Synthetic molecular machines for active self-assembly : prototype algorithms, designs, and experimental study

Computer science and electrical engineering have been the great success story of the twentieth century. The neat modularity and mapping of a language onto circuits has led to robots on Mars, desktop computers and smartphones. But these devices are not yet able to do some of the things that life takes for granted: repair a scratch, reproduce, regenerate, or grow exponentially fast–all while remaining functional.

This thesis explores and develops algorithms, molecular implementations, and theoretical proofs in the context of “active self-assembly” of molecular systems. The long-term vision of active self-assembly is the theoretical and physical implementation of materials that are composed of reconfigurable units with the programmability and adaptability of biology’s numerous molecular machines. En route to this goal, we must first find a way to overcome the memory limitations of molecular systems, and to discover the limits of complexity that can be achieved with individual molecules.

One of the main thrusts in molecular programming is to use computer science as a tool for figuring out what can be achieved. While molecular systems that are Turing-complete have been demonstrated [Winfree, 1996], these systems still cannot achieve some of the feats biology has achieved.

One might think that because a system is Turing-complete, capable of computing “anything,” that it can do any arbitrary task. But while it can simulate any digital computational problem, there are many behaviors that are not “computations” in a classical sense, and cannot be directly implemented. Examples include exponential growth and molecular motion relative to a surface.

Passive self-assembly systems cannot implement these behaviors because (a) molecular motion relative to a surface requires a source of fuel that is external to the system, and (b) passive systems are too slow to assemble exponentially-fast-growing structures. We call these behaviors “energetically incomplete” programmable behaviors. This class of behaviors includes any behavior where a passive physical system simply does not have enough physical energy to perform the specified tasks in the requisite amount of time.

As we will demonstrate and prove, a sufficiently expressive implementation of an “active” molecular self-assembly approach can achieve these behaviors. Using an external source of fuel solves part of the the problem, so the system is not “energetically incomplete.” But the programmable system also needs to have sufficient expressive power to achieve the specified behaviors. Perhaps surprisingly, some of these systems do not even require Turing completeness to be sufficiently expressive.

Building on a large variety of work by other scientists in the fields of DNA nanotechnology, chemistry and reconfigurable robotics, this thesis introduces several research contributions in the context of active self-assembly.

We show that simple primitives such as insertion and deletion are able to generate complex and interesting results such as the growth of a linear polymer in logarithmic time and the ability of a linear polymer to treadmill. To this end we developed a formal model for active-self assembly that is directly implementable with DNA molecules. We show that this model is computationally equivalent to a machine capable of producing strings that are stronger than regular languages and, at most, as strong as context-free grammars. This is a great advance in the theory of active self- assembly as prior models were either entirely theoretical or only implementable in the context of macro-scale robotics.

We developed a chain reaction method for the autonomous exponential growth of a linear DNA polymer. Our method is based on the insertion of molecules into the assembly, which generates two new insertion sites for every initial one employed. The building of a line in logarithmic time is a first step toward building a shape in logarithmic time. We demonstrate the first construction of a synthetic linear polymer that grows exponentially fast via insertion. We show that monomer molecules are converted into the polymer in logarithmic time via spectrofluorimetry and gel electrophoresis experiments. We also demonstrate the division of these polymers via the addition of a single DNA complex that competes with the insertion mechanism. This shows the growth of a population of polymers in logarithmic time. We characterize the DNA insertion mechanism that we utilize in Chapter 4. We experimentally demonstrate that we can control the kinetics of this re- action over at least seven orders of magnitude, by programming the sequences of DNA that initiate the reaction.

In addition, we review co-authored work on programming molecular robots using prescriptive landscapes of DNA origami; this was the first microscopic demonstration of programming a molec- ular robot to walk on a 2-dimensional surface. We developed a snapshot method for imaging these random walking molecular robots and a CAPTCHA-like analysis method for difficult-to-interpret imaging data.

Transceiver designs and analysis for LTI, LTV and broadcast channels - new matrix decompositions and majorization theory

Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.

In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.

The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.

In the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.

The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.

Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.

λ-designs and related combinatorial configurations

This thesis deals with two problems. The first is the determination of λ-designs, combinatorial configurations which are essentially symmetric block designs with the condition that each subset be of the same cardinality negated. We construct an infinite family of such designs from symmetric block designs and obtain some basic results about their structure. These results enable us to solve the problem for λ = 3 and λ = 4. The second problem deals with configurations related to both λ -designs and (ѵ, k, λ)-configurations. We have (n-1) k-subsets of {1, 2, ..., n}, S₁, ..., S_n-1 such that S_i ∩ S_j is a λ-set for i ≠ j. We obtain specifically the replication numbers of such a design in terms of n, k, and λ with one exceptional class which we determine explicitly. In certain special cases we settle the problem entirely.

Comparative map between the domestic pig and dog

Cross-species chromosome painting with probes derived from flow-sorted dog and human chromosomes was used to construct a high-resolution comparative map for the pig. In total 98 conserved autosomal segments between pig and dog were detected by probes specific for the 38 autosomes and X Chromosome of the dog. Further integration of our results with the published human-dog and cat-dog comparative maps, and with data from comparative gene mapping, increases the resolution of the current pig-human comparative map. It allows for the conserved syntenies detected in the pig, human, and cat to be aligned against the putative ancestral karyotype of eutherian mammals and for the history of karyotype evolution of the pig lineage to be reconstructed. Fifteen fusions, 17 fissions, and 23 inversions are required to convert the ancestral mammalian karyotype into the extant karyotype of the pig.

Content Based Integration of Construction Site Images in Architecture, Engineering, Construction, and Facilities Management (AEC/FM) Model based Systems

This book explores the processes for retrieval, classification, and integration of construction images in AEC/FM model based systems. The author describes a combination of techniques from the areas of image and video processing, computer vision, information retrieval, statistics and content-based image and video retrieval that have been integrated into a novel method for the retrieval of related construction site image data from components of a project model. This method has been tested on available construction site images from a variety of sources like past and current building construction and transportation projects and is able to automatically classify, store, integrate and retrieve image data files in inter-organizational systems so as to allow their usage in project management related tasks. objects. Therefore, automated methods for the integration of construction images are important for construction information management. During this research, processes for retrieval, classification, and integration of construction images in AEC/FM model based systems have been explored. Specifically, a combination of techniques from the areas of image and video processing, computer vision, information retrieval, statistics and content-based image and video retrieval have been deployed in order to develop a methodology for the retrieval of related construction site image data from components of a project model. This method has been tested on available construction site images from a variety of sources like past and current building construction and transportation projects and is able to automatically classify, store, integrate and retrieve image data files in inter-organizational systems so as to allow their usage in project management related tasks.

ART-EMAP: A Neural Network Architecture for Learning and Prediction by Evidence Accumulation

This paper introduces ART-EMAP, a neural architecture that uses spatial and temporal evidence accumulation to extend the capabilities of fuzzy ARTMAP. ART-EMAP combines supervised and unsupervised learning and a medium-term memory process to accomplish stable pattern category recognition in a noisy input environment. The ART-EMAP system features (i) distributed pattern registration at a view category field; (ii) a decision criterion for mapping between view and object categories which can delay categorization of ambiguous objects and trigger an evidence accumulation process when faced with a low confidence prediction; (iii) a process that accumulates evidence at a medium-term memory (MTM) field; and (iv) an unsupervised learning algorithm to fine-tune performance after a limited initial period of supervised network training. ART-EMAP dynamics are illustrated with a benchmark simulation example. Applications include 3-D object recognition from a series of ambiguous 2-D views.

Psyche and the arts: Jungian approaches to music, architecture, literature, painting and film

Does art connect the individual psyche to history and culture? Psyche and the Arts challenges existing ideas about the relationship between Jung and art, and offers exciting new dimensions to key issues such as the role of image in popular culture, and the division of psyche and matter in art form. Divided into three sections - Getting into Art, Challenging the Critical Space and Interpreting Art in the World - the text shows how Jungian ideas can work with the arts to illuminate both psychological theory and aesthetic response. Psyche and the Arts offers new critical visions of literature, film, music, architecture and painting, as something alive in the experience of creators and audiences challenging previous Jungian criticism. This approach demonstrates Jung’s own belief that art is a healing response to collective cultural norms. This diverse yet focused collection from international contributors invites the reader to seek personal and cultural value in the arts, and will be essential reading for Jungian analysts, trainees and those more generally interested in the arts. [From the Publisher]

Within-Otolith Variability in Chemical Fingerprints: Implications for Sampling Designs and Possible Environmental Interpretation

Largely used as a natural biological tag in studies of dispersal/connectivity of fish, otolith elemental fingerprinting is usually analyzed by laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS). LA-ICP-MS produces an elemental fingerprint at a discrete time-point in the life of a fish and can generate data on within-otolith variability of that fingerprint. The presence of within-otolith variability has been previously acknowledged but not incorporated into experimental designs on the presumed, but untested, grounds of both its negligibility compared to among-otolith variability and of spatial autocorrelation among multiple ablations within an otolith. Here, using a hierarchical sampling design of spatial variation at multiple scales in otolith chemical fingerprints for two Mediterranean coastal fishes, we explore: 1) whether multiple ablations within an otolith can be used as independent replicates for significance tests among otoliths, and 2) the implications of incorporating within-otolith variability when assessing spatial variability in otolith chemistry at a hierarchy of spatial scales (different fish, from different sites, at different locations on the Apulian Adriatic coast). We find that multiple ablations along the same daily rings do not necessarily exhibit spatial dependency within the otolith and can be used to estimate residual variability in a hierarchical sampling design. Inclusion of within-otolith measurements reveals that individuals at the same site can show significant variability in elemental uptake. Within-otolith variability examined across the spatial hierarchy identifies differences between the two fish species investigated, and this finding leads to discussion of the potential for within-otolith variability to be used as a marker for fish exposure to stressful conditions. We also demonstrate that a 'cost'-optimal allocation of sampling effort should typically include some level of within-otolith replication in the experimental design. Our findings provide novel evidence to aid the design of future sampling programs and improve our general understanding of the mechanisms regulating elemental fingerprints.