4,533 research outputs found
Near-Optimal Algorithms for Differentially-Private Principal Components
Principal components analysis (PCA) is a standard tool for identifying good
low-dimensional approximations to data in high dimension. Many data sets of
interest contain private or sensitive information about individuals. Algorithms
which operate on such data should be sensitive to the privacy risks in
publishing their outputs. Differential privacy is a framework for developing
tradeoffs between privacy and the utility of these outputs. In this paper we
investigate the theory and empirical performance of differentially private
approximations to PCA and propose a new method which explicitly optimizes the
utility of the output. We show that the sample complexity of the proposed
method differs from the existing procedure in the scaling with the data
dimension, and that our method is nearly optimal in terms of this scaling. We
furthermore illustrate our results, showing that on real data there is a large
performance gap between the existing method and our method.Comment: 37 pages, 8 figures; final version to appear in the Journal of
Machine Learning Research, preliminary version was at NIPS 201
Evidence for two spin-glass transitions with magnetoelastic and magnetoelectric couplings in the multiferroic (BiBa)(FeTi)O system
For disordered Heisenberg systems with small single ion anisotropy, two spin
glass transitions below the long range ordered phase transition temperature has
been predicted theoretically for compositions close to the percolation
threshold. Experimental verification of these predictions is still
controversial for conventional spin glasses. We show that multiferroic spin
glass systems can provide a unique platform for verifying these theoretical
predictions via a study of change in magnetoelastic and magnetoelectric
couplings, obtained from an analysis of diffraction data, at the spin glass
transition temperatures. Results of macroscopic and microscopic (x-ray and
neutron scattering) measurements are presented on disordered BiFeO3, a
canonical Heisenberg system with small single ion anisotropy, which reveal
appearance of two spin glass phases SG1 and SG2 in coexistence with the LRO
phase below the A-T and G-T lines. It is shown that the temperature dependence
of the integrated intensity of the antiferromagnetic peak shows dips with
respect to the Brillouin function behaviour around the SG1 and SG2 transition
temperatures. The ferroelectric polarisation changes significantly at the two
spin glass transition temperatures. These results, obtained using microscopic
techniques, clearly demonstrate that the SG1 and SG2 transitions occur on the
same magnetic sublattice and are intrinsic to the system. We also construct a
phase diagram showing all the magnetic phases in BF-xBT system. While our
results on the two spin glass transitions support the theoretical predictions,
it also raises several open questions which need to be addressed by revisiting
the existing theories of spin glass transitions by taking into account the
effect of magnetoelastic and magnetoelectric couplings as well as
electromagnons.Comment: 59 pages 21 figure
Decay of Spin-One Particle into Two Photons in Presence of Uniform External Magnetic Field
Yang's theorem states that an initial J=1 state cannot decay into two
photons. Because of this result some reactions relating to elementary particles
or atomic transitions can be ruled out. The theorem is not valid in the
presence of background electric or magnetic fields. In this work we show that
the decay of a J=1 particle into two photons is permitted by Bose symmetry and
rotational invariance when the background of the decay process is not pure
vacuum but contains an external classical magnetic/electric field. We also
discuss constraints on these amplitudes from {\bf CP} invariance.Comment: Tex fil
Disclination-mediated thermo-optical response in nematic glass sheets
Nematic solids respond strongly to changes in ambient heat or light,
significantly differently parallel and perpendicular to the director. This
phenomenon is well characterized for uniform director fields, but not for
defect textures. We analyze the elastic ground states of a nematic glass in the
membrane approximation as a function of temperature for some disclination
defects with an eye towards reversibly inducing three-dimensional shapes from
flat sheets of material, at the nano-scale all the way to macroscopic objects,
including non-developable surfaces. The latter offers a new paradigm to
actuation via switchable stretch in thin systems.Comment: Specific results for spiral defects now added. References to Witten,
Mahadevan and Ben Amar now added
Stability of Lending Rate Stickiness: A Case Study of India
The paper postulates that in an environment of continuous financial reforms, the lending rate stickiness in an economy could be changing over the period. The financial reforms (of which deregulation of interest rates formed a major part) during the 1990s and the early 2000s and the changing role attributed to different policy rates during the reforms make India an interesting case study. The paper finds evidence of diminishing lending rate stickiness in case of India. During the major part of the study, Indian policymakers used the discount rate for policy signaling. The paper observes that as a result, the long-term rates like the lending rates did not react sufficiently to the changes in the short-term rates (e.g., repo rate) in this period unless the discount rate was also changed. Such behavior changed when policymakers started to use short-term rates like repo rates for policy signaling. Results in this paper suggest that when the impacts are added together, a change of 100 basis points in all policy rates towards the end of the reference period could change the lending rate in India almost by similar magnitude. These findings help to reconcile some of the contrasting findings on lending rate stickiness in case of India. Among possible factors still responsible for lending rate stickiness, the study identifies inelastic credit demand in India as an important factor. From policymaking perspective, however, it is postulated that as demand for personal and housing loans in India are likely to increase in future due to demographic factor, it is likely that such increase could tend to increase inflexibility in loan rates.Lending Rate Stickiness, Discount Rate Addiction, Monetary Policy Transmission
The Linearly Independent Non Orthogonal yet Energy Preserving (LINOEP) vectors
It is well known that, in any inner product space, a set of linearly
independent (LI) vectors can be transformed to a set of orthogonal vectors,
spanning the same space, by the Gram-Schmidt Orthogonalization Method (GSOM).
In this paper, we propose a transformation from a set of LI vectors to a set of
LI non orthogonal yet energy (square of the norm) preserving (LINOEP) vectors
in an inner product space and we refer it as LINOEP method. We also show that
there are various solutions to preserve the square of the norm.Comment: 6 pages, 2 figure
Magnonic spin-transfer torque MRAM with low power, high speed, and error-free switching
A new class of spin-transfer torque magnetic random access memory (STT-MRAM)
is discussed, in which writing is achieved using thermally initiated magnonic
current pulses as an alternative to conventional electric current pulses. The
magnonic pulses are used to destabilize the magnetic free layer from its
initial direction, and are followed immediately by a bipolar electric current
exerting conventional spin-transfer torque on the free layer. The combination
of thermal and electric currents greatly reduces switching errors, and
simultaneously reduces the electric switching current density by more than an
order of magnitude as compared to conventional STT-MRAM. The energy efficiency
of several possible electro-thermal circuit designs have been analyzed
numerically. As compared to STT-MRAM with perpendicular magnetic anisotropy,
magnonic STT-MRAM reduces the overall switching energy by almost 80%.
Furthermore, the lower electric current density allows the use of thicker
tunnel barriers, which should result in higher tunneling magneto-resistance and
improved tunnel barrier reliability. The combination of lower power, improved
reliability, higher integration density, and larger read margin make magnonic
STT-MRAM a promising choice for future non-volatile storage.Comment: 9 Pages, 11 Figure
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