5,603 research outputs found
The Energy of n Identical Bosons in a Finite Volume at O(L^{-7})
The volume dependence of the ground-state energy of n identical bosons with
short-range interactions in a periodic spatial volume with sides of length L is
calculated at order L^{-7} in the large volume expansion. This result will
enable a refined determination of the pi^+ pi^+ pi^+ interaction from lattice
QCD calculations.Comment: 3 page
Sizing Up Allometric Scaling Theory
Metabolic rate, heart rate, lifespan, and many other physiological properties vary with body mass in systematic and interrelated ways. Present empirical data suggest that these scaling relationships take the form of power laws with exponents that are simple multiples of one quarter. A compelling explanation of this observation was put forward a decade ago by West, Brown, and Enquist (WBE). Their framework elucidates the link between metabolic rate and body mass by focusing on the dynamics and structure of resource distribution networks—the cardiovascular system in the case of mammals. Within this framework the WBE model is based on eight assumptions from which it derives the well-known observed scaling exponent of 3/4. In this paper we clarify that this result only holds in the limit of infinite network size (body mass) and that the actual exponent predicted by the model depends on the sizes of the organisms being studied. Failure to clarify and to explore the nature of this approximation has led to debates about the WBE model that were at cross purposes. We compute analytical expressions for the finite-size corrections to the 3/4 exponent, resulting in a spectrum of scaling exponents as a function of absolute network size. When accounting for these corrections over a size range spanning the eight orders of magnitude observed in mammals, the WBE model predicts a scaling exponent of 0.81, seemingly at odds with data. We then proceed to study the sensitivity of the scaling exponent with respect to variations in several assumptions that underlie the WBE model, always in the context of finite-size corrections. Here too, the trends we derive from the model seem at odds with trends detectable in empirical data. Our work illustrates the utility of the WBE framework in reasoning about allometric scaling, while at the same time suggesting that the current canonical model may need amendments to bring its predictions fully in line with available datasets.EJD acknowledges financial support from a National Institutes of Health/National Research Service Award (1F32 GM080123-01)
Prevalence and patterns of higher-order drug interactions in Escherichia coli.
Interactions and emergent processes are essential for research on complex systems involving many components. Most studies focus solely on pairwise interactions and ignore higher-order interactions among three or more components. To gain deeper insights into higher-order interactions and complex environments, we study antibiotic combinations applied to pathogenic Escherichia coli and obtain unprecedented amounts of detailed data (251 two-drug combinations, 1512 three-drug combinations, 5670 four-drug combinations, and 13608 five-drug combinations). Directly opposite to previous assumptions and reports, we find higher-order interactions increase in frequency with the number of drugs in the bacteria's environment. Specifically, as more drugs are added, we observe an elevated frequency of net synergy (effect greater than expected based on independent individual effects) and also increased instances of emergent antagonism (effect less than expected based on lower-order interaction effects). These findings have implications for the potential efficacy of drug combinations and are crucial for better navigating problems associated with the combinatorial complexity of multi-component systems
Identifying single electron charge sensor events using wavelet edge detection
The operation of solid-state qubits often relies on single-shot readout using
a nanoelectronic charge sensor, and the detection of events in a noisy sensor
signal is crucial for high fidelity readout of such qubits. The most common
detection scheme, comparing the signal to a threshold value, is accurate at low
noise levels but is not robust to low-frequency noise and signal drift. We
describe an alternative method for identifying charge sensor events using
wavelet edge detection. The technique is convenient to use and we show that,
with realistic signals and a single tunable parameter, wavelet detection can
outperform thresholding and is significantly more tolerant to 1/f and
low-frequency noise.Comment: 11 pages, 4 figure
Nucleon-Nucleon Scattering from Effective Field Theory
We perform a nonperturbative calculation of the 1S0 NN scattering amplitude
using an effective field theory (EFT) expansion. The expansion we advocate is a
modification of what has been used previously; it is no a chiral expansion in
powers of the pion mass. We use dimensional regularization throughout and the
MS-bar subtraction scheme; our final result depends only on physical
observables. We show that the EFT expansion of the quantity |p|cot delta(p)
converges at momenta much greater than the scale that characterizes the
derivative expansion of the EFT Lagrangian. Our conclusions are optimistic
about the applicability of an EFT approach to the quantitative study of nuclear
matter.Comment: Revised discussion of power counting in the EFT expansion. Tex file
uses harvmac, epsf macros, 35 pages with 9 postscript figure
Low-speed impact craters in loose granular media
We report on craters formed by balls dropped into dry, non-cohesive, granular
media. By explicit variation of ball density , diameter , and
drop height , the crater diameter is confirmed to scale as the 1/4 power of
the energy of the ball at impact:
. Against expectation, a different
scaling law is discovered for the crater depth:
. The scaling with properties of
the medium is also established. The crater depth has significance for granular
mechanics in that it relates to the stopping force on the ball.Comment: experiment; 4 pages, 3 figure
Branching principles of animal and plant networks identified by combining extensive data, machine learning, and modeling
Branching in vascular networks and in overall organismic form is one of the
most common and ancient features of multicellular plants, fungi, and animals.
By combining machine-learning techniques with new theory that relates vascular
form to metabolic function, we enable novel classification of diverse branching
networks--mouse lung, human head and torso, angiosperm and gymnosperm plants.
We find that ratios of limb radii--which dictate essential biologic functions
related to resource transport and supply--are best at distinguishing branching
networks. We also show how variation in vascular and branching geometry
persists despite observing a convergent relationship across organisms for how
metabolic rate depends on body mass.Comment: 55 pages, 8 figures, 8 table
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