5,742 research outputs found
A composition theorem for the Fourier Entropy-Influence conjecture
The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai [FK96]
seeks to relate two fundamental measures of Boolean function complexity: it
states that holds for every Boolean function , where
denotes the spectral entropy of , is its total influence,
and is a universal constant. Despite significant interest in the
conjecture it has only been shown to hold for a few classes of Boolean
functions.
Our main result is a composition theorem for the FEI conjecture. We show that
if are functions over disjoint sets of variables satisfying the
conjecture, and if the Fourier transform of taken with respect to the
product distribution with biases satisfies the conjecture,
then their composition satisfies the conjecture. As
an application we show that the FEI conjecture holds for read-once formulas
over arbitrary gates of bounded arity, extending a recent result [OWZ11] which
proved it for read-once decision trees. Our techniques also yield an explicit
function with the largest known ratio of between and
, improving on the previous lower bound of 4.615
The Problematic Use of the Kill Zone Theory
The kill zone theory is a legal doctrine that does not exist in statute but has been used in jury instructions to aid in securing convictions for attempted murder charges. As a result of the kill zone theory, individuals in California have received lengthier sentences and, in some cases, have been convicted of crimes that fail to meet the requisite specific intent for attempted murder cases. The kill zone theory has no purpose in California law but to make the path to conviction easier and to put defendants in jail for longer. The kill zone theory is an unnecessary tool because there are several alternatives that would serve the same purpose of ensuring individuals do not evade punishment for endangering the lives of others. This Note will discuss the kill zone theory and how it came to be, explain the problematic aspects of the doctrine that end up harming defendants, propose alternative solutions to the kill zone theory, and conclude that the kill zone theory should no longer be used in California
Fourier-based Function Secret Sharing with General Access Structure
Function secret sharing (FSS) scheme is a mechanism that calculates a
function f(x) for x in {0,1}^n which is shared among p parties, by using
distributed functions f_i:{0,1}^n -> G, where G is an Abelian group, while the
function f:{0,1}^n -> G is kept secret to the parties. Ohsawa et al. in 2017
observed that any function f can be described as a linear combination of the
basis functions by regarding the function space as a vector space of dimension
2^n and gave new FSS schemes based on the Fourier basis. All existing FSS
schemes are of (p,p)-threshold type. That is, to compute f(x), we have to
collect f_i(x) for all the distributed functions. In this paper, as in the
secret sharing schemes, we consider FSS schemes with any general access
structure. To do this, we observe that Fourier-based FSS schemes by Ohsawa et
al. are compatible with linear secret sharing scheme. By incorporating the
techniques of linear secret sharing with any general access structure into the
Fourier-based FSS schemes, we show Fourier-based FSS schemes with any general
access structure.Comment: 12 page
An exact quantification of backreaction in relativistic cosmology
An important open question in cosmology is the degree to which the
Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations
are able to model the large-scale behaviour of the locally inhomogeneous
observable universe. We investigate this problem by considering a range of
exact n-body solutions of Einstein's constraint equations. These solutions
contain discrete masses, and so allow arbitrarily large density contrasts to be
modelled. We restrict our study to regularly arranged distributions of masses
in topological 3-spheres. This has the benefit of allowing straightforward
comparisons to be made with FLRW solutions, as both spacetimes admit a discrete
group of symmetries. It also provides a time-symmetric hypersurface at the
moment of maximum expansion that allows the constraint equations to be solved
exactly. We find that when all the mass in the universe is condensed into a
small number of objects (<10) then the amount of backreaction in dust models
can be large, with O(1) deviations from the predictions of the corresponding
FLRW solutions. When the number of masses is large (>100), however, then our
measures of backreaction become small (<1%). This result does not rely on any
averaging procedures, which are notoriously hard to define uniquely in general
relativity, and so provides (to the best of our knowledge) the first exact and
unambiguous demonstration of backreaction in general relativistic cosmological
modelling. Discrete models such as these can therefore be used as laboratories
to test ideas about backreaction that could be applied in more complicated and
realistic settings.Comment: 13 pages, 9 figures. Corrections made to Tables IV and
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Dyspnea affective response: comparing COPD patients with healthy volunteers and laboratory model with activities of daily living
Background: Laboratory-induced dyspnea (breathing discomfort) in healthy subjects is widely used to study perceptual mechanisms, yet the relationship between laboratory-induced dyspnea in healthy volunteers and spontaneous dyspnea in patients with chronic lung disease is not well established. We compared affective responses to dyspnea 1) in COPD patients vs. healthy volunteers (HV) undergoing the same laboratory stimulus; 2) in COPD during laboratory dyspnea vs. during activities of daily living (ADL). Methods: We induced moderate and high dyspnea levels in 13 COPD patients and 12 HV by increasing end-tidal CO2 (PETCO2) during restricted ventilation, evoking air hunger. We used the multidimensional dyspnea profile (MDP) to measure intensity of sensory qualities (e.g., air hunger (AH) and work/effort (W/E)) as well as immediate discomfort (A1) and secondary emotions (A2). Ten of the COPD subjects also completed the MDP outside the laboratory following dyspnea evoked by ADL. Results: COPD patients and HV reported similar levels of immediate discomfort relative to sensory intensity. COPD patients and HV reported anxiety and frustration during laboratory-induced dyspnea; variation among individuals far outweighed the small differences between subject groups. COPD patients reported similar intensities of sensory qualities, discomfort, and emotions during ADL vs. during moderate laboratory dyspnea. Patients with COPD described limiting ADL to avoid greater dyspnea. Conclusions: In this pilot study, we found no evidence that a history of COPD alters the affective response to laboratory-induced dyspnea, and no difference in affective response between dyspnea evoked by this laboratory model and dyspnea evoked by ADL
Thermodynamic metrics and optimal paths
A fundamental problem in modern thermodynamics is how a molecular-scale
machine performs useful work, while operating away from thermal equilibrium
without excessive dissipation. To this end, we derive a friction tensor that
induces a Riemannian manifold on the space of thermodynamic states. Within the
linear-response regime, this metric structure controls the dissipation of
finite-time transformations, and bestows optimal protocols with many useful
properties. We discuss the connection to the existing thermodynamic length
formalism, and demonstrate the utility of this metric by solving for optimal
control parameter protocols in a simple nonequilibrium model.Comment: 5 page
An Integrated Telemetric Thermocouple Sensor for Process Monitoring of CFRP Milling Operations
AbstractA wireless temperature measurement system was developed and integrated into a cutting tool holder via a thermocouple embedded within the cutting tool. The primary purpose of such an embedded thermal measurement sensor/system is for online process monitoring of machining processes within which thermal damage poses a significant threat both for the environment and productivity alike – as is the case with the machining of carbon fibre reinforced polymer (CFRP) components. A full system calibration was performed on the device. Response times were investigated and thermal errors, in the form of damping and lag, were identified. Experimental temperature results are presented which demonstrate the performance of the integrated wireless telemetry sensor during the edge trimming of CFRP composite materials. Thermocouple positioning relative to heat source effect was among the statistical factors investigated during machining experiments. Initial results into the thermal response of the sensor were obtained and a statistical package was used to determine the presence of significant main effects and interactions between a number of tested factors. The potential application of the embedded wireless temperature measurement sensor for online process monitoring in CFRP machining is demonstrated and recommendations are made for future advancements in such sensor technology
Quantum matchgate computations and linear threshold gates
The theory of matchgates is of interest in various areas in physics and
computer science. Matchgates occur in e.g. the study of fermions and spin
chains, in the theory of holographic algorithms and in several recent works in
quantum computation. In this paper we completely characterize the class of
boolean functions computable by unitary two-qubit matchgate circuits with some
probability of success. We show that this class precisely coincides with that
of the linear threshold gates. The latter is a fundamental family which appears
in several fields, such as the study of neural networks. Using the above
characterization, we further show that the power of matchgate circuits is
surprisingly trivial in those cases where the computation is to succeed with
high probability. In particular, the only functions that are
matchgate-computable with success probability greater than 3/4 are functions
depending on only a single bit of the input
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