Simon Fraser University Undergraduate Collection

The standard cosmological model, known as the ΛCDM model, is the simplest model that accurately describes a variety of aspects of the Universe, including the cosmic microwave background (CMB), large scale structure, and accelerated expansion. Independent observational data, including data from the CMB, baryon acoustic oscillations (BAO), and supernovae type Ia (SNe Ia) provide significant statistical support for the ΛCDM model. Despite this support the Hubble expansion rate determined from these observations is inconsistent with direct measurements, presenting a tension of over 4σ. In this examination we attempt to alleviate this tension by looking at an important assumption of the ΛCDM model, the assumption that the energy densities of the different cosmic fluid components evolve independently. To test this we consider pairwise interactions between dark sector cosmic fluid components by introducing terms which allow for energy exchange between components to the right hand side of the Friedmann fluid equations. Making use of Markov Chain Monte Carlo methods we find that energy exchange between cold dark matter (CDM) and dark energy can correct for the discrepancy between CMB measurements of the Hubble expansion rate and direct measurements, but that adding the BAO measurements to the analysis prevents this tension from being fully alleviated. Our findings suggest dark sector cosmic fluid interactions are a strong candidate for physics beyond ΛCDM and warrant additional research.

Cellular networks in biological systems are complex and as such, identifying the molecular interactions that give rise to the complex behavior observed can require an immense amount of data. Often, statistical and machine learning techniques are used to analyze this data and extract a global picture of network dynamics. One of the challenges of network analysis in systems biology is finding the connections between genes, proteins, or both, and predicting additional ones that have not yet been detected experimentally. This problem is easily mappable to the inverse problem of statistical physics: inferring the microscopic particle-particle interactions given macroscopic observations of a system. In particular, the focus of this work is to investigate whether perturbations can be introduced into the system so as to improve the output data quality. Specifically, we explore how perturbations in the form of magnetic field can be used to improve the inference of interactions for a three-spin Ising system. Utilizing a maximum likelihood approach, we empirically show that there exists an optimal field where learning is most ecient. Such a field seems to counteract the individual interactions between spins, allowing for optimal inference.

A stochastic system under the influence of a stochastic environment will become correlated with both present and future states of the environment. Such a system can be seen as a predictive model of future environmental states. The non-predictive model complexity in such a model has been shown in a recent paper to be fundamentally equivalent to thermodynamic dissipation. In this dissertation, this abstract result is explored in concrete models in order to illustrate how it emerges in realistic systems. In steady-state, this model complexity is found to be the dominant form of dissipation when the system is strongly driven and quick to relax back to equilibrium. Model complexity being the dominant form of dissipation is shown to be equivalent to the rate at which the system learns about its environment being large compared to the heat dissipation.

Biological processes are inherently stochastic, and to achieve directionality, consume free energy. In most cases, the total free energy for a single cycle is fixed. We investigate how this fixed free energy can be allocated throughout different states to maximize the probability flux. We adopt a formalism based on the master equation to find exact solutions to the probability distribution for a specific state at a given time in Laplace space. With this analytical expression for probability distributions, we can calculate the probability flux for a 2-state and 3-state systems using two different energy landscapes, forward=labile, and reverse-labile schemes. We find the optimal allocation of free energy is unevenly distributed to compensate for slower transitions rates in the cycle.

To study how gene-gene interactions may be controlled, and driven toward particular gene states, an Ising model has been proposed to model genes as binary interacting spins. To determine the effect of ‘clamping’ the states of particular genes requires accounting for the other interactions in the network through the renormalization scheme proposed in this thesis.

In recent years, the amount of data available on biological systems such as genetic regulatory networks and neural networks has increased exponentially, thanks to improvements in experimental methods such as drop-seq [1], which enables biologists to simultaneously analyze RNA expression in thousands of cells. To keep pace with the available data, modern machine learning requires efficient methods for using this data to develop predictive models about the natural world. Using a canonical statistical physics example, the Inverse Ising problem, we ask how physical factors such as temperature affect the learning efficiency. In a network governed by a Hamiltonian with spin-spin interactions, we construct a linear system of equations based on equilibrium observations of spin states, and use linear algebra to solve for the underlying spin-spin couplings. We show that there exists an optimal temperature Topt for which learning is most efficient. Furthermore, we discuss several physical correlates for the scaling of Topt with network size for a simple uniform-coupling network and discuss the extension to more general distributions of couplings. The Fisher information, which depends strongly on the variance of the spin-spin alignment, is shown to predict this scaling most accurately.

Recent experimental advancements have allowed for the precise spatial and temporal control of chemical potentials between proteins in the vicinity of one another through optogenetic techniques [3]. This new technique allows for the investigation of cell signalling. Cells communicate by sending chemical signals to induce changes in chemical potentials which then leads to a change of cellular state. In this thesis we apply non-equilibrium theory [6] to model the response of cells to changes in chemical potential, then, by assuming cells want to minimize wasted energy we derive the optimal protocol for cells to change their cellular state through changes in chemical potential. We provide the theoretical framework to derive this optimal protocol for three separate two state chemical reactions: a discrete open system attached to a bath of proteins, a discrete closed system where the total number of proteins is fixed and a continuous closed system where we consider both the spatial and temporal dependence. Although the theory developed is applicable to these reactions for any transition rates, we assume a specific form which closely resembles cell signalling. The resistance to changes in chemical potential is shown to increase exponentially with chemical potential for an open system, to increase exponentially then decay slowly with chemical potential for a closed system and decreases as 1/r where r is the distance from the change. From this we find the optimal protocol and compare the excess work required to change the cellular state using the optimal and naive (constant velocity) protocols. For an open system the optimal protocol is much better than the naive if the chemical potential is varied across a large distance. For a closed system we find similar behaviour for smaller chemical potentials but the improvement then peaks and decreases slowly for very large distances. The spatial dependence of the continuous system has the added effect of decreasing the improvement and smoothing out the peak. We show that our results are consistent with one another in the limiting cases. From this we conclude that cells which require changes in chemical potential within the peak region to change their cellular state will gain the largest benefit from the optimal protocols derived. The optimal protocol has a simple logarithmic form in time µ(t) = ln(ct + b), with c and b constants, for the open system, for the closed and continuous systems it has a more complex shape. Proof of concept of directly simulating the system for comparison is shown, and issues with simulation are discussed.

A circadian clock (sometimes called a circadian oscillator or rhythm) oscillates roughly once every 24 hours, enabling us to organize our physical and mental activities at the time that is most optimal. The Nobel Prize in physiology or medicine in 2017 was awarded to the scientists who discovered the molecular mechanisms controlling the circadian clock.[1] In this thesis, we study the circadian clock in a physical and mathematical setting. The modified Kuramoto model which describes the synchronization between coupled oscillators is chosen as the equation of motion to study the circadian clock of living organisms. More specifically, we picture our physical system as two individual oscillators, one the solar-cycle oscillator and the other an internal-clock oscillator of a living organism. As in the real world, there is always random noise that prevents living organisms from having perfect knowledge of the outside world. Noise can either come from the environmental background or uncertainty in the internal processing of the organism. The deterministic and stochastic versions of the modified Kuramoto model are separately analyzed. The cost analysis based on the phase synchronization between the two oscillators in both deterministic and stochastic environments can reflect the optimization problem of an organism’s circadian clock. Our approach of analyzing the circadian clock can provide us an insight to regulate the operation of a circadian clock within a noisy environment and with internal noise.

Molecular machines are stochastic systems that interconvert different forms of energy, such as chemical potential energy and mechanical energy. These machines are generally comprised of many subunits that each perform a specific function. We develop a novel model that captures some of the important behaviours of rotary stochastic coupled systems. This model contains an explicit reference to the degree of coupling between subunits and allows for the investigation of energy transduction as a function of coupling strength. Evolving the system using Fokker-Planck dynamics, we find that the efficiency of this energy transduction is tightly correlated with coupling strength. In addition, recent developments in theoretical studies have established links between information theory and stochastic thermodynamics. Prompted by these developments, we investigate the information-theoretic quantities of nostalgia and learning rate. We find that, in this model, these quantities lose their link to the thermodynamics of the system, as here we consider the case of symmetric coupling between subsystems whereas these quantities were originally derived for asymmetric coupling.

This paper is a study of the influence and reception of the mythological tropes of descent and return as seen in Thomas Mann’s 1924 novel, The Magic Mountain and, more broadly, within the context of the early twentieth-century modernity. Making reference to Friedrich Nietzsche, Walter Strauss, and Modris Eksteins, it draws connections between Castorp’s desire-driven journey of descent and Germany’s own inwards turn. Moreover, by analyzing the traces of the Orphic myth noticeable in the novel and examining the importance of Orpheus myth to modernist sensibilities, this paper argues that despite the promise of unity the novel appears to signal, Castorp’s inability to retain his vision reveals Mann’s novel as a satirical commentary not only on the individual’s fragmentation but, significantly, on the cultural atomization of early twentieth century Germany.