Bound on quantum computation time: Quantum error correction in a critical environment

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user. © 2010 The American Physical Society.

Broadband chaos generated by an optoelectronic oscillator.

We study an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive approximate mappings that do an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks.

Probabilistic Fréchet means for time varying persistence diagrams

© 2015, Institute of Mathematical Statistics. All rights reserved.In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp, Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards. We fix this problem by altering the original definition of Fréchet mean so that it now becomes a probability measure on the set of persistence diagrams; in a nutshell, the mean of a set of diagrams will be a weighted sum of atomic measures, where each atom is itself a persistence diagram determined using a perturbation of the input diagrams. This definition gives for each N a map (Dp)^N→ℙ(Dp). We show that this map is Hölder continuous on finite diagrams and thus can be used to build a useful statistic on vineyards.

Stability in autobiographical memories.

A total of 30 undergraduates recalled the same 20 autobiographical memories at two sessions separated by 2 weeks. At each session they dated their memories and rated them on 18 properties commonly studied in autobiographical memory experiments. Individuals showed moderate stability in their ratings on the 18 scales (r approximately .5), with consistency of dating being much higher (r = .96). There was more stability in the individuals' average rating on each scale (r approximately .8), even when the averages were calculated on different memories in the different sessions. The results are consistent with a constructive view of autobiographical memory, in which stable individual differences in cognitive style are important.

Frontal eye field neurons assess visual stability across saccades.

The image on the retina may move because the eyes move, or because something in the visual scene moves. The brain is not fooled by this ambiguity. Even as we make saccades, we are able to detect whether visual objects remain stable or move. Here we test whether this ability to assess visual stability across saccades is present at the single-neuron level in the frontal eye field (FEF), an area that receives both visual input and information about imminent saccades. Our hypothesis was that neurons in the FEF report whether a visual stimulus remains stable or moves as a saccade is made. Monkeys made saccades in the presence of a visual stimulus outside of the receptive field. In some trials, the stimulus remained stable, but in other trials, it moved during the saccade. In every trial, the stimulus occupied the center of the receptive field after the saccade, thus evoking a reafferent visual response. We found that many FEF neurons signaled, in the strength and timing of their reafferent response, whether the stimulus had remained stable or moved. Reafferent responses were tuned for the amount of stimulus translation, and, in accordance with human psychophysics, tuning was better (more prevalent, stronger, and quicker) for stimuli that moved perpendicular, rather than parallel, to the saccade. Tuning was sometimes present as well for nonspatial transaccadic changes (in color, size, or both). Our results indicate that FEF neurons evaluate visual stability during saccades and may be general purpose detectors of transaccadic visual change.

Temporal Stability of Molecular Diversity Measures in Natural Populations of Drosophila pseudoobscura and Drosophila persimilis

Many molecular ecological and evolutionary studies sample wild populations at a single point in time, failing to consider that data they collect represents genetic variation from a potentially unrepresentative snapshot in time. Variation across time in genetic parameters may occur quickly in species that produce multiple generations of offspring per year. However, many studies of rapid contemporary microevolution examine phenotypic trait divergence as opposed to molecular evolutionary divergence. Here, we compare genetic diversity in wild caught populations of Drosophila persimilis and D. pseudoobscura collected 16 years apart at the same time of year and same site at four X-linked and two mitochondrial loci to assess genetic stability. We found no major changes in nucleotide diversity in either species, but we observed a drastic shift in Tajima’s D between D. pseudoobscura timepoints at one locus associated with the increased abundance of a set of related haplotypes. Our data also suggests that D. persimilis may have recently accelerated its demographic expansion. While the changes we observed were modest, this study reinforces the importance of considering potential temporal variation in genetic parameters within single populations over short evolutionary timescales.