Response of multiple simultaneously recorded macaque area LIP neurons in a memory saccade task

Cells in the lateral intraparietal cortex (LIP) of rhesus macaques respond vigorously and in spatially-tuned fashion to briefly memorized visual stimuli. Responses to stimulus presentation, memory maintenance, and task completion are seen, in varying combination from neuron to neuron. To help elucidate this functional segmentation a new system for simultaneous recording from multiple neighboring neurons was developed. The two parts of this dissertation discuss the technical achievements and scientific discoveries, respectively.

Technology. Simultanous recordings from multiple neighboring neurons were made with four-wire bundle electrodes, or tetrodes, which were adapted to the awake behaving primate preparation. Signals from these electrodes were partitionable into a background process with a 1/f-like spectrum and foreground spiking activity spanning 300-6000 Hz. Continuous voltage recordings were sorted into spike trains using a state-of-the-art clustering algorithm, producing a mean of 3 cells per site. The algorithm classified 96% of spikes correctly when tetrode recordings were confirmed with simultaneous intracellular signals. Recording locations were verified with a new technique that creates electrolytic lesions visible in magnetic resonance imaging, eliminating the need for histological processing. In anticipation of future multi-tetrode work, the chronic chamber microdrive, a device for long-term tetrode delivery, was developed.

Science. Simultaneously recorded neighboring LIP neurons were found to have similar preferred targets in the memory saccade paradigm, but dissimilar peristimulus time histograms, PSTH). A majority of neighboring cell pairs had a difference in preferred directions of under 45° while the trial time of maximal response showed a broader distribution, suggesting homogeneity of tuning with het erogeneity of function. A continuum of response characteristics was present, rather than a set of specific response types; however, a mapping experiment suggests this may be because a given cell's PSTH changes shape as well as amplitude through the response field. Spike train autocovariance was tuned over target and changed through trial epoch, suggesting different mechanisms during memory versus background periods. Mean frequency-domain spike-to-spike coherence was concentrated below 50 Hz with a significant maximum of 0.08; mean time-domain coherence had a narrow peak in the range ±10 ms with a significant maximum of 0.03. Time-domain coherence was found to be untuned for short lags (10 ms), but significantly tuned at larger lags (50 ms).

The Role of Fucose in Learning and Memory: The Identification of a Fucosylprotein, Synapsin I, in the Rat Brain and the Characterization of its Fucosylation

Previous studies have shown that the glycoproteins containing the fucose moiety are involved in neuronal communication phenomena such as long-term potentiation and memory formation. These results imply that fucose containing glycoproteins might play an important role in learning and memory. To understand the role of fucose in neuronal communication, and the mechanisms by which fucose may be involved in information storage, the identification of fucosylproteins is essential. This report describes the identification and characterization of fucosylproteins in the brain, which will provide new insights into the role of the fucose involved molecular interactions.

Lattice quantum codes and exotic topological phases of matter

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.

Rewriting Schemes for Flash Memory

Flash memory is a leading storage media with excellent features such as random access and high storage density. However, it also faces significant reliability and endurance challenges. In flash memory, the charge level in the cells can be easily increased, but removing charge requires an expensive erasure operation. In this thesis we study rewriting schemes that enable the data stored in a set of cells to be rewritten by only increasing the charge level in the cells. We consider two types of modulation scheme; a convectional modulation based on the absolute levels of the cells, and a recently-proposed scheme based on the relative cell levels, called rank modulation. The contributions of this thesis to the study of rewriting schemes for rank modulation include the following: we

•propose a new method of rewriting in rank modulation, beyond the previously proposed method of “push-to-the-top”;

•study the limits of rewriting with the newly proposed method, and derive a tight upper bound of 1 bit per cell;

•extend the rank-modulation scheme to support rankings with repetitions, in order to improve the storage density;

•derive a tight upper bound of 2 bits per cell for rewriting in rank modulation with repetitions;

•construct an efficient rewriting scheme that asymptotically approaches the upper bound of 2 bit per cell.

The next part of this thesis studies rewriting schemes for a conventional absolute-levels modulation. The considered model is called “write-once memory” (WOM). We focus on WOM schemes that achieve the capacity of the model. In recent years several capacity-achieving WOM schemes were proposed, based on polar codes and randomness extractors. The contributions of this thesis to the study of WOM scheme include the following: we

•propose a new capacity-achievingWOM scheme based on sparse-graph codes, and show its attractive properties for practical implementation;

•improve the design of polarWOMschemes to remove the reliance on shared randomness and include an error-correction capability.

The last part of the thesis studies the local rank-modulation (LRM) scheme, in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. The LRM scheme is used to simulate a single conventional multi-level flash cell. The simulated cell is realized by a Gray code traversing all the relative-value states where, physically, the transition between two adjacent states in the Gray code is achieved by using a single “push-to-the-top” operation. The main results of the last part of the thesis are two constructions of Gray codes with asymptotically-optimal rate.