We present a divide-and-merge methodology for clustering a set of objects that combines a top-dow... more We present a divide-and-merge methodology for clustering a set of objects that combines a top-down divide phase with a bottom-up merge phase. In contrast, previous algorithms use either top-down or bottom-up methods to construct a hierarchical clustering or produce a ...
This paper reports a study of size-heterogeneous colloid filtration in a new bed using different ... more This paper reports a study of size-heterogeneous colloid filtration in a new bed using different types of colloids under different conditions of flow and solution chemistry. Depth-wise variation of the particle-size-distributions fi(x), and the total liquid-phase colloid concentration, C(x) are measured which are used to estimate the depth-wise variation of the liquid-phase concentration for each distinct section of the heterogeneous population, Ci(x). It is observed that log Ci(x) is linear with depth, for some systems, while it shows deviation from linearity, with the slope decreasing with depth, for others. Deposition-rates for these distinct sections of the heterogeneous population, ki, are estimated from the slopes of the log Ci(x) data. These deposition-rates were then compared with predicted homogeneous-population deposition-rates from Colloid Filtration Theory (CFT), which shows agreement between the CFT-based-deposition-rates and heterogeneous-population-data based deposition-rates, for low flow velocities. At higher flow velocities a gap between the CFT-based and Data-based deposition-rates is observed. Deposition-rates from CFT are then used in a heterogeneous-colloid-filtration model, to examine if heterogeneous colloid deposition can be expressed as the sum of its parts. It is observed that, the sum-of-parts model provides a reasonable estimate of colloidal deposition from heterogeneous populations. Based on these results, it is possible to make predictions of colloidal deposition from complex heterogeneous suspensions. A new method for studying heterogeneous colloid filtration is also proposed.
For improving reliability of communication in communication networks, where edges are subject to ... more For improving reliability of communication in communication networks, where edges are subject to failure, Kishimoto [Reliable flow with failures in a network, IEEE Trans. Reliability, 46 (1997) 308–315] defined a δδ-reliable flow, for a given source-sink pair of nodes, in a network for δ∈(0,1]δ∈(0,1], where no edge carries a flow more than a fraction δδ of the total flow in the network, and proved a max-flow min-cut theorem with cut-capacites defined suitably. Kishimoto and Takeuchi in [A method for obtaining δδ-reliable flow in a network, IECCE Fundamentals E-81A (1998) 776–783] provided an efficient algorithm for finding such a flow.When (1/δ)(1/δ) is an integer, say qq, Kishimoto and Takeuchi [On mm-route flows in a network, IEICE Trans. J-76-A (1993) 1185–1200 (in Japanese)] introduced the notion of a q-path flow. Kishimoto [A method for obtaining the maximum multi-route flows in a network, Networks 27 (1996) 279–291] proved a max-flow min-cut theorem for q-path flow between a given source-sink pair (s,ts,t) of nodes and provided a strongly polynomial algorithm for finding a q-path flow from s to t of maximum flow-value.In this paper, we extend the concept of q-path flow to any real number q⩾1q⩾1. When q(=1/δ)(=1/δ) is fractional, we show that this general q-path flow can be viewed as a sum of some ⌈q⌉q-path flow and some ⌊q⌋q-path flow. We discuss several applications of this results, which include a simpler proof and generalization of a known result on wavelength division multiplexing problem.Finally we present a strongly polynomial, combinatorial algorithm for synthesizing an undirected network with minimum sum of edge capacities that satisfies (non-simultaneously) specified minimum requirements of q-path flow-values between all pairs of nodes, for a given real number q⩾1q⩾1.
We present here an enhanced broadband supercontinuum generation in a potassium di-hydrogen phosph... more We present here an enhanced broadband supercontinuum generation in a potassium di-hydrogen phosphate (KDP) crystal. The enhancement in the bandwidth of the white light is obtained towards the shorter wavelength regime (<400 nm) by employing supercontinuum generation and sum frequency generation in tandem. The tunability in the blue region of the spectrum with angle is demonstrated. The bandwidth of supercontinuum achieved spans from 350 nm to 1300 nm. Further, we show the excellent polarization maintenance of continuum generated in KDP in comparison to that generated in water and BK-7 glass.
IEEE Transactions on Information Theory, Jan 1, 1987
Techniques from coding theory are applied to study rigorously the capacity of the Hopfield associ... more Techniques from coding theory are applied to study rigorously the capacity of the Hopfield associative memory. Such a memory storesn-tuple ofpm 1's. The components change depending on a hard-limited version of linear functions of all other components. With symmetric connections between components, a stable state is ultimately reached. By building up the connection matrix as a sum-of-outer products ofmfundamental memories, one hopes to be able to recover a certain one of themmemories by using an initialn-tuple probe vector less than a Hamming distancen/2away from the fundamental memory. Ifmfundamental memories are chosen at random, the maximum asympotic value ofmin order that most of themoriginal memories are exactly recoverable isn/(2 log n). With the added restriction that every one of themfundamental memories be recoverable exactly,mcan be no more thann/(4 log n)asymptotically asnapproaches infinity. Extensions are also considered, in particular to capacity under quantization of the outer-product connection matrix. This quantized memory capacity problem is closely related to the capacity of the quantized Gaussian channel.
We present a divide-and-merge methodology for clustering a set of objects that combines a top-dow... more We present a divide-and-merge methodology for clustering a set of objects that combines a top-down divide phase with a bottom-up merge phase. In contrast, previous algorithms use either top-down or bottom-up methods to construct a hierarchical clustering or produce a ...
This paper reports a study of size-heterogeneous colloid filtration in a new bed using different ... more This paper reports a study of size-heterogeneous colloid filtration in a new bed using different types of colloids under different conditions of flow and solution chemistry. Depth-wise variation of the particle-size-distributions fi(x), and the total liquid-phase colloid concentration, C(x) are measured which are used to estimate the depth-wise variation of the liquid-phase concentration for each distinct section of the heterogeneous population, Ci(x). It is observed that log Ci(x) is linear with depth, for some systems, while it shows deviation from linearity, with the slope decreasing with depth, for others. Deposition-rates for these distinct sections of the heterogeneous population, ki, are estimated from the slopes of the log Ci(x) data. These deposition-rates were then compared with predicted homogeneous-population deposition-rates from Colloid Filtration Theory (CFT), which shows agreement between the CFT-based-deposition-rates and heterogeneous-population-data based deposition-rates, for low flow velocities. At higher flow velocities a gap between the CFT-based and Data-based deposition-rates is observed. Deposition-rates from CFT are then used in a heterogeneous-colloid-filtration model, to examine if heterogeneous colloid deposition can be expressed as the sum of its parts. It is observed that, the sum-of-parts model provides a reasonable estimate of colloidal deposition from heterogeneous populations. Based on these results, it is possible to make predictions of colloidal deposition from complex heterogeneous suspensions. A new method for studying heterogeneous colloid filtration is also proposed.
For improving reliability of communication in communication networks, where edges are subject to ... more For improving reliability of communication in communication networks, where edges are subject to failure, Kishimoto [Reliable flow with failures in a network, IEEE Trans. Reliability, 46 (1997) 308–315] defined a δδ-reliable flow, for a given source-sink pair of nodes, in a network for δ∈(0,1]δ∈(0,1], where no edge carries a flow more than a fraction δδ of the total flow in the network, and proved a max-flow min-cut theorem with cut-capacites defined suitably. Kishimoto and Takeuchi in [A method for obtaining δδ-reliable flow in a network, IECCE Fundamentals E-81A (1998) 776–783] provided an efficient algorithm for finding such a flow.When (1/δ)(1/δ) is an integer, say qq, Kishimoto and Takeuchi [On mm-route flows in a network, IEICE Trans. J-76-A (1993) 1185–1200 (in Japanese)] introduced the notion of a q-path flow. Kishimoto [A method for obtaining the maximum multi-route flows in a network, Networks 27 (1996) 279–291] proved a max-flow min-cut theorem for q-path flow between a given source-sink pair (s,ts,t) of nodes and provided a strongly polynomial algorithm for finding a q-path flow from s to t of maximum flow-value.In this paper, we extend the concept of q-path flow to any real number q⩾1q⩾1. When q(=1/δ)(=1/δ) is fractional, we show that this general q-path flow can be viewed as a sum of some ⌈q⌉q-path flow and some ⌊q⌋q-path flow. We discuss several applications of this results, which include a simpler proof and generalization of a known result on wavelength division multiplexing problem.Finally we present a strongly polynomial, combinatorial algorithm for synthesizing an undirected network with minimum sum of edge capacities that satisfies (non-simultaneously) specified minimum requirements of q-path flow-values between all pairs of nodes, for a given real number q⩾1q⩾1.
We present here an enhanced broadband supercontinuum generation in a potassium di-hydrogen phosph... more We present here an enhanced broadband supercontinuum generation in a potassium di-hydrogen phosphate (KDP) crystal. The enhancement in the bandwidth of the white light is obtained towards the shorter wavelength regime (<400 nm) by employing supercontinuum generation and sum frequency generation in tandem. The tunability in the blue region of the spectrum with angle is demonstrated. The bandwidth of supercontinuum achieved spans from 350 nm to 1300 nm. Further, we show the excellent polarization maintenance of continuum generated in KDP in comparison to that generated in water and BK-7 glass.
IEEE Transactions on Information Theory, Jan 1, 1987
Techniques from coding theory are applied to study rigorously the capacity of the Hopfield associ... more Techniques from coding theory are applied to study rigorously the capacity of the Hopfield associative memory. Such a memory storesn-tuple ofpm 1's. The components change depending on a hard-limited version of linear functions of all other components. With symmetric connections between components, a stable state is ultimately reached. By building up the connection matrix as a sum-of-outer products ofmfundamental memories, one hopes to be able to recover a certain one of themmemories by using an initialn-tuple probe vector less than a Hamming distancen/2away from the fundamental memory. Ifmfundamental memories are chosen at random, the maximum asympotic value ofmin order that most of themoriginal memories are exactly recoverable isn/(2 log n). With the added restriction that every one of themfundamental memories be recoverable exactly,mcan be no more thann/(4 log n)asymptotically asnapproaches infinity. Extensions are also considered, in particular to capacity under quantization of the outer-product connection matrix. This quantized memory capacity problem is closely related to the capacity of the quantized Gaussian channel.
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Papers by Santosh Sum