting bacteria content in drinking water
(2023) Eric, Jonsson; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Axelson-Fisk, Marina; Dannélls, Dana; Cahn, Jacob
The current method for finding whether drinking water contains bacterial contamination is a very slow process and it can take up to eight days before the results are obtained. During this time, a significant proportion of the population has potentially obtained diseases from contaminated water. As a mitigating action, this thesis aimed to understand if machine learning could be a promising method for forecasting the bacteria level and how such a model could be designed. The project was performed in association with a case company called Nocoli, which is spun out of Chalmers Ventures and desired an examination of the potential implementation. A literature review including eight different case studies of how machine learning was previously applied in the field and three semi-structured interviews with industryspecific stakeholders were conducted. The research methodology originated from the fact that both an overview of the current industry situation as well as machine learning applicability was required. Moreover, by using an extracted theory of machine learning algorithms for different objectives, the case studies were evaluated to find patterns that could meet the case companys demands. It was found that machine learning is promising and desired in the industry to improve current operations. The Random Forest algorithm was recommended in the initial stage due to its trade-off between accuracy and interpretability. Data on bacterial content and other factors including weather was intended as the data source. The recommendation included a 3:1:1 split between training-, validation-, and test sets as well as using a recursive feature selection algorithm. Additionally, a combination of error measures was recommended including Mean Squared Error with an out-of-bag supplement to reduce overfitting. Furthermore, although no data could be obtained to evaluate the recommended model, it was concluded that machine learning could have a positive impact on today’s approach and contribute to improved water management and safety by enabling reliable forecasts.
A mathematical investigation of breast cancer and tumor growth - Statistical analysis and stochastic modeling
(2009) Mattsson, Hanna; Nyquist, Pierre; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
A methodology and algorithm for automatically classifying text documents to strategic intents
(2011) Karmakar, Robin; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
A Model for an Augmented Reality Tool in Tumour Removal Laparoscopic Surgery
(2020) Månsson, Lisa; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Lundh, Torbjörn; Modin, Klas; Lundh, Torbjörn
One of the most lethal types of cancer is hepatocellular carcinoma, cancer in the liver. Because of the many risks entailed with open surgery, the use of laparoscopic surgery has increased, with no exception in liver resections. Instead of a big cut, minimally invasive techniques are used, placing small ports on the abdomen where surgical tools as well as a laparoscope can be inserted. The surgeons orient themselves from the outside, creating a perception of the inside through the 2D images from the camera and a preoperative 3D image on the side as a map. Since the liver is an essentially homogeneous organ, it can be hard to orient from this information, why surgeons in Gothenburg have developed markers to place on the liver’s surface. With help of such markers, the goal is to develop an augmented reality tool for intraoperative guidance, mapping the laparoscopic 2D image to the corresponding 3D position, and be able to project a tumour area in the laparoscopic view. In this work, an inventory of laparoscopic liver resection was performed and a camera model as well as a simulated liver environment was developed. To map a 2D image to the 3D environment, an algorithm for estimation of the camera pose, named POSIT, was examined. It was concluded that the limitations of POSIT were not compatible with the problem, but the platform developed, consisting of a simulated liver environment and the camera model, can be used as a framework for future work, in which testing of other algorithms to estimate the camera pose can be performed.
A Model for Object Recognition in Liver Resection Surgery
(2020) AL-MALEH, CHRISTIAN; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Lundh, Torbjörn; Lundh, Torbjörn
Laparoscopic liver resection is a safer alternative to open surgery for treatment of liver cancer, a disease which claims almost 800 000 lives every year. The procedure involves making small incisions in the abdomen where instruments and a camera, called a laparoscope, are inserted. One of the major drawbacks of laparoscopic surgery is the restricted view and orientation, as well as lack of haptic feedback. Incorporating Augmented Reality, or AR, in the laparoscopic view is a proposed method of facilitating the navigation. This work extends a previous model for projecting information from 3D to 2D and vice versa using reference points, which correctly visualizes the shape, angle and size of a tumor in AR in the 2D laparoscopic view. To enable the 2D-to-3D projection, two object recognition models based on image segmentation and edge detection, respectively, were developed where white reference objects were distinguished from the darker tones of the liver tissue. The positions of the reference objects were then measured. The latter model, albeit effective given certain frames, failed to identify fiducials over the course of a test film. Since the process of image segmentation is computationally heavy, it was localized to an area of interest in a given frame, reducing the algorithm’s runtime. Statistical error estimation was used to validate the positions found by this recognition model. The average position error produced was between 1 to 5 pixels, where the frames had a pixel height of 1080. Future work involves combining the recognition algorithm with the projection model to examine the effect of the deviations of the estimated positions in the 2D laparoscopic view.
A Pipeline for Comparison of Clustering Methods in Flow Cytometry Analysis
(2013) Farahbod, Marjan; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
A space-time cut finite element method for a time-dependent parabolic model problem
(2015) Lundholm, Carl; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
In this thesis, a space-time finite element method for the heat equation on overlapping meshes is presented. Here, overlapping meshes means that we have a stationary mesh of the solution domain with an additional mesh that is allowed to move around in and through the solution domain. The thesis contains a derivation, an analysis, and results from an implementation of the method. The derivation starts with a strong formulation of the problem and ends with a finite element variational formulation together with adequate function spaces. For the finite element solution, we use continuous Galerkin in space and discontinuous Galerkin in time, with the addition of a discontinuity in the solution on the space-time boundary between the two meshes. In the analysis, we propose an a priori error estimate for the method with discontinuous Galerkin of order zero and one, i.e., dG(0) and dG(1). For dG(1), the error estimate indicates that the movement of the additional mesh decreases the order of convergence of the error, with respect to the time step, from the third to the second order, when the speed of the moving mesh is large enough. The order of convergence with respect to the step size for dG(1), as well as the error convergence for dG(0), are unaffected by the moving mesh and are thus as in the case with only a stationary mesh, presented in [2, 3]. An implementation of the method in one spatial dimension, with piecewise linear elements in space, and dG(0) and dG(1) in time, has also been performed. The numerical results of the implementation show the superiority of using dG(1) instead of dG(0) for overlapping meshes. The numerical results also confirm the behaviour of the error convergence, indicated by the a priori error estimate. Keywords: partial differential equation, finite element method, space-time cut, time-dependent, parabolic problem, heat equation, overlapping mesh, moving mesh, discontinuous Galerkin, a priori.
A Space-Time Finite Element Method for the Heat Equation
(2010) Tantardini, Francesca; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
A study of the stratification of plane cubic curves and its various generalizations
(2013) Boutry, Pierre; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
A surrogate-based parameter tuning heuristic for Carmen crew optimizers
(2010) Häglund, Staffan; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
A two-fold analysis of Value Creating Learn- ing
(2024) Meijer, Edvin; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Gerlee, Philip; Gerlee, Philip
Value Creating Learning (VCL) is a pedagogical method, based in entrepreneurial learning, that aims to spark the intrinsic motivation in students by making them par- ticipate in real missions towards external recipients outside their own group, class, or school. In the mission of ”Attefallshuset” the teachers at an upper secondary school in the Gothenburg region wanted to evaluate a progression of VCL missions. The pro- gression lies in the level of foreignness that the external recipient had to the students, and thus how arduous the students experienced, and perceived, it to make and have contact with the external recipient. Through empirical research, the aim of this thesis was to see if a progression would ease the students’ feelings and attitudes towards working with more foreign external recipients. Another aim of this thesis was to the- oretically, and critically, analyse VCL in order to better understand its educational implications and students’ perception of it and their learning. Results from the quantitative data showed no statistically significant difference made by the progression. However, the results from the qualitative data showed that the progression seemed to change the students’ attitude of the external recipients, as well as to improve student-to-student feedback. Two critical investigations of VCL were also carried out, one about the educational functions of VCL in relation to the concept of Bildung. The other one investigates if VCL fits all students and VCL’s relational capacity, analysed through resonance theory. There were three main conclusions. The first was that progression in VCL seemed to ease the interaction with external re- cipients and generate a better climate for student-to-student feedback. The second was that the students generally overcame a feeling of being nervous when they in- teracted with external recipients, which led to that the students felt more self-secure and acquired a higher degree of self-efficacy. The third was that the teacher have to put careful attention to the group dynamics and the personality of the class when deciding the level of external interaction in a VCL mission.
Abstractive Document Summarisation using Generative Adversarial Networks
(2018) Svensson, Karl; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
The use of automatically generated summaries for long texts is commonly used in digital services. In this thesis, one method for such document summarisation is created by combining existing techniques for abstractive document summarization with LeakGAN – a successful approach at text generation using generative adversarial networks (GAN). The resulting model is tested on two diﬀerent datasets originating from conventional newspapers and the world’s largest online community: Reddit. The datasets are examined and several important diﬀerences are highlighted. The evaluations show that the summaries generated by the model do not correlate with the corresponding documents. Possible reasons are discussed and several suggestions for future research are presented.
Active Learning and Malware Entity Extraction. A survey of active learning methods specifically implemented with a CRF for finding malware names - The hunt for Red October.
(2016) Romare, Elin; Bijelovic, Milica; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
Active Safety for car-to-bicyclist accidents
(2014) Ranjbar, Arian; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
During the last years the rapid development of countermeasures has led to an overall decreasing number of fatalities in road traffic accidents. However, the positive trend does not hold at the same rate for bicyclists. It is therefore desireable to investigate these type of accidents and discuss possible countermeasures. In this work the car-to-bicyclist accidents were studied to understand the context in which they occur. Data was collected from the German In-Depth Accident Study (GIDAS) database and the Pre-Crash Matrix (PCM) extension which contained reconstructed accidents. A geometrical classification method was developed to find the most common type of accident scenarios and descriptive statistics was gathered. Further on, a risk model was derived to find the probability of an accident to result in severe injuries. The model was also used to calculate the theoretical effectiveness of a simplified Autonomous Emergency Braking (AEB) system. The study showed that the most common car-to-bicyclist accidents were lateral and longitudinal scenarios in intersections, where the car was travelling straight forward. This was also connected to the risk analysis which showed that the most risk in uencing parameter was the impact speed of the car in the collision. Finally, the effectiveness study indicated that AEB has a considerable potential to mitigate car-to-bicyclist accidents.
Adaptive Driver Modelling for Forward Collision Warning Systems
(2021) Forsman, Oscar; Warnqvist, Johanna; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Lundh, Torbjörn; Irekvist, Daniel; Runhäll, Andreas
In this work, driving behaviour is analysed with the purpose of finding connections between a drivers routine driving and their behaviour in collision and near-collision situations. The ambition is to improve the Forward Collision Warning (FCW) system on Volvo cars by taking information from previous driving situations of the current driver into account when determining the best timing for issuing a collision warning. The analysis is performed by means of feature extraction on multivariate time series data, containing measurements from various sensors. Using principal component analysis (PCA) and clustering methods such as k-means and DBSCAN, no connections relevant to the formulated aim could be found in the investigation. The conclusion drawn is that a more thorough evaluation of the available data is required. Removing parts of drive sequences that are not of interest or categorise the sequences into different scenarios can make the information more comparable and hence yield a better result. A more careful data cleaning of the available time series could also lead to an improvement.

Browse

Browsar Matematiska vetenskaper // Mathematical Sciences efter Titel

Sökresultat per sida

Sortera efter