The dawn of the RNA World:toward functional complexity through ligation of random RNA oligomers

A main unsolved problem in the RNA World scenario for the origin of life is how a template-dependent RNA polymerase ribozyme emerged from short RNA oligomers obtained by random polymerization on mineral surfaces. A number of computational studies have shown that the structural repertoire yielded by that process is dominated by topologically simple structures, notably hairpin-like ones. A fraction of these could display RNA ligase activity and catalyze the assembly of larger, eventually functional RNA molecules retaining their previous modular structure: molecular complexity increases but template replication is absent. This allows us to build up a stepwise model of ligation- based, modular evolution that could pave the way to the emergence of a ribozyme with RNA replicase activity, step at which information-driven Darwinian evolution would be triggered. Copyright © 2009 RNA Society.

Random walks in local dynamics of network losses

We suggest a model for data losses in a single node (memory buffer) of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that for a finite-capacity buffer at the critical point the loss rate exhibits strong fluctuations and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process.

Freezing process optimisation of pharmaceutical formulations for freeze drying

The body of work presented in this thesis are in three main parts: [1] the effect of ultrasound on freezing events of ionic systems, [2] the importance of formulation osmolality in freeze drying, and [3] a novel system for increasing primary freeze drying rate. Chapter 4 briefly presents the work on method optimisation, which is still very much in its infancy. Aspects of freezing such as nucleation and ice crystal growth are strongly related with ice crystal morphology; however, the ice nucleation process typically occurs in a random, non-deterministic and spontaneous manner. In view of this, ultrasound, an emerging application in pharmaceutical sciences, has been applied to aid in the acceleration of nucleation and shorten the freezing process. The research presented in this thesis aimed to study the effect of sonication on nucleation events in ionic solutions, and more importantly how sonication impacts on the freezing process. This work confirmed that nucleation does occur in a random manner. It also showed that ultrasonication aids acceleration of the ice nucleation process and increases the freezing rate of a solution. Cryopreservation of animal sperm is an important aspect of breeding in animal science especially for endangered species. In order for sperm cryopreservation to be successful, cryoprotectants as well as semen extenders are used. One of the factors allowing semen preservation media to be optimum is the osmolality of the semen extenders used. Although preservation of animal sperm has no relation with freeze drying of pharmaceuticals, it was used in this thesis to make a case for considering the osmolality of a formulation (prepared for freeze drying) as a factor for conferring protein protection against the stresses of freeze drying. The osmolalities of some common solutes (mostly sugars) used in freeze drying were determined (molal concentration from 0.1m to 1.2m). Preliminary investigation on the osmolality and osmotic coefficients of common solutes were carried out. It was observed that the osmotic coefficient trend for the sugars analysed could be grouped based on the types of sugar they are. The trends observed show the need for further studies to be carried out with osmolality and to determine how it may be of importance to protein or API protection during freeze drying processes. Primary drying is usually the longest part of the freeze drying process, and primary drying times lasting days or even weeks are not uncommon; however, longer primary drying times lead to longer freeze drying cycles, and consequently increased production costs. Much work has been done previously by others using different processes (such as annealing) in order to improve primary drying times; however, these do not come without drawbacks. A novel system involving the formation of a frozen vial system which results in the creation of a void between the formulation and the inside wall of a vial has been devised to increase the primary freeze drying rate of formulations without product damage. Although the work is not nearly complete, it has been shown that it is possible to improve and increase the primary drying rate of formulations without making any modifications to existing formulations, changing storage vials, or increasing the surface area of freeze dryer shelves.

On the Maximum of a Branching Process Conditioned on the Total Progeny

The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

Shortest node-disjoint paths on random graphs

A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process global information and distribute paths optimally. Statistical properties such as scaling with system size and number of paths, average path-length and the transition to the frustrated regime are analyzed. The performance of the suggested algorithm is evaluated through a comparison against a greedy algorithm. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points

2000 Mathematics Subject Classification: 60J60, 62M99.

Limit Theorems for Branching Processes with Random Migration Components

The classical Bienaymé-Galton-Watson (BGW) branching process can be interpreted as mathematical model of population dynamics when the members of an isolated population reproduce themselves independently of each other according to a stochastic law.

Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

Limit Theorems for Maxima of Heavy-Tailed Terms with Random Dependent Weights

2000 Mathematics Subject Classification: Primary 60F17, 60G52, 60G70 secondary 60E07, 62E20.

Recent Results for Supercritical Controlled Branching Processes with Control Random Functions

2000 Mathematics Subject Classification: 60J80, 60F05

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

Resonance Energy Transfer-Based Molecular Switch Designed Using a Systematic Design Process Based on Monte Carlo Methods and Markov Chains

A RET network consists of a network of photo-active molecules called chromophores that can participate in inter-molecular energy transfer called resonance energy transfer (RET). RET networks are used in a variety of applications including cryptographic devices, storage systems, light harvesting complexes, biological sensors, and molecular rulers. In this dissertation, we focus on creating a RET device called closed-diffusive exciton valve (C-DEV) in which the input to output transfer function is controlled by an external energy source, similar to a semiconductor transistor like the MOSFET. Due to their biocompatibility, molecular devices like the C-DEVs can be used to introduce computing power in biological, organic, and aqueous environments such as living cells. Furthermore, the underlying physics in RET devices are stochastic in nature, making them suitable for stochastic computing in which true random distribution generation is critical.

In order to determine a valid configuration of chromophores for the C-DEV, we developed a systematic process based on user-guided design space pruning techniques and built-in simulation tools. We show that our C-DEV is 15x better than C-DEVs designed using ad hoc methods that rely on limited data from prior experiments. We also show ways in which the C-DEV can be improved further and how different varieties of C-DEVs can be combined to form more complex logic circuits. Moreover, the systematic design process can be used to search for valid chromophore network configurations for a variety of RET applications.

We also describe a feasibility study for a technique used to control the orientation of chromophores attached to DNA. Being able to control the orientation can expand the design space for RET networks because it provides another parameter to tune their collective behavior. While results showed limited control over orientation, the analysis required the development of a mathematical model that can be used to determine the distribution of dipoles in a given sample of chromophore constructs. The model can be used to evaluate the feasibility of other potential orientation control techniques.

A Molecular-scale Programmable Stochastic Process Based On Resonance Energy Transfer Networks: Modeling And Applications

While molecular and cellular processes are often modeled as stochastic processes, such as Brownian motion, chemical reaction networks and gene regulatory networks, there are few attempts to program a molecular-scale process to physically implement stochastic processes. DNA has been used as a substrate for programming molecular interactions, but its applications are restricted to deterministic functions and unfavorable properties such as slow processing, thermal annealing, aqueous solvents and difficult readout limit them to proof-of-concept purposes. To date, whether there exists a molecular process that can be programmed to implement stochastic processes for practical applications remains unknown.

In this dissertation, a fully specified Resonance Energy Transfer (RET) network between chromophores is accurately fabricated via DNA self-assembly, and the exciton dynamics in the RET network physically implement a stochastic process, specifically a continuous-time Markov chain (CTMC), which has a direct mapping to the physical geometry of the chromophore network. Excited by a light source, a RET network generates random samples in the temporal domain in the form of fluorescence photons which can be detected by a photon detector. The intrinsic sampling distribution of a RET network is derived as a phase-type distribution configured by its CTMC model. The conclusion is that the exciton dynamics in a RET network implement a general and important class of stochastic processes that can be directly and accurately programmed and used for practical applications of photonics and optoelectronics. Different approaches to using RET networks exist with vast potential applications. As an entropy source that can directly generate samples from virtually arbitrary distributions, RET networks can benefit applications that rely on generating random samples such as 1) fluorescent taggants and 2) stochastic computing.

By using RET networks between chromophores to implement fluorescent taggants with temporally coded signatures, the taggant design is not constrained by resolvable dyes and has a significantly larger coding capacity than spectrally or lifetime coded fluorescent taggants. Meanwhile, the taggant detection process becomes highly efficient, and the Maximum Likelihood Estimation (MLE) based taggant identification guarantees high accuracy even with only a few hundred detected photons.

Meanwhile, RET-based sampling units (RSU) can be constructed to accelerate probabilistic algorithms for wide applications in machine learning and data analytics. Because probabilistic algorithms often rely on iteratively sampling from parameterized distributions, they can be inefficient in practice on the deterministic hardware traditional computers use, especially for high-dimensional and complex problems. As an efficient universal sampling unit, the proposed RSU can be integrated into a processor / GPU as specialized functional units or organized as a discrete accelerator to bring substantial speedups and power savings.