Faster K-Means Cluster Estimation

There has been considerable work on improving popular clustering algorithm `K-means' in terms of mean squared error (MSE) and speed, both. However, most of the k-means variants tend to compute distance of each data point to each cluster centroid for every iteration. We propose a fast heuristic to overcome this bottleneck with only marginal increase in MSE. We observe that across all iterations of K-means, a data point changes its membership only among a small subset of clusters. Our heuristic predicts such clusters for each data point by looking at nearby clusters after the first iteration of k-means. We augment well known variants of k-means with our heuristic to demonstrate effectiveness of our heuristic. For various synthetic and real-world datasets, our heuristic achieves speed-up of up-to 3 times when compared to efficient variants of k-means.Comment: 6 pages, Accepted at ECIR 201

Compositional Verification for Autonomous Systems with Deep Learning Components

As autonomy becomes prevalent in many applications, ranging from recommendation systems to fully autonomous vehicles, there is an increased need to provide safety guarantees for such systems. The problem is difficult, as these are large, complex systems which operate in uncertain environments, requiring data-driven machine-learning components. However, learning techniques such as Deep Neural Networks, widely used today, are inherently unpredictable and lack the theoretical foundations to provide strong assurance guarantees. We present a compositional approach for the scalable, formal verification of autonomous systems that contain Deep Neural Network components. The approach uses assume-guarantee reasoning whereby {\em contracts}, encoding the input-output behavior of individual components, allow the designer to model and incorporate the behavior of the learning-enabled components working side-by-side with the other components. We illustrate the approach on an example taken from the autonomous vehicles domain

Cretaceous (Albian-Turonian) calcareous nannofossil biostratigraphy of the onshore Cauvery Basin, southeastern India

A suite of outcrop samples from the Cauvery Basin belonging to the mudrock-claystone dominated Karai Formation were analysed for nannofossil biostratigraphy in two newly measured sections at Karai and Garudamangalam. The age of the Karai Section is interpreted as early Albian to early Turonian, whereas the Garudamangalam Section is interpreted as late Albian to late Cenomanian. The Albian ‘BC’ zones of Bown et al. (1998) are applicable in both sections, whereas the Cenomanian and Turonian ‘UC’ zones of Burnett (1998), are only partially applicable, due to some problematic primary and secondary markers. The Albian-Cenomanian boundary appears to be continuous and is approximated in both sections using the FO of lower Cenomanian ammonites of the M. mantelli Zone. The Cenomanian-Turonian boundary interval is incomplete in the two sections, with a hiatus of ~0.66 myr, indicated by the absence of the upper Cenomanian Nannofossil Zone UC5. The nannoplankton assemblages are composed of broadly cosmopolitan taxa, despite the relatively high-latitude setting of SE India during the Albian (~45°S), which is reflected in the common occurrence of biogeographically bipolar taxa such as Repagulum parvidentatum and Seribiscutum primitivum. The palaeobiogeographic affinity of the nannoplankton, however, does not bear a distinct Austral stamp, as typical Austral taxa, such as Sollasites falklandensis and Zeugrhabdotus kerguelenensis are very rare in the studied sections. The early appearance of Crucibiscutum hayi in the lower Albian, and Gartnerago segmentatum in the upper Albian in the Cauvery Basin suggests that these two species may have originated in southern high latitudes before migrating to the northern Boreal regions. Four new calcareous nannofossil species, Calculites karaiensis, Loxolithus bicyclus, Manivitella fibrosa and Tranolithus simplex are described

Inelastic scattering of protons from 6,8^{6,8}He and 7,11^{7,11}Li in a folding model approach

The proton-inelastic scattering from $^{6,8}$He and $^{7,11}$Li nuclei are studied in a folding model approach. A finite-range, momentum, density and isospin dependent nucleon-nucleon interaction (SBM) is folded with realistic density distributions of the above nuclei. The renormalization factors N$_R$ and N$_I$ on the real and volume imaginary part of the folded potentials are obtained by analyzing the respective elastic scattering data and kept unaltered for the inelastic analysis at the same energy. The form factors are generated by taking derivatives of the folded potentials and therefore required renormalizations. The $\beta$ values are extracted by fitting the p + $^{6,8}$He,$^{7,11}$Li inelastic angular distributions. The present analysis of p + $^8$He inelastic scattering to the 3.57 MeV excited state, including unpublished forward angle data (RIKEN) confirms L = 2 transition. Similar analysis of the p + $^6$He inelastic scattering angular distribution leading to the 1.8 MeV (L = 2) excited state fails to satisfactorily reproduce the data.Comment: one LaTeX file, five PostScript figure

A new insight into the observation of spectroscopic strength reduction in atomic nuclei: implication for the physical meaning of spectroscopic factors

Experimental studies of one nucleon knockout from magic nuclei suggest that their nucleon orbits are not fully occupied. This conflicts a commonly accepted view of the shell closure associated with such nuclei. The conflict can be reconciled if the overlap between initial and final nuclear states in a knockout reaction are calculated by a non-standard method. The method employs an inhomogeneous equation based on correlation-dependent effective nucleon-nucleon (NN) interactions and allows the simplest wave functions, in which all nucleons occupy only the lowest nuclear orbits, to be used. The method also reproduces the recently established relation between reduction of spectroscopic strength, observed in knockout reactions on other nuclei, and nucleon binding energies. The implication of the inhomogeneous equation method for the physical meaning of spectroscopic factors is discussed.Comment: 4 pages, accepted by Phys. Rev. Let

Elastic and total reaction cross sections of oxygen isotopes in Glauber theory

We systematically calculate the total reaction cross sections of oxygen isotopes, $^{15-24}$O, on a $^{12}$C target at high energies using the Glauber theory. The oxygen isotopes are described with Slater determinants generated from a phenomenological mean-field potential. The agreement between theory and experiment is generally good, but a sharp increase of the reaction cross sections from ^{21}O to ^{23}O remains unresolved. To examine the sensitivity of the diffraction pattern of elastic scattering to the nuclear surface, we study the differential elastic-scattering cross sections of proton-^{20,21,23}O at the incident energy of 300 MeV by calculating the full Glauber amplitude.Comment: 9 pages, 8 figure

Privacy Preserving Multi-Server k-means Computation over Horizontally Partitioned Data

The k-means clustering is one of the most popular clustering algorithms in data mining. Recently a lot of research has been concentrated on the algorithm when the dataset is divided into multiple parties or when the dataset is too large to be handled by the data owner. In the latter case, usually some servers are hired to perform the task of clustering. The dataset is divided by the data owner among the servers who together perform the k-means and return the cluster labels to the owner. The major challenge in this method is to prevent the servers from gaining substantial information about the actual data of the owner. Several algorithms have been designed in the past that provide cryptographic solutions to perform privacy preserving k-means. We provide a new method to perform k-means over a large set using multiple servers. Our technique avoids heavy cryptographic computations and instead we use a simple randomization technique to preserve the privacy of the data. The k-means computed has exactly the same efficiency and accuracy as the k-means computed over the original dataset without any randomization. We argue that our algorithm is secure against honest but curious and passive adversary.Comment: 19 pages, 4 tables. International Conference on Information Systems Security. Springer, Cham, 201

Non-equilibrium VLS-grown stable ST12-Ge thin film on Si substrate: A study on strain-induced band-engineering

The current work describes a novel method of growing thin films of stable crystalline ST12-Ge, a high pressure polymorph of Ge, on Si substrate by a non-equilibrium VLS-technique. The study explores the scheme of band engineering of ST12-Ge by inducing process-stress into it as a function of the growth temperature and film thickness. In the present work, ST12-Ge films are grown at 180 C - 250 C to obtain thicknesses of ~4.5-7.5 nm, which possess extremely good thermal stability up to a temperature of ~350 C. Micro-Raman study shows the stress induced in such ST12-Ge films to be compressive in nature and vary in the range of ~0.5-7.5 GPa. The measured direct band gap is observed to vary within 0.688 eV to 0.711 eV for such stresses, and four indirect band gaps are obtained to be 0.583 eV, 0.614-0.628 eV, 0.622-0.63 eV and 0.623-0.632 eV, accordingly. The corresponding band structures for unstrained and strained ST12-Ge are calculated by performing DFT simulation, which shows that a compressive stress transforms the fundamental band gap at M-G valley from indirect to direct one. Henceforth, the possible route of strain induced band engineering in ST12-Ge is explored by analyzing all the transitions in strained and unstrained band structures along with substantiation of the experimental results and theoretical calculations. The investigation shows that unstrained ST12-Ge is a natural n-type semiconductor which transforms into p-type upon incorporation of a compressive stress of ~5 GPa, with the in-plane electron effective mass components at M-G band edge to be ~0.09 me. Therefore, such band engineered ST12-Ge exhibits superior mobility along with its thermal stability and compatibility with Si, which can have potential applications to develop high-speed MOS devices for advanced CMOS technology