57,930 research outputs found
Circuits with Medium Fan-In
We consider boolean circuits in which every gate may compute an arbitrary boolean function of k other gates, for a parameter k. We give an explicit function $f:{0,1}^n -> {0,1} that requires at least Omega(log^2(n)) non-input gates when k = 2n/3. When the circuit is restricted to being layered and depth 2, we prove a lower bound of n^(Omega(1)) on the number of non-input gates. When the circuit is a formula with gates of fan-in k, we give a lower bound Omega(n^2/k*log(n)) on the total number of gates.
Our model is connected to some well known approaches to proving lower bounds in complexity theory. Optimal lower bounds for the Number-On-Forehead model in communication complexity, or for bounded depth circuits in AC_0, or extractors for varieties over small fields would imply strong lower bounds in our model. On the other hand, new lower bounds for our model would prove new time-space tradeoffs for branching programs and impossibility results for (fan-in 2) circuits with linear size and logarithmic depth. In particular, our lower bound gives a different proof for a known time-space tradeoff for oblivious branching programs
Comparator Design in Sensors for Environmental Monitoring
This paper presents circuit design considerations of comparator in analog-to-digital converters (ADC) applied for a portable, low-cost and high performance nano-sensor chip which can be applied to detect the airborne magnetite pollution nano particulate matter (PM) for environmental monitoring. High-resolution ADC plays a vital important role in high perfor-mance nano-sensor, while high-resolution comparator is a key component in ADC. In this work, some important design issues related to comparators in analog-to-digital converters (ADCs) are discussed, simulation results show that the resolution of the comparator proposed can achieve 5µV , and it is appropriate for high-resolution application
Strongly interacting photons in one-dimensional continuum
Photon-photon scattering in vacuum is extremely weak. However, strong
effective interactions between single photons can be realized by employing
strong light-matter coupling. These interactions are a fundamental building
block for quantum optics, bringing many-body physics to the photonic world and
providing important resources for quantum photonic devices and for optical
metrology. In this Colloquium, we review the physics of strongly-interacting
photons in one-dimensional systems with no optical confinement along the
propagation direction. We focus on two recently-demonstrated experimental
realizations: superconducting qubits coupled to open transmission lines, and
interacting Rydberg atoms in a cold gas. Advancements in the theoretical
understanding of these systems are presented in complementary formalisms and
compared to experimental results. The experimental achievements are summarized
alongside a description of the quantum optical effects and quantum devices
emerging from them.Comment: Updated version, accepted for publication in Reviews of Modern
Physic
Fan-out in Gene Regulatory Networks
In synthetic biology, gene regulatory circuits are often constructed by
combining smaller circuit components. Connections between components are
achieved by transcription factors acting on promoters. If the individual
components behave as true modules and certain module interface conditions are
satisfied, the function of the composite circuits can in principle be
predicted. In this paper, we investigate one of the interface conditions:
fan-out. We quantify the fan-out, a concept widely used in electric
engineering, to indicate the maximum number of the downstream inputs that an
upstream output transcription factor can regulate. We show that the fan-out is
closely related to retroactivity studied by Del Vecchio, et al. We propose an
efficient operational method for measuring the fan-out that can be applied to
various types of module interfaces. We also show that the fan-out can be
enhanced by self-inhibitory regulation on the output. We discuss the potential
role of the inhibitory regulations found in gene regulatory networks and
protein signal pathways. The proposed estimation method for fanout not only
provides an experimentally efficient way for quantifying the level of
modularity in gene regulatory circuits but also helps characterize and design
module interfaces, enabling the modular construction of gene circuits.Comment: 28 pages, 5 figure
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