135,368 research outputs found
Counting Membrane Systems
A decision problem is one that has a yes/no answer, while
a counting problem asks how many possible solutions exist associated
with each instance. Every decision problem X has associated a counting
problem, denoted by #X, in a natural way by replacing the question
âis there a solution?â with âhow many solutions are there?â. Counting
problems are very attractive from a computational complexity point of
view: if X is an NP-complete problem then the counting version #X is
NP-hard, but the counting version of some problems in class P can also
be NP-hard.
In this paper, a new class of membrane systems is presented in order
to provide a natural framework to solve counting problems. The class is
inspired by a special kind of non-deterministic Turing machines, called
counting Turing machines, introduced by L. Valiant. A polynomial-time
and uniform solution to the counting version of the SAT problem (a
well-known #P-complete problem) is also provided, by using a family
of counting polarizationless P systems with active membranes, without
dissolution rules and division rules for non-elementary membranes but
where only very restrictive cooperation (minimal cooperation and minimal
production) in object evolution rules is allowed
Ultra-Broadband Coherence-Domain Imaging Using Parametric Downconversion and Superconducting Single-Photon Detectors at 1064 nm
Coherence-domain imaging systems can be operated in a single-photon counting
mode, offering low detector noise; this in turn leads to increased sensitivity
for weak light sources and weakly reflecting samples. We have demonstrated that
excellent axial resolution can be obtained in a photon-counting coherence
domain imaging (CDI) system that uses light generated via spontaneous
parametric down-conversion (SPDC) in a chirped periodically poled
stoichiometric lithium tantalate (chirped-PPSLT) structure, in conjunction with
a niobium nitride superconducting single-photon detector (SSPD). The bandwidth
of the light generated via SPDC, as well as the bandwidth over which the SSPD
is sensitive, can extend over a wavelength region that stretches from 700 to
1500 nm. This ultra-broad wavelength band offers a near-ideal combination of
deep penetration and ultra-high axial resolution for the imaging of biological
tissue. The generation of SPDC light of adjustable bandwidth in the vicinity of
1064 nm, via the use of chirped-PPSLT structures, had not been previously
achieved. To demonstrate the usefulness of this technique, we have constructed
images for a hierarchy of samples of increasing complexity: a mirror, a
nitrocellulose membrane, and a biological sample comprising onion-skin cells
A static analysis for Brane Calculi providing global occurrence counting information
In this paper we propose a static analysis for Brane Calculi [1], based on Abstract Interpretation [2] techniques. Our analysis statically approximates the dynamic behaviour of Brane systems, by providing a description of the possible hierarchical structure of membranes and of the processes possibly associated to each membrane, together with global occurrence counting information. Our analysis can be computed in polynomial time. We apply it to investigate several biological systems in which occurrence counting information plays a crucial role. In particular, our case study concerns the formation of the haemoglobin polymer in presence of alterations and investigate the influence that such alterations have on the ability of the haemoglobin polymer to bind oxygen molecules
A Global Occurrence Counting Analysis for Brane Calculi
We propose a polynomial static analysis for Brane Calculi, based on Abstract Interpretation techniques. The analysis provides a description of the possible hierarchical structure of membranes and of the processes possibly associated to each membrane, together with global occurrence counting information. Our analysis
can be applied in the biological setting to investigate systems in which the information
on the number of membranes occurring in the system plays a crucial role
Simulating counting oracles with cooperation
We prove that monodirectional shallow chargeless P systems with active
membranes and minimal cooperation working in polynomial time precisely characterise
P#P
k , the complexity class of problems solved in polynomial time by deterministic
Turing machines with a polynomial number of parallel queries to an oracle for a counting
problem
Phonon counting thermometry of an ultracoherent membrane resonator near its motional ground state
Generation of non-Gaussian quantum states of macroscopic mechanical objects
is key to a number of challenges in quantum information science, ranging from
fundamental tests of decoherence to quantum communication and sensing. Heralded
generation of single-phonon states of mechanical motion is an attractive way
towards this goal, as it is, in principle, not limited by the object size. Here
we demonstrate a technique which allows for generation and detection of a
quantum state of motion by phonon counting measurements near the ground state
of a 1.5 MHz micromechanical oscillator. We detect scattered photons from a
membrane-in-the-middle optomechanical system using an ultra-narrowband optical
filter, and perform Raman-ratio thermometry and second-order intensity
interferometry near the motional ground state ( phonons).
With an effective mass in the nanogram range, our system lends itself for
studies of long-lived non-Gaussian motional states with some of the heaviest
objects to date.Comment: 11 pages, 10 figure
Generation of mechanical interference fringes by multi-photon counting
Exploring the quantum behaviour of macroscopic objects provides an intriguing
avenue to study the foundations of physics and to develop a suite of
quantum-enhanced technologies. One prominent path of study is provided by
quantum optomechanics which utilizes the tools of quantum optics to control the
motion of macroscopic mechanical resonators. Despite excellent recent progress,
the preparation of mechanical quantum superposition states remains outstanding
due to weak coupling and thermal decoherence. Here we present a novel
optomechanical scheme that significantly relaxes these requirements allowing
the preparation of quantum superposition states of motion of a mechanical
resonator by exploiting the nonlinearity of multi-photon quantum measurements.
Our method is capable of generating non-classical mechanical states without the
need for strong single photon coupling, is resilient against optical loss, and
offers more favourable scaling against initial mechanical thermal occupation
than existing schemes. Moreover, our approach allows the generation of larger
superposition states by projecting the optical field onto NOON states. We
experimentally demonstrate this multi-photon-counting technique on a mechanical
thermal state in the classical limit and observe interference fringes in the
mechanical position distribution that show phase superresolution. This opens a
feasible route to explore and exploit quantum phenomena at a macroscopic scale.Comment: 16 pages, 4 figures. v1: submitted for review on 28 Jan 2016. v2:
significantly revised manuscript. v3: some further revisions and some extra
results included. v3: new results added, extra author added, close to
published version, supplementary material available with published versio
Correlation functions quantify super-resolution images and estimate apparent clustering due to over-counting
We present an analytical method to quantify clustering in super-resolution
localization images of static surfaces in two dimensions. The method also
describes how over-counting of labeled molecules contributes to apparent
self-clustering and how the effective lateral resolution of an image can be
determined. This treatment applies to clustering of proteins and lipids in
membranes, where there is significant interest in using super-resolution
localization techniques to probe membrane heterogeneity. When images are
quantified using pair correlation functions, the magnitude of apparent
clustering due to over-counting will vary inversely with the surface density of
labeled molecules and does not depend on the number of times an average
molecule is counted. Over-counting does not yield apparent co-clustering in
double label experiments when pair cross-correlation functions are measured. We
apply our analytical method to quantify the distribution of the IgE receptor
(Fc{\epsilon}RI) on the plasma membranes of chemically fixed RBL-2H3 mast cells
from images acquired using stochastic optical reconstruction microscopy (STORM)
and scanning electron microscopy (SEM). We find that apparent clustering of
labeled IgE bound to Fc{\epsilon}RI detected with both methods arises from
over-counting of individual complexes. Thus our results indicate that these
receptors are randomly distributed within the resolution and sensitivity limits
of these experiments.Comment: 22 pages, 5 figure
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