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Optimal Error Correcting Index Codes for Some Generalized Index Coding Problems
No full textThe index coding with side-information problem introduced by Birk and Kol has been generalized to the case, where the transmissions are subjected to errors by Dau et al.. Lower and upper bounds on the optimal number of transmissions required to correct a specified number delta of errors were established. In another generalization of index coding problem, namely, generalized index coding (GIC) problem introduced by Dai et al., linear combination of the messages can be demanded and held as side information by the receivers. Error correction for GIC problems was studied and the bounds for optimal number of transmissions required for delta-error correcting generalized index codes were established by Byrne and Calderini. In this paper, for a particular class of GIC problems construction of optimal scalar linear index codes are discussed. For this class of GIC problems, the optimal linear delta-error correcting index codes are also constructed. As special cases, optimal linear error correcting codes are obtained for two classes of original index coding problems, namely, single-prior index coding problems and single unicast index coding problems with symmetric neighboring consecutive side information
Universal evaporation dynamics of ordered arrays of sessile droplets
No full textManipulation of an array of surface droplets organised in an ordered structure turns out to be of immense consequence in a wide variety of applications ranging from photonics, near field imaging and inkjet printing on the one hand to bio-molecular analysis and DNA sequencing on the other. While evaporation of a single isolated sessile droplet has been well studied, the collective evaporative dynamics of an ordered array of droplets on a solid substrate remains elusive. Physically, the closed region between the centre and side droplets in the ordered array reduces the mobility of the diffusing vapour, resulting in its accumulation along with enhanced local concentration and a consequent increment in the lifetime of the centre droplet. Here, we present a theoretical model to account for evaporation lifetime scaling in closely placed ordered linear droplet arrays. In addition, the present theory predicts the limiting cases of droplet interaction; namely, critical droplet separation for which interfacial interaction ceases to exist and minimum possible droplet separation (droplets on the verge of coalescence) for which the droplet system achieves maximum lifetime scaling. Further experimental evidence demonstrates the applicability of the present scaling theory to extended dimensions of the droplet array, generalising our physical conjecture. It is also worth noting that the theoretical time scale is applicable across a wide variety of drop-substrate combinations and initial droplet volumes. We also highlight that the scaling law proposed here can be extended seamlessly to other forms of confinement such as an evaporating droplet inside a mini-channel, as encountered in countless applications ranging from biomedical engineering to surface patterning. © 2019 Cambridge University Press
On optimal mechanisms in the two-item single-buyer unit-demand setting
No full textWe consider the problem of designing a revenue-optimal mechanism in the two-item, single-buyer, unit-demand setting when the buyer's valuations, (z 1 ,z 2 ), are uniformly distributed in an arbitrary rectangle c,c+b 1 �c,c+b 2 in the positive quadrant. We provide a complete and explicit solution for arbitrary nonnegative values of (c,b 1 ,b 2 ). We identify five simple structures, each with at most five (possibly stochastic) menu items, and prove that the optimal mechanism has one of the five structures. We also characterize the optimal mechanism as a function of b 1 ,b 2 , and c. When c is low, the optimal mechanism is a posted price mechanism with an exclusion region; when c is high, it is a posted price mechanism without an exclusion region. Our results are the first to show the existence of optimal mechanisms with no exclusion region, to the best of our knowledge. © 2019 Elsevier B.V
Multifunctional Self-Assembled Macrocycles with Enhanced Emission and Reversible Photochromic Behavior
No full textA series of self-Assembled functional Pt(II) molecular hexagons (M1-M3) is reported. Hexagons M1 and M2 were designed employing aggregation induced emissive and photochromic building blocks, respectively, while macrocycle M3 is a bifunctional, containing both the kinds of building units. Hexagons M1 and M3 were found to inherit the enhanced emission with aggregate formation which was explored using UV-Vis and fluorescence spectroscopy. The enhanced emission of macrocycle M3 compared to that of its building units was driven both by metal-Ligand coordination and formation of nanoaggregates as evident from SEM, DLS and TEM analyses. Two of the macrocycles (M2 and M3) were also found to be photochromic due to the presence of spiropyran in the molecular backbone. Due to the virtue of protonation-Deprotonation equilibrium of the spiropyran, these macrocycles (M2 and M3) showed reversible acidochromic behavior. Macrocycle M3 represents the first example of a self-Assembled Pt(II) architecture which is multifunctional with aggregation-Induced emission (AIE), photochromic, and acidochromic properties. This new generation macrocycle (M3) also showed coordination-Driven enhanced emission and light-Induced color change behavior compared to the starting building blocks. Our present approach of incorporating multiple functions into a single self-Assembled structure with enhanced functionality compared to the starting building blocks via coordination self-Assembly is noteworthy and has huge potential for the development of multifunctional materials. © 2019 American Chemical Society
Rupture of the Indian Slab in the 2011 Mw 6.9 Sikkim Himalaya Earthquake and Its Tectonic Implications
No full textUnlike the other Himalayan plate boundary segments, the eastern Nepal to Bhutan Himalayan region is not known to have generated prominent shallow thrust faulting earthquakes, typical of the ongoing convergence. This region features strike-slip earthquakes over the depth ranges of 40�120 km, indicating intraslab deformation. Here we present for the first time a slip distribution model for the largest recorded intraslab strike-slip earthquake in this region, the Mw 6.9 Sikkim event that occurred on 18 September 2011. Relying on kinematic source process modeling, our results indicate a NE-SW trending, steeply dipping sinistral source zone within the underthrusting Indian slab. The rupture propagated radially, with a low rupture velocity of 1.7 km/s, breaking a large asperity of 20 � 20 km 2 with a maximum slip of 1.6 m. The rupture nucleated at a depth of 45 km and reached upper mantle depths. The computed coseismic stress drop value is 13.6 MPa. We suggest that most of the aftershocks occurred on the conjugate plane, possibly due to stress triggering. Stress inversion of focal mechanisms indicates a transpressive stress regime throughout the crust and pure strike-slip regime in the upper mantle. We observed a unimodal distribution of earthquakes beneath the Higher Himalaya. This indicates a strong, brittle Indian slab and unravels a scenario of an eventual breakup of the lithosphere; the key trigger might be variation in the convergence rates along the Himalayan arc. ©2019. American Geophysical Union. All Rights Reserved
The aryne Sommelet-Hauser rearrangement
No full textAn aryne induced transition-metal-free and mild Sommelet-Hauser rearrangement of tertiary benzylamines for the synthesis of α-aryl amino acid derivatives in moderate to good yields is presented. Unlike the conventional Sommelet-Hauser rearrangement of ammonium salts, the methodology developed herein requires neither harsh conditions nor strong bases. Moreover, a temperature dependent switchable selectivity for the Sommelet-Hauser and Stevens 1,2 rearrangements has been observed. © The Royal Society of Chemistry
P- and T-wave delineation in ECG signals using parametric mixture Gaussian and dynamic programming
No full textDetection and tracking of the P- and T-waves are important issues in the analysis and interpretation of the ECG signals. This paper addresses the problem by using two mixture Gaussian function and the Dynamic programming. A key feature of the proposed algorithm is that it allows to incorporate the prior knowledge about the P/T wave location variations and robustness to errors in QRS detection. The proposed algorithm is evaluated on the annotated QT-database and compared against the algorithms based on differential evolution optimization strategy (DEOS) and generating blocks of interest (GBI). The experiments show that the proposed method determines the P- and T-peak locations with a root mean square error of 0.085 s and 0.091 s respectively. Both these values are better than the corresponding values from DEOS and GBI. Similarly, the proposed algorithm achieves a sensitivity of 96.13 and predictivity of 97.70. While the predictivity is higher than both DEOS and GBI, the sensitivity is on par with GBOI and higher than that of DEOS
Measurement Bounds for Observability of Linear Dynamical Systems under Sparsity Constraints
No full textIn this paper, we address the problem of observability of a linear dynamical system from compressive measurements and the knowledge of its external inputs. Observability of a high-dimensional system state in general requires a correspondingly large number of measurements. We show that if the initial state vector admits a sparse representation, the number of measurements can be significantly reduced by using random projections for obtaining the measurements. Our analysis gives sufficient conditions for the restricted isometry property of the observability matrix to hold, which leads to guarantees for the observability of the system. Our results depend only on the properties of system transfer and observation matrices, and are derived using tools from probability theory and compressed sensing. Unlike the prior work in this direction, our results are applicable to systems with an arbitrary nonzero system transfer matrix. Moreover, our results are stronger than the existing results in the regime where they are comparable
Structural and Femtosecond Third-Order Nonlinear Optical Properties of Sodium Borate Oxide Glasses: Effect of Antimony
No full textStructural and optical properties of antimony-containing sodium borate glasses were studied and their ultrafast third-order nonlinear optical (NLO) properties have been evaluated using Z-scan measurements with femtosecond (fs) pulses (?150 fs, 80 MHz) at 750, 800, and 880 nm wavelengths. Glasses in the (mol ) 20Na 2 O-(80 - x)B 2 O 3 -xSb 2 O 3 (where x = 0, 10, 20, and 30) system have been fabricated via melt quench technique. The structural modifications were analyzed using the Raman and magic angle spinning (MAS)-nuclear magnetic resonance (NMR) ( 11 B MAS-NMR and 23 Na MAS-NMR) techniques. The optical absorption spectra revealed that the absorption edge was red-shifted, suggesting the decrease in band gap energy with increase of antimony content in the glasses. Raman scattering results revealed that the boroxol rings are depressed with the incorporation of Sb 2 O 3 for replacing B 2 O 3 . 11 B MAS-NMR results showed a progressive increase of B 4 units at the expense of B 3 units. The Raman and 11 B MAS-NMR results support the formation of Sb 5+ ions due to oxidation of Sb 3+ that played the role of charge compensation. 23 Na MAS-NMR spectra revealed a decreasing trend in the average of bond lengths of Na-O with increasing Sb 2 O 3 contents. This suggested that sodium changed its role from charge compensator to modifier cation. The antimony-containing glasses demonstrated a reverse saturable absorption in open-aperture Z-scan mode due to two-photon absorption, while closed-aperture Z-scan signatures depicted positive nonlinear refraction due to self-focusing effect. The NLO coefficients were found to increase with Sb 2 O 3 due to the increased nonbridging oxygens and also due to the hyperpolarizability of Sb 3+ and Sb 5+ ions. The observed NLO data clearly suggest that the investigated glasses are beneficial for optical limiting applications
Effects of superelasticity and plasticity on the spherical indentation response of shape memory alloys: A finite element analysis
No full textInstrumented indentation is particularly useful for characterizing the mechanical behavior of shape memory alloys (SMAs), which are often used as 'small volume' elements such as thin films or wires. Deciphering the measured indentation response, which is as such difficult for elastic-plastic materials due to the inhomogeneous state of stress underneath the indenter, becomes more complex for SMAs owing to the simultaneous occurrence of stress induced martensite transformation (SIMT) in conjunction with plastic deformation. In this work, a constitutive model that is able to capture the coupled nature of phase transformation and plastic deformation is employed to study, through finite element analyses, the spherical indentation behavior of SMAs at a temperature above the austenite finish temperature, A f . It is found that the concurrent development of plastic yielding and SIMT leads to slower evolution of martensite volume and a smaller transformed zone size. Also, in the absence of plastic yielding, the proportion of depth recovered by superelasticity is fairly constant. It is also observed, from a systematic comparison with a conventional elastic-plastic material, that the presence of the transformed zone significantly alters the stress distribution beneath the indenter. © 2019 IOP Publishing Ltd