Economic Inequality: Is it Natural?

Mounting evidences are being gathered suggesting that income and wealth distribution in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium, but also deviating significantly for high income groups. Application of physics models seem to provide illuminating ideas and understanding, complimenting the observations.Comment: 7 pages, 2 eps figs, 2 boxes with text and 2 eps figs; Popular review To appear in Current Science; typos in refs and text correcte

HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces

Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor search. In this paper, we propose a novel yet simple indexing scheme, HD-Index, to solve the problem of approximate k-nearest neighbor queries in massive high-dimensional databases. HD-Index consists of a set of novel hierarchical structures called RDB-trees built on Hilbert keys of database objects. The leaves of the RDB-trees store distances of database objects to reference objects, thereby allowing efficient pruning using distance filters. In addition to triangular inequality, we also use Ptolemaic inequality to produce better lower bounds. Experiments on massive (up to billion scale) high-dimensional (up to 1000+) datasets show that HD-Index is effective, efficient, and scalable.Comment: PVLDB 11(8):906-919, 201

State Dependence of Krylov Complexity in 2d2d CFTs

We compute the Krylov Complexity of a light operator $\mathcal{O}_L$ in an eigenstate of a $2d$ CFT at large central charge $c$. The eigenstate corresponds to a primary operator $\mathcal{O}_H$ under the state-operator correspondence. We observe that the behaviour of K-complexity is different (either bounded or exponential) depending on whether the scaling dimension of $\mathcal{O}_H$ is below or above the critical dimension $h_H=c/24$, marked by the $1st$ order Hawking-Page phase transition point in the dual $AdS_3$ geometry. Based on this feature, we hypothesize that the notions of operator growth and K-complexity for primary operators in $2d$ CFTs are closely related to the underlying entanglement structure of the state in which they are computed, thereby demonstrating explicitly their state-dependent nature. To provide further evidence for our hypothesis, we perform an analogous computation of K-complexity in a model of free massless scalar field theory in $2d$, and in the integrable $2d$ Ising CFT, where there is no such transition in the spectrum of states.Comment: 24 pages, 5 figures, minor corrections, references adde

Imaging using volume holograms

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2004.Includes bibliographical references (p. 185-196).Volume holograms can be thought of as self-aligned 3D stacks of diffractive elements that operate coherently on incident fields as they propagate through the structure. In this thesis, we propose, design and implement imaging systems that incorporate a volume hologram as one of the elements that operate on the optical field incident on the imaging system. We show that a volume hologram acts like a "smart" lens that can perform several useful functions in an imaging system and demonstrate the same experimentally. To this end, we first develop the theory of volume holographic imaging and calculate the imaging properties of the field diffracted by a volume hologram for the special cases of coherent and incoherent monochromatic illumination. We concentrate on two simple imaging system configurations, viz. volume holograms recorded using a planar signal and either a spherical or a planar reference beam. We pay particular attention to the depth resolution of each system and discuss how appropriately designed objective optics placed before the volume hologram can enhance the depth resolution. We also derive the imaging properties of the volume holographic "smart" lens under conditions of incoherent broadband illumination. We show that multiple volume holographic sensors can be configured to acquire different perspectives of an object with enhanced resolution. We experimentally verify the developed theories and implement several volume holographic imaging systems for a wide range of imaging applications. We compare volume holographic imaging with some commonly used 3D imaging systems and discuss the merits of each system. We find that volume holograms with low diffraction efficiencies result in lower photon counts(cont.) and information loss and hence poorer imaging performance. We present an optical method to solve this problem by resonating the volume hologram inside an optical cavity. Finally, we conclude with some directions for future work in this emerging field.by Arnab Sinha.Ph.D

Imaging using volume holograms

We present an overview of imaging systems that incorporate a volume hologram as one of the optical field processing elements in the system. We refer to these systems as volume holographic imaging (VHI) systems. The volume hologram is recorded just once, and the recording parameters depend on the functional requirements of the imaging system. The recording step offers great flexibility in designing application-specific imaging systems. We discuss how a VHI system can be configured for diverse imaging applications ranging from surface profilometry to real-time hyperspectral microscopy, and summarize recent developments in this field

Deep uGMRT observations of the ELAIS-North 1 field: statistical properties of radio--infrared relations up to z∼z \sim2

Comprehending the radio--infrared (IR) relations of the faint extragalactic radio sources is important for using radio emission as a tracer of star-formation in high redshift ($z$) star-forming galaxies (SFGs). Using deep uGMRT observations of the ELAIS-N1 field in the 0.3--0.5\,GHz range, we study the statistical properties of the radio--IR relations and the variation of the `$q$-parameter' up to $z=2$ after broadly classifying the faint sources as SFGs and AGN. We find the dust temperature (\tdust) to increase with $z$. This gives rise to \qmir, measured at 24\,\upmum, to increase with $z$ as the peak of IR emission shifts towards shorter wavelengths, resulting in the largest scatter among different measures of $q$-parameters. \qfir measured at 70\,\upmum, and $q_{\rm TIR}$ using total-IR (TIR) emission are largely unaffected by \tdust. We observe strong, non-linear correlations between the radio luminosities at 0.4 and 1.4\,GHz with 70\,\upmum luminosity and TIR luminosity(\ltir). To assess the possible role of the radio-continuum spectrum in making the relations non-linear, for the first time we study them at high $z$ using integrated radio luminosity (\lrc) in the range 0.1--2\,GHz. In SFGs, the \lrc--\ltir relation remains non-linear with a slope of $1.07\pm0.02$, has a factor of 2 lower scatter compared to monochromatic radio luminosities, and \qtirbol decreases with $z$ as \qtirbol = (2.27 \pm 0.03)\,(1+z)^{-0.12 \pm 0.03}. A redshift variation of $q$ is a natural consequence of non-linearity. We suggest that a redshift evolution of magnetic field strengths and/or cosmic ray acceleration efficiency in high-$z$ SFGs could give rise to non-linear radio--IR relations.Comment: Accepted for publication in MNRAS (20 pages, 20 Figures and one Appendix