Cellular Structures for Computation in the Quantum Regime

We present a new cellular data processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For conventional computing, the CA-like external clocking avoids the time-scale problems associated with ground-state relaxation schemes. For quantum computing, the architecture constitutes a novel paradigm whereby the algorithm is embedded in spatial, as opposed to temporal, structure. The architecture can be exploited to produce highly efficient algorithms: for example, a list of length N can be searched in time of order cube root N.Comment: 11 pages (LaTeX), 3 figure

Understanding visual map formation through vortex dynamics of spin Hamiltonian models

The pattern formation in orientation and ocular dominance columns is one of the most investigated problems in the brain. From a known cortical structure, we build spin-like Hamiltonian models with long-range interactions of the Mexican hat type. These Hamiltonian models allow a coherent interpretation of the diverse phenomena in the visual map formation with the help of relaxation dynamics of spin systems. In particular, we explain various phenomena of self-organization in orientation and ocular dominance map formation including the pinwheel annihilation and its dependency on the columnar wave vector and boundary conditions.Comment: 4 pages, 15 figure

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

A census of cell types and paracrine interactions in colorectal cancer

In colorectal cancer, oncogenic mutations transform a hierarchically organized and homeostatic epithelium into invasive cancer tissue. To define differences in cellular composition between the normal colon and colorectal cancer, and to map potential cellular interactions between tumor cells and their microenvironment, we profiled transcriptomes of >50,000 single cells from tumors and matched normal tissues of eight colorectal cancer patients. We find that tumor formation is accompanied by changes in epithelial, immune and stromal cell compartments in all patients. In the epithelium, we identify a continuum of five tumor-specific stem cell and progenitor-like populations, and persistent multilineage differentiation. We find multiple stromal and immune cell types to be consistently expanded in tumor compared to the normal colon, including cancer-associated fibroblasts, pericytes, monocytes, macrophages and a subset of T cells. We identify epithelial tumor cells and cancer-associated fibroblasts as relevant for assigning colorectal cancer consensus molecular subtypes. Our survey of growth factors in the tumor microenvironment identifies cell types responsible for increased paracrine EGFR, MET and TGF-β signaling in tumor tissue compared to the normal colon. We show that matched colorectal cancer organoids retain cell type heterogeneity, allowing to define a distinct differentiation trajectory encompassing stem and progenitor-like tumor cells. In summary, our single-cell analyses provide insights into cell types and signals shaping colorectal cancer cell plasticity

Generation of maximum spin entanglement induced by cavity field in quantum-dot systems

Equivalent-neighbor interactions of the conduction-band electron spins of quantum dots in the model of Imamoglu et al. [Phys. Rev. Lett. 83, 4204 (1999)] are analyzed. Analytical solution and its Schmidt decomposition are found and applied to evaluate how much the initially excited dots can be entangled to the remaining dots if all of them are initially disentangled. It is demonstrated that the perfect maximally entangled states (MES) can only be generated in the systems of up to 6 dots with a single dot initially excited. It is also shown that highly entangled states, approximating the MES with a good accuracy, can still be generated in systems of odd number of dots with almost half of them being excited. A sudden decrease of entanglement is observed by increasing the total number of dots in a system with a fixed number of excitations.Comment: 6 pages, 7 figures, to appear in Phys. Rev.

Two-Bit Gates are Universal for Quantum Computation

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase breaking (i.e., quantum phase coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.Comment: 21 pages, REVTeX 3.0, two .ps figures available from author upon reques

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

A Simple Quantum Computer

We propose an implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail qubit representation as a simple form of error correction, our machine can tolerate some amount of decoherence and still give the correct result with high probability. The design which we employ also demonstrates a signature for quantum parallelism which unambiguously delineates the desired quantum behavior from the merely classical. The experimental demonstration of our proposal using quantum optical components calls for the development of several key technologies common to single photonics.Comment: 8 pages RevTeX + 6 figures in postscrip

Impact of FTO genotypes on BMI and weight in polycystic ovary syndrome : a systematic review and meta-analysis

Aims/hypothesis FTO gene single nucleotide polymorphisms (SNPs) have been shown to be associated with obesity-related traits and type 2 diabetes. Several small studies have suggested a greater than expected effect of the FTO rs9939609 SNP on weight in polycystic ovary syndrome (PCOS). We therefore aimed to examine the impact of FTO genotype on BMI and weight in PCOS. Methods A systematic search of medical databases (PubMed, EMBASE and Cochrane CENTRAL) was conducted up to the end of April 2011. Seven studies describing eight distinct PCOS cohorts were retrieved; seven were genotyped for SNP rs9939609 and one for SNP rs1421085. The per allele effect on BMI and body weight increase was calculated and subjected to meta-analysis. Results A total of 2,548 women with PCOS were included in the study; 762 were TT homozygotes, 1,253 had an AT/CT genotype, and 533 were AA/CC homozygotes. Each additional copy of the effect allele (A/C) increased the BMI by a mean of 0.19 z score units (95% CI 0.13, 0.24; p = 2.26 × 10−11) and body weight by a mean of 0.20 z score units (95% CI 0.14, 0.26; p = 1.02 × 10−10). This translated into an approximately 3.3 kg/m2 increase in BMI and an approximately 9.6 kg gain in body weight between TT and AA/CC homozygotes. The association between FTO genotypes and BMI was stronger in the cohorts with PCOS than in the general female populations from large genome-wide association studies. Deviation from an additive genetic model was observed in heavier populations. Conclusions/interpretation The effect of FTO SNPs on obesity-related traits in PCOS seems to be more than two times greater than the effect found in large population-based studies. This suggests an interaction between FTO and the metabolic context or polygenic background of PCOS