Nearly Optimal Private Convolution

We study computing the convolution of a private input $x$ with a public input $h$, while satisfying the guarantees of $(\epsilon, \delta)$-differential privacy. Convolution is a fundamental operation, intimately related to Fourier Transforms. In our setting, the private input may represent a time series of sensitive events or a histogram of a database of confidential personal information. Convolution then captures important primitives including linear filtering, which is an essential tool in time series analysis, and aggregation queries on projections of the data. We give a nearly optimal algorithm for computing convolutions while satisfying $(\epsilon, \delta)$-differential privacy. Surprisingly, we follow the simple strategy of adding independent Laplacian noise to each Fourier coefficient and bounding the privacy loss using the composition theorem of Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal noise to add to each Fourier coefficient using convex programming duality. Our algorithm is very efficient -- it is essentially no more computationally expensive than a Fast Fourier Transform. To prove near optimality, we use the recent discrepancy lowerbounds of Muthukrishnan and Nikolov and derive a spectral lower bound using a characterization of discrepancy in terms of determinants

Chemical telemetry of OH observed to measure interstellar magnetic fields

We present models for the chemistry in gas moving towards the ionization front of an HII region. When it is far from the ionization front, the gas is highly depleted of elements more massive than helium. However, as it approaches the ionization front, ices are destroyed and species formed on the grain surfaces are injected into the gas phase. Photodissociation removes gas phase molecular species as the gas flows towards the ionization front. We identify models for which the OH column densities are comparable to those measured in observations undertaken to study the magnetic fields in star forming regions and give results for the column densities of other species that should be abundant if the observed OH arises through a combination of the liberation of H2O from surfaces and photodissociation. They include CH3OH, H2CO, and H2S. Observations of these other species may help establish the nature of the OH spatial distribution in the clouds, which is important for the interpretation of the magnetic field results.Comment: 11 pages, 2 figures, accepted by Astrophysics and Space Scienc

Quantization and Compressive Sensing

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta ($\Sigma\Delta$) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing and Its Applications", 201

Quantum Coherence in a Single Ion due to strong Excitation of a metastable Transition

We consider pump-probe spectroscopy of a single ion with a highly metastable (probe) clock transition which is monitored by using the quantum jump technique. For a weak clock laser we obtain the well known Autler-Townes splitting. For stronger powers of the clock laser we demonstrate the transition to a new regime. The two regimes are distinguished by the transition of two complex eigenvalues to purely imaginary ones which can be very different in magnitude. The transition is controlled by the power of the clock laser. For pump on resonance we present simple analytical expressions for various linewidths and line positions.Comment: 6 figures. accepted for publication in PR

ALS/FTD‐associated FUS activates GSK‐3β to disrupt the VAPB–PTPIP51 interaction and ER–mitochondria associations

Defective FUS metabolism is strongly associated with amyotrophic lateral sclerosis and frontotemporal dementia (ALS/FTD), but the mechanisms linking FUS to disease are not properly understood. However, many of the functions disrupted in ALS/FTD are regulated by signalling between the endoplasmic reticulum (ER) and mitochondria. This signalling is facilitated by close physical associations between the two organelles that are mediated by binding of the integral ER protein VAPB to the outer mitochondrial membrane protein PTPIP51, which act as molecular scaffolds to tether the two organelles. Here, we show that FUS disrupts the VAPB–PTPIP51 interaction and ER–mitochondria associations. These disruptions are accompanied by perturbation of Ca2+ uptake by mitochondria following its release from ER stores, which is a physiological read‐out of ER–mitochondria contacts. We also demonstrate that mitochondrial ATP production is impaired in FUS‐expressing cells; mitochondrial ATP production is linked to Ca2+ levels. Finally, we demonstrate that the FUS‐induced reductions to ER–mitochondria associations and are linked to activation of glycogen synthase kinase‐3β (GSK‐3β), a kinase already strongly associated with ALS/FTD

Environmental disclosure in Spain: Corporate characteristics and media exposure

Social and environmental issues have become a major concern for accounting research over the past two decades. Social and Environmental Accounting has attracted the attention of a number of researchers attempting to understand, explain and predict the disclosure of information on the social and environmental implications of business activities. Empirical research has hypothesized that size, profitability and the potential environmental impact of the firm are the main factors explaining the amount of information disclosed. On the other hand, several studies have focused on the motivations for disclosing environmental information, hypothesizing that disclosures are aimed at building or sustaining corporate legitimacy. We test the main hypotheses developed to date by empirical research with regard to the disclosure of environmental information based on a sample of companies listed on the Madrid Stock Exchange. Results of a content analysis show that firms disclosing environmental information tend to be larger, have higher risk (measured by the beta coefficient) and operate in industries that have a high potential environmental impact. The environmental implications of the activities carried out by these companies also seem to receive more attention from print media. Our results also provide evidence that two factors directly associated with the amount of environmental information disclosed are the potential environmental impact of the industry and the extent of media coverage of the firms

Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3

Recently a novel large-N reduction has been proposed as a maximally supersymmetric regularization of N=4 super Yang-Mills theory on RxS^3 in the planar limit. This proposal, if it works, will enable us to study the theory non-perturbatively on a computer, and hence to test the AdS/CFT correspondence analogously to the recent works on the D0-brane system. We provide a nontrivial check of this proposal by performing explicit calculations in the large-N reduced model, which is nothing but the so-called plane wave matrix model, around a particular stable vacuum corresponding to RxS^3. At finite temperature and at weak coupling, we reproduce precisely the deconfinement phase transition in the N=4 super Yang-Mills theory on RxS^3. This phase transition is considered to continue to the strongly coupled regime, where it corresponds to the Hawking-Page transition on the AdS side. We also perform calculations around other stable vacua, and reproduce the phase transition in super Yang-Mills theory on the corresponding curved space-times such as RxS^3/Z_q and RxS^2.Comment: 24 pages, 4 figure

Quantum charges and spacetime topology: The emergence of new superselection sectors

In which is developed a new form of superselection sectors of topological origin. By that it is meant a new investigation that includes several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum theories. At first we generalize the notion of representations of nets of C*-algebras, then we provide a brand new view on selection criteria by adopting one with a strong topological flavour. We prove that it is coherent with the older point of view, hence a clue to a genuine extension. In this light, we extend Roberts' cohomological analysis to the case where 1--cocycles bear non trivial unitary representations of the fundamental group of the spacetime, equivalently of its Cauchy surface in case of global hyperbolicity. A crucial tool is a notion of group von Neumann algebras generated by the 1-cocycles evaluated on loops over fixed regions. One proves that these group von Neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type I. All that amounts to a new invariant, in a topological sense, which can be defined as the dimension of the factor. We prove that any 1-cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored. This second part resembles much what in literature are known as geometric phases. Indeed, by the very geometrical origin of the 1-cocycles that we discuss in the paper, they are essential tools in the theory of net bundles, and the topological part is related to their holonomy content. At the end we prove the existence of net representations