2,120 research outputs found
Resetting uncontrolled quantum systems
We consider a scenario where we wish to bring a closed system of known
Hilbert space dimension (the target), subject to an unknown Hamiltonian
evolution, back to its quantum state at a past time . The target is out of
our control: this means that we ignore both its free Hamiltonian and how the
system interacts with other quantum systems we may use to influence it. Under
these conditions, we prove that there exist protocols within the framework of
non-relativistic quantum physics which reset the target system to its exact
quantum state at . Each "resetting protocol" is successful with non-zero
probability for all possible free Hamiltonians and interaction unitaries, save
a subset of zero measure. When the target is a qubit and the interaction is
sampled from the Haar measure, the simplest resetting circuits have a
significant average probability of success and their implementation is within
reach of current quantum technologies. Finally, we find that, in case the
resetting protocol fails, it is possible to run a further protocol that, if
successful, undoes both the natural evolution of the target and the effects of
the failed protocol over the latter. By chaining in this fashion several such
protocols, one can substantially increase the overall probability of a
successful resetting.Comment: Published version. This work was not funded by the European Research
Counci
EVOLUTION OF THE CIRCADIAN CLOCK IN EXTREME ENVIRONMENT: LESSONS FROM CAVEFISH.
Evolution has been strongly influenced by the daily cycles of temperature and light imposed by the rotation of the Earth. Fascinating demonstrations of this are seen in extreme environments such as caves where some animals have remained completely isolated from the day-night cycle for millions of years. Most of these species show convergent evolution, sharing a range of striking physical properties such as eye loss. One fundamental issue is whether “hypogean” species retain a functional circadian clock. This highly conserved, physiological timing mechanism allows organisms to anticipate daily environmental changes and is synchronized primarily by light. The Somalian cavefish, Phreatichthys andruzzii does possess a circadian clock that is entrained by a daily regular feeding time but strikingly, not by light. Under constant conditions the P. andruzzii clock oscillates with an extremely long period and also lacks normal temperature compensation. We document multiple mutations affecting a light-induced clock gene, Period2 as well as the genes encoding the extra-retinal photoreceptors Melanopsin (Opn4m2) and TMT-opsin. Remarkably, we show that ectopic expression of zebrafish homologs of these opsins rescues light induced clock gene expression in P. andruzzii cells. Thus, by studying this natural mutant we provide direct evidence for a peripheral light-sensing function of extra-retinal opsins in vertebrates. Furthermore, the properties of this cavefish illustrate that evolution in constant darkness leads not only to anatomical changes but also to loss of gene function linked with the detection and anticipation of the day-night cycle
Robustness from flexibility in the fungal circadian clock
Background
Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa.
Results
The circuit modelled in this work consists of a central negative feedback loop, in which the frequency (frq) gene inhibits its transcriptional activator white collar-1 (wc-1), interlocked with a positive feedback loop in which FRQ protein upregulates WC-1 production. Importantly, our model reproduces the observed entrainment of this circuit under light/dark cycles with varying photoperiod and cycle duration. Our simulations show that whilst the level of frq mRNA is driven directly by the light input, the falling phase of FRQ protein, a molecular correlate of conidiation, maintains a constant phase that is uncoupled from the times of dawn and dusk. The model predicts the behaviour of mutants that uncouple WC-1 production from FRQ's positive feedback, and shows that the positive loop enhances the buffering of conidiation phase against seasonal photoperiod changes. This property is quantified using Kitano's measure for the overall robustness of a regulated system output. Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure.
Conclusions
Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator. More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators
Preserving Stabilization while Practically Bounding State Space
Stabilization is a key dependability property for dealing with unanticipated
transient faults, as it guarantees that even in the presence of such faults,
the system will recover to states where it satisfies its specification. One of
the desirable attributes of stabilization is the use of bounded space for each
variable. In this paper, we present an algorithm that transforms a stabilizing
program that uses variables with unbounded domain into a stabilizing program
that uses bounded variables and (practically bounded) physical time. While
non-stabilizing programs (that do not handle transient faults) can deal with
unbounded variables by assigning large enough but bounded space, stabilizing
programs that need to deal with arbitrary transient faults cannot do the same
since a transient fault may corrupt the variable to its maximum value. We show
that our transformation algorithm is applicable to several problems including
logical clocks, vector clocks, mutual exclusion, leader election, diffusing
computations, Paxos based consensus, and so on. Moreover, our approach can also
be used to bound counters used in an earlier work by Katz and Perry for adding
stabilization to a non-stabilizing program. By combining our algorithm with
that earlier work by Katz and Perry, it would be possible to provide
stabilization for a rich class of problems, by assigning large enough but
bounded space for variables.Comment: Moved some content from the Appendix to the main paper, added some
details to the transformation algorithm and to its descriptio
Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation
Sensor networks potentially feature large numbers of nodes that can sense
their environment over time, communicate with each other over a wireless
network, and process information. They differ from data networks in that the
network as a whole may be designed for a specific application. We study the
theoretical foundations of such large scale sensor networks, addressing four
fundamental issues- connectivity, capacity, clocks and function computation.
To begin with, a sensor network must be connected so that information can
indeed be exchanged between nodes. The connectivity graph of an ad-hoc network
is modeled as a random graph and the critical range for asymptotic connectivity
is determined, as well as the critical number of neighbors that a node needs to
connect to. Next, given connectivity, we address the issue of how much data can
be transported over the sensor network. We present fundamental bounds on
capacity under several models, as well as architectural implications for how
wireless communication should be organized.
Temporal information is important both for the applications of sensor
networks as well as their operation.We present fundamental bounds on the
synchronizability of clocks in networks, and also present and analyze
algorithms for clock synchronization. Finally we turn to the issue of gathering
relevant information, that sensor networks are designed to do. One needs to
study optimal strategies for in-network aggregation of data, in order to
reliably compute a composite function of sensor measurements, as well as the
complexity of doing so. We address the issue of how such computation can be
performed efficiently in a sensor network and the algorithms for doing so, for
some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE
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