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 $H[f] \leq C Inf[f]$ holds for every Boolean function $f$, where $H[f]$ denotes the spectral entropy of $f$, $Inf[f]$ is its total influence, and $C > 0$ 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 $g_1,...,g_k$ are functions over disjoint sets of variables satisfying the conjecture, and if the Fourier transform of $F$ taken with respect to the product distribution with biases $E[g_1],...,E[g_k]$ satisfies the conjecture, then their composition $F(g_1(x^1),...,g_k(x^k))$ 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 $C \geq 6.278$ between $H[f]$ and $Inf[f]$, 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

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