Accurate Telescope Mount Positioning with MEMS Accelerometers

This paper describes the advantages and challenges of applying microelectromechanical accelerometer systems (MEMS accelerometers) in order to attain precise, accurate and stateless positioning of telescope mounts. This provides a completely independent method from other forms of electronic, optical, mechanical or magnetic feedback or real-time astrometry. Our goal is to reach the sub-arcminute range which is well smaller than the field-of-view of conventional imaging telescope systems. Here we present how this sub-arcminute accuracy can be achieved with very cheap MEMS sensors and we also detail how our procedures can be extended in order to attain even finer measurements. In addition, our paper discusses how can a complete system design be implemented in order to be a part of a telescope control system.Comment: Accepted for publication in PASP, 12 page

Order 3 Symmetry in the Clifford Hierarchy

We investigate the action of the first three levels of the Clifford hierarchy on sets of mutually unbiased bases comprising the Ivanovic MUB and the Alltop MUBs. Vectors in the Alltop MUBs exhibit additional symmetries when the dimension is a prime number equal to 1 modulo 3 and thus the set of all Alltop vectors splits into three Clifford orbits. These vectors form configurations with so-called Zauner subspaces, eigenspaces of order 3 elements of the Clifford group highly relevant to the SIC problem. We identify Alltop vectors as the magic states that appear in the context of fault-tolerant universal quantum computing, wherein the appearance of distinct Clifford orbits implies a surprising inequivalence between some magic states.Comment: 20 pages, 2 figures. Published versio

Proof Complexity of Systems of (Non-Deterministic) Decision Trees and Branching Programs

This paper studies propositional proof systems in which lines are sequents of decision trees or branching programs, deterministic or non-deterministic. Decision trees (DTs) are represented by a natural term syntax, inducing the system LDT, and non-determinism is modelled by including disjunction, ?, as primitive (system LNDT). Branching programs generalise DTs to dag-like structures and are duly handled by extension variables in our setting, as is common in proof complexity (systems eLDT and eLNDT). Deterministic and non-deterministic branching programs are natural nonuniform analogues of log-space (L) and nondeterministic log-space (NL), respectively. Thus eLDT and eLNDT serve as natural systems of reasoning corresponding to L and NL, respectively. The main results of the paper are simulation and non-simulation results for tree-like and dag-like proofs in LDT, LNDT, eLDT and eLNDT. We also compare them with Frege systems, constant-depth Frege systems and extended Frege systems

An evolutionary and functional assessment of regulatory network motifs.

BackgroundCellular functions are regulated by complex webs of interactions that might be schematically represented as networks. Two major examples are transcriptional regulatory networks, describing the interactions among transcription factors and their targets, and protein-protein interaction networks. Some patterns, dubbed motifs, have been found to be statistically over-represented when biological networks are compared to randomized versions thereof. Their function in vitro has been analyzed both experimentally and theoretically, but their functional role in vivo, that is, within the full network, and the resulting evolutionary pressures remain largely to be examined.ResultsWe investigated an integrated network of the yeast Saccharomyces cerevisiae comprising transcriptional and protein-protein interaction data. A comparative analysis was performed with respect to Candida glabrata, Kluyveromyces lactis, Debaryomyces hansenii and Yarrowia lipolytica, which belong to the same class of hemiascomycetes as S. cerevisiae but span a broad evolutionary range. Phylogenetic profiles of genes within different forms of the motifs show that they are not subject to any particular evolutionary pressure to preserve the corresponding interaction patterns. The functional role in vivo of the motifs was examined for those instances where enough biological information is available. In each case, the regulatory processes for the biological function under consideration were found to hinge on post-transcriptional regulatory mechanisms, rather than on the transcriptional regulation by network motifs.ConclusionThe overabundance of the network motifs does not have any immediate functional or evolutionary counterpart. A likely reason is that motifs within the networks are not isolated, that is, they strongly aggregate and have important edge and/or node sharing with the rest of the network

Using rewriting to synthesize functional languages to digital circuits

A straightforward synthesis from functional languages to digital circuits transforms variables to wires. The types of these variables determine the bit-width of the wires. Assigning a bit-width to polymorphic and function-type variables within this direct synthesis scheme is impossible. Using a term rewrite system, polymorphic and function-type binders can be completely eliminated from a circuit description, given only minor and reasonable restrictions on the input. The presented term rewrite system is used in the compiler for CλaSH: a polymorphic, higher-order, functional hardware description language

Synchronization and Redundancy: Implications for Robustness of Neural Learning and Decision Making

Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by non-ideal biological building blocks which can impose significant error. We explore quantitatively how the brain might cope with this inherent source of error by taking advantage of two ubiquitous mechanisms, redundancy and synchronization. In particular we consider a neural process whose goal is to learn a decision function by implementing a nonlinear gradient dynamics. The dynamics, however, are assumed to be corrupted by perturbations modeling the error which might be incurred due to limitations of the biology, intrinsic neuronal noise, and imperfect measurements. We show that error, and the associated uncertainty surrounding a learned solution, can be controlled in large part by trading off synchronization strength among multiple redundant neural systems against the noise amplitude. The impact of the coupling between such redundant systems is quantified by the spectrum of the network Laplacian, and we discuss the role of network topology in synchronization and in reducing the effect of noise. A range of situations in which the mechanisms we model arise in brain science are discussed, and we draw attention to experimental evidence suggesting that cortical circuits capable of implementing the computations of interest here can be found on several scales. Finally, simulations comparing theoretical bounds to the relevant empirical quantities show that the theoretical estimates we derive can be tight.Comment: Preprint, accepted for publication in Neural Computatio

More on complexity of operators in quantum field theory

Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten $p$-norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as $k$-local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU($n$) groups.Comment: Modified the Sec. 4.1, where we offered a powerful proof: if (1) the ket vector and bra vector in quantum mechanics contain same physics, or (2) adding divergent terms to a Lagrangian will not change underlying physics, then complexity in quantum mechanics must be bi-invariant