A Hausdorff-Young theorem for rearrangement-invariant spaces

The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 <_ p <_ 2, p[-1] + q[-1] = 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p[-1], it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to q[-1] such that the Fourier transform is a bounded linear operator from X into X. Conversely, for any rearrangement-invariant space Y on Z with indices equal to q[-1], 2 < q <__ oo, there is a rearrangement-invariant space Y on T with indices equal to p[-1] such that J is bounded from Y into Y. Analogous results for other groups are indicated and examples are discussed when X is L[p] or a Lorentz space L[pr]

Banach function spaces and interpolation methods I. The abstract theory

AbstractInterpolation methods are introduced which have specific application in the function space setting. The methods are indexed by (ϱ; j) or (ϱ; k), where ϱ is a rearrangement-invariant norm and j and k are natural modifications of the J- and K-functionals of Peetre. Theorems of interpolation, equivalence, stability, and duality are established under simple restrictions on the indices of ϱ. Applications are given (in Part II) to the interpolation of weak-type operators and, in particular, to the Hilbert transform and the conjugate operator. In part III, the ϱ-methods are used to establish generalized Hausdorff-Young estimates for the Fourier transform

Reconstruction of gasoline engine in-cylinder pressures using recurrent neural networks

Knowledge of the pressure inside the combustion chamber of a gasoline engine would provide very useful information regarding the quality and consistency of combustion and allow significant improvements in its control, leading to improved efficiency and refinement. While measurement using incylinder pressure transducers is common in laboratory tests, their use in production engines is very limited due to cost and durability constraints. This thesis seeks to exploit the time series prediction capabilities of recurrent neural networks in order to build an inverse model accepting crankshaft kinematics or cylinder block vibrations as inputs for the reconstruction of in-cylinder pressures. Success in this endeavour would provide information to drive a real time combustion control strategy using only sensors already commonly installed on production engines. A reference data set was acquired from a prototype Ford in-line 3 cylinder direct injected, spark ignited gasoline engine of 1.125 litre swept volume. Data acquired concentrated on low speed (1000-2000 rev/min), low load (10-30 Nm brake torque) test conditions. The experimental work undertaken is described in detail, along with the signal processing requirements to treat the data prior to presentation to a neural network. The primary problem then addressed is the reliable, efficient training of a recurrent neural network to result in an inverse model capable of predicting cylinder pressures from data not seen during the training phase, this unseen data includes examples from speed and load ranges other than those in the training case. The specific recurrent network architecture investigated is the non-linear autoregressive with exogenous inputs (NARX) structure. Teacher forced training is investigated using the reference engine data set before a state of the art recurrent training method (Robust Adaptive Gradient Descent – RAGD) is implemented and the influence of the various parameters surrounding input vectors, network structure and training algorithm are investigated. Optimum parameters for data, structure and training algorithm are identified

Data-Driven Elections and Political Parties in Canada: Privacy Implications, Privacy Policies and Privacy Obligations

In light of the revelations concerning Cambridge Analytica, we are now in an era of heightened publicity and concern about the role of voter analytics in elections. Parties in Canada need to enhance their privacy management practices and commit to complying with national privacy principles in all their operations. As shown in this article’s comparative analysis of the privacy policies of federal and provincial political parties in Canada, policies are often difficult to find, unclear, and, with a couple of exceptions, do not address all the privacy principles. Accountability and complaints mechanisms are often not clearly publicized, and many are silent on procedures for the access and correction of data, and unsubscribing from lists. Vague and expansive statements of purpose are also quite common. However, this article shows that parties could comply with all 10 principles within the Canadian Standard Association (CSA)’s National Standard of Canada, upon which Canadian privacy law is based, without difficulty; though compliance will require a thorough process of self-assessment and a commitment across the political spectrum to greater transparency. The early experience in British Columbia (B.C.), where parties are regulated under the provincial Personal Information Protection Act, suggests that this process is beneficial for all concerned. In contrast to the system of self-regulation incorporated into the Elections Modernization Act, there is no inherent reason why parties could not be legally mandated to comply with all 10 principles, under the oversight of the Office of the Privacy Commissioner of Canada

A crank-kinematics based engine cylinder pressure reconstruction model

A new inverse model is proposed for reconstructing steady-state and transient engine cylinder pressure using measured crank kinematics. An adaptive nonlinear time-dependent relationship is assumed between windowed-subsections of cylinder pressure and measured crank kinematics in a time-domain format (rather than in crank-angle-domain). This relationship comprises a linear sum of four separate nonlinear functions of crank jerk, acceleration, velocity, and crank angle. Each of these four nonlinear functions is obtained at each time instant by fitting separate m-term Chebychev polynomial expansions, where the total 4m instantaneous expansion coefficients are found using a standard (over-determined) linear least-square solution method. A convergence check on the calibration accuracy shows this initially improves as more Chebychev polynomial terms are used, but with further increase, the over-determined system becomes singular. Optimal accuracy Chebychev expansions are found to be of degree m=4, using 90 or more cycles of engine data to fit the model. To confirm the model accuracy in predictive mode, a defined measure is used, namely the ‘calibration peak pressure error’. This measure allows effective a priori exclusion of occasionally unacceptable predictions. The method is tested using varying speed data taken from a 3-cylinder DISI engine fitted with cylinder pressure sensors, and a high resolution shaft encoder. Using appropriately-filtered crank kinematics (plus the ‘calibration peak pressure error’), the model produces fast and accurate predictions for previously unseen data. Peak pressure predictions are consistently within 6.5% of target, whereas locations of peak pressure are consistently within ± 2.7˚ CA. The computational efficiency makes it very suitable for real-time implementation

Weak randomness completely trounces the security of QKD

In usual security proofs of quantum protocols the adversary (Eve) is expected to have full control over any quantum communication between any communicating parties (Alice and Bob). Eve is also expected to have full access to an authenticated classical channel between Alice and Bob. Unconditional security against any attack by Eve can be proved even in the realistic setting of device and channel imperfection. In this Letter we show that the security of QKD protocols is ruined if one allows Eve to possess a very limited access to the random sources used by Alice. Such knowledge should always be expected in realistic experimental conditions via different side channels