Factor Analysis for Spectral Estimation

Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model where a signal is given by a random linear combination of fixed, yet unknown, stochastic sources. Given multiple such signals, we estimate the subspace spanned by the power spectra of these fixed sources. Projecting individual power spectrum estimates onto this subspace increases estimation accuracy. We provide accuracy guarantees for this method and demonstrate it on simulated and experimental data from cryo-electron microscopy.Comment: 5 pages, 3 figures; 12th International Conference Sampling Theory and Applications, July 3-7, 2017, Tallinn, Estoni

Multitaper estimation on arbitrary domains

Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain. Unfortunately, the numerical calculation of these Slepian tapers is only tractable for certain symmetric domains, such as rectangles or disks. In addition, no performance bounds are currently available for the mean squared error of the spectral density estimate. This situation is inadequate for applications such as cryo-electron microscopy, where noise models must be estimated from irregular domains with small sample sizes. We show that the multitaper estimator only depends on the linear space spanned by the tapers. As a result, Slepian tapers may be replaced by proxy tapers spanning the same subspace (validating the common practice of using partially converged solutions to the Slepian eigenproblem as tapers). These proxies may consequently be calculated using standard numerical algorithms for block diagonalization. We also prove a set of performance bounds for multitaper estimators on arbitrary domains. The method is demonstrated on synthetic and experimental datasets from cryo-electron microscopy, where it reduces mean squared error by a factor of two or more compared to traditional methods.Comment: 28 pages, 11 figure

Structural Variability from Noisy Tomographic Projections

In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low-rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For $n$ images of size $N$-by-$N$ pixels, we propose an algorithm for calculating this covariance estimator with computational complexity $\mathcal{O}(nN^4+\sqrt{\kappa}N^6 \log N)$, where the condition number $\kappa$ is empirically in the range $10$--$200$. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in 6D. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed non-consistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrices, we introduce a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.Comment: 52 pages, 11 figure

Covariance estimation using conjugate gradient for 3D classification in Cryo-EM

Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimensional structure present in the molecules being imaged. Our proposed method allows for incorporation of contrast transfer function and non-uniform distribution of viewing angles, making it more suitable for real-world data. We evaluate its performance on a synthetic dataset and an experimental dataset obtained by imaging a 70S ribosome complex

Towards a Business Model that promotes Sustainable Solutions

Purpose: The purpose of this study is to increase the understanding of how the business model of an architecture firm needs to adapt when the company decides to offer sustainable construction. This by identifying what characterizes the business model in an architecture firm that actively works with sustainable construction. When relevant, the study will also provide insights about the transformation process the firm needs to go through in order to adapt its business model. Methodology: The starting point for the study was to review existing theory within the research domains; the offensive sustainability approach, business models, and architecture firms. This phase was deductive and resulted in a preliminary theoretical framework. Thereafter a multiple case study was conducted with the purpose to develop theory by complementing, rejecting and positioning the suggestions offered by the preliminary theoretical framework in an empirical context. Lastly, we analyzed the collected data and came up with a final framework using a pattern matching approach. Thus, the study is argued to be of semi-deductive character. Theoretical perspectives: The theoretical review concerns the three research domains; the offensive sustainability approach, business models, and architecture firms. Empirical foundation: The multiple case study consists of ten cases. Each case represents an architecture firm that operates within one or more of the Nordic countries. All architecture firms are considered to be in the forefront when it comes to offering sustainable constructions. Conclusion: The answer to our purpose is the final framework, which in our view offers a robust, rigorous and relevant perspective on what the business model of an architecture firm entails in order to successfully offer sustainable construction. The framework is structured into four different levels of analysis, which explain different relationships that a firm has to consider to successfully transform. Key at the market level is to start with defining the customer and its needs in order to build a personalized relationship and thus gain revenue in the long run. At the organizational level an organizational structure that facilitates engagement among employees and enables efficient distribution and development of knowledge is vital. At the industry level collaboration with other actors is argued to be necessary in order to realize a sustainable design. Finally, the society level considers the relationship an architecture firm needs to have with external actors in order drive the question and consequently influence the level of demand

Green areas during the grey season : a site analysis based on health-promoting environmental qualities

Psykisk ohälsa är ett problem i dagens samhälle. I Sverige ökar den psykiska ohälsan och av årstidsrelaterade depressioner är vintern den årstid som dominerar i statistiken. Forskning inom miljöpsykologi visar att utemiljöer kan fungera hälsofrämjande bland annat genom att bidra till återhämtning. Arbetets syfte är att identifiera kvaliteter i utemiljöer vintertid som främjar psykisk hälsa genom att ta fram ett ramverk och tillämpa det vid platsanalys. Arbetet ämnar bidra med kunskap kring hur stadsplanering och gestaltning av utemiljöer vintertid kan förebygga psykisk ohälsa samt bidra till återhämtning av exempelvis utmattning, depression och ångest. En platsanalys av Flogsta utförs. Resultaten visar att Flogsta erhåller ett flertal utemiljöer med kvaliteter som främjar psykisk hälsa. Å andra sidan brister området i vinterkvaliteter, speciellt när det kommer till de gestaltade element som skulle kunna öka kvaliteten på platserna. Exempel på detta är brist på skydd mot oönskat väder, på tillgängliggörandet av tydliga vinteraktiviteter och en generell brist på vinteranpassning i utemiljöerna. Det är istället förekomsten av mer naturlika områden som bidrar med många av kvaliteterna som kan nyttjas året om. Bristen på vinteranpassning antas resultera i minskad användning av utemiljöerna vintertid och därmed påverka de boendes psykiska hälsa. Med studien ville vi kunna bidra till att fylla den kunskapslucka som finns inom forskningen i hur utemiljöer påverkar människor under vintern. Med ramverkets hjälp kunde kvaliteter identifieras men samtidigt är ramverket i behov av utveckling för att nå sin fulla potential.Mental illness is a problem when it comes to public health today. In Sweden mental illness increases and the wintertime contribute to the majority of cases of seasonal depression. Research in environmental psychology show that the outdoor environment can serve as a resource of recovery and rehabilitation. The aim of this essay is to identify qualities in outdoor environments during winter that contribute to mental health through creating a framework and applying it to a field analysis. The study aims to contribute with knowledge on how city planning and design can prevent mental illness and have a positive impact on recovery of mental disorders such as fatigue, depression and anxiety. A site analysis is applied on Flogsta. The results show that in general the residents of Flogsta have access to a wide range of public outdoor spaces with qualities that contribute to mental health. On the other hand the area lacks winter qualities, especially when it comes to urban planning and man-made elements that could contribute to the quality of the spaces. Many of the health benefiting qualities in the area will only reach the people in the warmer months since there is no protection against bad weather, lack of winter activities and no clear adaptation to the colder months. Areas with nature contributes with qualities all year round. The lack of adaption to winter is assumed to result in less use of the outdoor environment in wintertime which is a lost opportunity to promote mental health. With the study we wanted to contribute to more research about how outdoor environments can affect mental health in the wintertime. With help of the framework we could identify qualities but at the same time the framework can be improved to reach its full potential