6,283 research outputs found
Lattice path matroids: enumerative aspects and Tutte polynomials
Fix two lattice paths P and Q from (0,0) to (m,r) that use East and North
steps with P never going above Q. We show that the lattice paths that go from
(0,0) to (m,r) and that remain in the region bounded by P and Q can be
identified with the bases of a particular type of transversal matroid, which we
call a lattice path matroid. We consider a variety of enumerative aspects of
these matroids and we study three important matroid invariants, namely the
Tutte polynomial and, for special types of lattice path matroids, the
characteristic polynomial and the beta invariant. In particular, we show that
the Tutte polynomial is the generating function for two basic lattice path
statistics and we show that certain sequences of lattice path matroids give
rise to sequences of Tutte polynomials for which there are relatively simple
generating functions. We show that Tutte polynomials of lattice path matroids
can be computed in polynomial time. Also, we obtain a new result about lattice
paths from an analysis of the beta invariant of certain lattice path matroids.Comment: 28 pages, 11 figure
Catalyzed relaxation of a metastable DNA fuel
Practically all of life's molecular processes, from chemical synthesis to replication, involve enzymes that carry out their functions through
the catalytic transformation of metastable fuels into waste products.
Catalytic control of reaction rates will prove to be as useful and
ubiquitous in nucleic-acid-based engineering as it is in biology. Here
we report a metastable DNA "fuel" and a corresponding DNA
"catalyst" that improve upon the original hybridization-based
catalyst system (Turberfield et al. Phys. Rev. Lett. 90,
118102-1118102-4) by more than 2 orders of magnitude. This is achieved
by identifying and purifying a fuel with a kinetically trapped
metastable configuration consisting of a "kissing loop" stabilized
by flanking helical domains; the catalyst strand acts by opening a
helical domain and allowing the complex to relax to its ground state by
a multistep pathway. The improved fuel/catalyst system shows a roughly
5000-fold acceleration of the uncatalyzed reaction, with each catalyst
molecule capable of turning over in excess of 40 substrates. With
k_(cat)/K_M ≈ 10^7/M/min, comparable to many protein
enzymes and ribozymes, this fuel system becomes a viable component
enabling future DNA-based synthetic molecular machines and logic
circuits. As an example, we designed and characterized a signal
amplifier based on the fuel-catalyst system. The amplifier uses a
single strand of DNA as input and releases a second strand with
unrelated sequence as output. A single input strand can catalytically
trigger the release of more than 10 output strands
Can biological quantum networks solve NP-hard problems?
There is a widespread view that the human brain is so complex that it cannot
be efficiently simulated by universal Turing machines. During the last decades
the question has therefore been raised whether we need to consider quantum
effects to explain the imagined cognitive power of a conscious mind.
This paper presents a personal view of several fields of philosophy and
computational neurobiology in an attempt to suggest a realistic picture of how
the brain might work as a basis for perception, consciousness and cognition.
The purpose is to be able to identify and evaluate instances where quantum
effects might play a significant role in cognitive processes.
Not surprisingly, the conclusion is that quantum-enhanced cognition and
intelligence are very unlikely to be found in biological brains. Quantum
effects may certainly influence the functionality of various components and
signalling pathways at the molecular level in the brain network, like ion
ports, synapses, sensors, and enzymes. This might evidently influence the
functionality of some nodes and perhaps even the overall intelligence of the
brain network, but hardly give it any dramatically enhanced functionality. So,
the conclusion is that biological quantum networks can only approximately solve
small instances of NP-hard problems.
On the other hand, artificial intelligence and machine learning implemented
in complex dynamical systems based on genuine quantum networks can certainly be
expected to show enhanced performance and quantum advantage compared with
classical networks. Nevertheless, even quantum networks can only be expected to
efficiently solve NP-hard problems approximately. In the end it is a question
of precision - Nature is approximate.Comment: 38 page
Physical Realization of a Supervised Learning System Built with Organic Memristive Synapses
International audienceMultiple modern applications of electronics call for inexpensive chips that can perform complex operations on natural data with limited energy. A vision for accomplishing this is implementing hardware neural networks, which fuse computation and memory, with low cost organic electronics. A challenge, however, is the implementation of synapses (analog memories) composed of such materials. In this work, we introduce robust, fastly programmable, nonvolatile organic memristive nanodevices based on electrografted redox complexes that implement synapses thanks to a wide range of accessible intermediate conductivity states. We demonstrate experimentally an elementary neural network, capable of learning functions, which combines four pairs of organic memristors as synapses and conventional electronics as neurons. Our architecture is highly resilient to issues caused by imperfect devices. It tolerates inter-device variability and an adaptable learning rule offers immunity against asymmetries in device switching. Highly compliant with conventional fabrication processes, the system can be extended to larger computing systems capable of complex cognitive tasks, as demonstrated in complementary simulations
System data communication structures for active-control transport aircraft, volume 2
The application of communication structures to advanced transport aircraft are addressed. First, a set of avionic functional requirements is established, and a baseline set of avionics equipment is defined that will meet the requirements. Three alternative configurations for this equipment are then identified that represent the evolution toward more dispersed systems. Candidate communication structures are proposed for each system configuration, and these are compared using trade off analyses; these analyses emphasize reliability but also address complexity. Multiplex buses are recognized as the likely near term choice with mesh networks being desirable for advanced, highly dispersed systems
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