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Arvind Kumar

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Papers by Arvind Kumar

Binomial expansion for saturated and symbolic powers of sums of ideals

Journal of Algebra

There are two different notions for symbolic powers of ideals existing in the literature, one def... more There are two different notions for symbolic powers of ideals existing in the literature, one defined in terms of associated primes, the other in terms of minimal primes. Elaborating on an idea known to Eisenbud, Herzog, Hibi, and Trung, we interpret both notions of symbolic powers as suitable saturations of the ordinary powers. We prove a binomial expansion formula for saturated powers of sums of ideals. This gives a uniform treatment to an array of existing and new results on both notions of symbolic powers of such sums: binomial expansion formulas, computations of depth and regularity, and criteria for the equality of ordinary and symbolic powers.

On the resurgence and asymptotic resurgence of homogeneous ideals

Mathematische Zeitschrift

Let K be a field and R = K[x 1 ,. .. , x n ]. We obtain an improved upper bound for asymptotic re... more Let K be a field and R = K[x 1 ,. .. , x n ]. We obtain an improved upper bound for asymptotic resurgence of squarefree monomial ideals in R. We study the effect on the resurgence when sum, product and intersection of ideals are taken. We obtain sharp upper and lower bounds for the resurgence and asymptotic resurgence of cover ideals of finite simple graphs in terms of associated combinatorial invariants. We also explicitly compute the resurgence and asymptotic resurgence of cover ideals of several classes of graphs. We characterize a graph being bipartite in terms of the resurgence and asymptotic resurgence of edge and cover ideals. We also compute explicitly the resurgence and asymptotic resurgence of edge ideals of some classes of graphs.

A Kamm’s Circle-Based Potential Risk Estimation Scheme in the Local Dynamic Map Computation Enhanced by Binary Decision Diagrams

Sensors

Autonomous vehicles (AV) are a hot topic for safe mobility, which inevitably requires sensors to ... more Autonomous vehicles (AV) are a hot topic for safe mobility, which inevitably requires sensors to achieve autonomy, but relying too heavily on sensors will be a risk factor. A high-definition map (HD map) reduces the risk by giving geographical information if it covers dynamic information from moving entities on the road. Cooperative intelligent transport systems (C-ITS) are a prominent approach to solving the issue and local dynamic maps (LDMs) are expected to realize the ideal C-ITS. An actual LDM implementation requires a fine database design to be able to update the information to represent potential risks based on future interactions of vehicles. In the present study, we proposed an advanced method for embedding the geographical future occupancy of vehicles into the database by using a binary decision diagram (BDD). In our method, the geographical future occupancy of vehicles was formulated with Kamm’s circle. In computer experiments, sharing BDD-based occupancy data was success...

Algebraic Symmetry and Self–Duality of an Open ASEP

Mathematical Physics, Analysis and Geometry

We consider the asymmetric simple exclusion process (ASEP) with open boundary condition at the le... more We consider the asymmetric simple exclusion process (ASEP) with open boundary condition at the left boundary, where particles exit at rate γ and enter at rate α = γτ 2 , and where τ is the asymmetry parameter in the bulk. At the right boundary, particles neither enter nor exit. By mapping the generator to the Hamiltonian of an XXZ quantum spin chain with reflection matrices, and using previously known results, we show algebraic symmetry and self-duality for the model.

Water-clustering in hygroscopic ionic liquids-an implicit solvent analysis

Most ionic liquids are known to be hygroscopic to varying degrees, and that can be detrimental or... more Most ionic liquids are known to be hygroscopic to varying degrees, and that can be detrimental or useful depending upon the application in question. Water can accumulate slowly over hours or days to saturation levels corresponding to the humidity level. When designing or deploying a new ionic liquid it is important to be able to estimate its maximum moisture absorbing ability at the temperature and pressure of its operation. With this goal in mind we have carried out computational studies on three ionic liquid systems based on [BF(4)](-), [PF(6)](-), and [Tf(2)N](-) anions and 1-alkyl-3-methyl-imidazolium ([C(n)mim](+)) cations within an implicit solvent formalism. For highly hygroscopic systems like [C(n)mim][BF(4)] we find that non-iterative calculations with single water molecules can lead to significant underestimation of the maximum moisture content, while iterative calculations can result in miscibility behavior qualitatively different from experimental observations. On the other hand, the inclusion of small hydrogen-bonded water-clusters up to an appropriately chosen size is shown to yield better quantitative agreements with experimentally observed water uptake. Additionally, such calculations appear consistent with a number of thermodynamically interesting phase behaviors, including limited-solubility to full-miscibility transitions as a function of temperature and as a function of the alkyl chain length of the imidazolium cation. For hydrophobic systems like [C(n)mim][PF(6)] and [C(n)mim][Tf(2)N] the computed solubility (for each n) is found to have a smooth convergence behavior as a function of the largest cluster-size considered with the results for the larger clusters being close to that obtained by iterative calculations with single water molecules.

Photopatterned electrochromic conjugated polymer films via precursor approach

Polymer, 2008

Herein we report the photolithography of electrochromic conjugated polymer (CP) films on the micr... more Herein we report the photolithography of electrochromic conjugated polymer (CP) films on the micron scale without exposing the CP to high energy UV radiation. The synthesis of polynorbornene-based precursor copolymers having units with pendant terthiophenes and photocrosslinkable units allows for photopatterning at an earlier stage with respect to the polymerization (chemically or electrochemically) that yields the conducting polymer. The effect that the composition of the photocrosslinkable unit has on the overall process was studied, showing no effect on the electrochemical and optical performance of the conducting polymer. Electrochromic photopatterned structures down to 1 mm were obtained, together with some basic structures for microelectronics. This technique does not have any specific substrate restrictions, and can be used to pattern conducting polymers on flexible, rigid, conducting, or insulating substrates using the present photolithography facilities available to industry and academia.

Newton’s contributions to optics

Resonance, 2006

His main areas of interest are theoretical physics and physics education. He has been involved in... more

Green’s functions for spin half field theory in Rindler space

Pramana, 1977

The solutions of Dirac equation in different regions of the complete extension of Rindler space a... more The solutions of Dirac equation in different regions of the complete extension of Rindler space are obtained near the event horizons and in the asymptotic limits. Continuity of these solutions across the event horizons is established. The Green's functions are written down in the two causally disconnected regions, continued in the future (F) and past (P) regions using the techniques a la Boulware and a consistent scheme of Green's functions in all regions is exhibited.

Beyond Statistical Significance: Implications of Network Structure on Neuronal Activity

PLoS Computational Biology, 2012

It is a common and good practice in experimental sciences to assess the statistical significance ... more It is a common and good practice in experimental sciences to assess the statistical significance of measured outcomes. For this, the probability of obtaining the actual results is estimated under the assumption of an appropriately chosen null-hypothesis. If this probability is smaller than some threshold, the results are deemed statistically significant and the researchers are content in having revealed, within their own experimental domain, a ''surprising'' anomaly, possibly indicative of a hitherto hidden fragment of the underlying ''ground-truth''. What is often neglected, though, is the actual importance of these experimental outcomes for understanding the system under investigation. We illustrate this point by giving practical and intuitive examples from the field of systems neuroscience. Specifically, we use the notion of embeddedness to quantify the impact of a neuron's activity on its downstream neurons in the network. We show that the network response strongly depends on the embeddedness of stimulated neurons and that embeddedness is a key determinant of the importance of neuronal activity on local and downstream processing. We extrapolate these results to other fields in which networks are used as a theoretical framework.

Emergence of population synchrony in a layered network of the cat visual cortex

Neurocomputing, 2007

Recently, a quantitative wiring diagram for the local neuronal network of cat visual cortex was d... more Recently, a quantitative wiring diagram for the local neuronal network of cat visual cortex was described [T. Binzegger, R.J. Douglas, K.A.C. Martin, A quantitative map of the circuit of the cat primary visual cortex, J. Neurosci. 39 (24) (2004) 8441-8453.] giving the first complete estimate of synaptic connectivity among various types of neurons in different cortical layers. Here we numerically studied the activity dynamics of the resulting heterogeneous layered network of spiking integrate-and-fire neurons, connected with conductancebased synapses. The layered network exhibited, among other states, an interesting asynchronous activity with intermittent populationwide synchronizations. These population bursts (PB) were initiated by a network hot spot, and then spread into the other parts of the network. The cause of this PB is the correlation amplifying nature of recurrent connections, which becomes significant in densely coupled networks. The hot spot was located in layer 2=3, the part of the network with the highest number of excitatory recurrent connections. We conclude that in structured networks, regions with a high degree of recurrence and many outgoing fibres may be a source for population-wide synchronization.

The High-Conductance State of Cortical Networks

Neural Computation, 2008

We studied the dynamics of large networks of spiking neurons with conductance-based (nonlinear) s... more We studied the dynamics of large networks of spiking neurons with conductance-based (nonlinear) synapses and compared them to networks with current-based (linear) synapses. For systems with sparse and inhibition-dominated recurrent connectivity, weak external inputs induced asynchronous irregular firing at low rates. Membrane potentials fluctuated a few millivolts below threshold, and membrane conductances were increased by a factor 2 to 5 with respect to the resting state. This combination of parameters characterizes the ongoing spiking activity typically recorded in the cortex in vivo. Many aspects of the asynchronous irregular state in conductance-based networks could be sufficiently well characterized with a simple numerical mean field approach. In particular, it correctly predicted an intriguing property of conductance-based networks that does not appear to be shared by current-based models: they exhibit states of low-rate asynchronous irregular activity that persist for some p...

Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding

Nature Reviews Neuroscience, 2010

When two elementary brain-processes have been active together or in immediate succession, one of ... more

Nanopatterned Electrochromic Conjugated Poly(terthiophene)s via Thermal Nanoimprint Lithography of Precursor Polymer

Journal of Macromolecular Science, Part A, 2007

Abstract: Polyterthiophene nanostructures consisting of periodic nanolines were prepared using th... more Abstract: Polyterthiophene nanostructures consisting of periodic nanolines were prepared using the precursor polymer approach in conjunction with nanoimprint lithography. Precursor polynorbornylenes consisting of terthiophene side chains were prepared from their corresponding norbornylene monomers via ring opening metathesis polymerization. A copolymer consisting of terthiophene norbornylene and acetate norbornylene repeat units with a 50: 50 composition exhibited a glass transition temperature of 52 C. Nanolines of ...

Simulation of genotype performances across a larger number of environments for rice breeding using ORYZA2000

Field Crops Research, 2013

Breeding line selection with conventional field methods is limited by time, cost, and appropriate... more Breeding line selection with conventional field methods is limited by time, cost, and appropriate environments. Crop models can be used as a tool to assist in breeding line selection by extrapolating the results of multiple-environment trials (MET) to large environments in a cost-effective and faster manner. This study is the first attempt to use ORYZA2000 for the selection of drought-resistant rice genotypes, and it provides a 'virtual' platform for a large number of environmental trials. In a case study, ORYZA2000 results from two field experiments in two environments were extrapolated to 669 environments in South Asia. For these two field experiments, the differences between simulated and field-measured grain yield and total above-ground biomass for all the 69 genotypes were within the standard deviations of the field measurements. This result confirmed that ORYZA2000 has the capability to correctly represent the growth and yield of rice genotypes under different environments. Using simulation outputs for 69 genotypes in 669 environments, the performance of these genotypes was evaluated for rainfed conditions with various drought stress. With the increase in the number of environments, the effect of the genotype on phenotypic performances across environments become much more significant than that of the effects of environment and genotype-environment interactions, and heritability was also increased. Desirable rice genotypes could then be selected by breeders based on the expected yield and adaptability to various environments generated by the model. The evaluation of rice genotypic performance by ORYZA2000, as 'virtual' multiple-environment trials, can improve the reliability of selected genotypes for a wide range of environments and enhance efficiency in terms of time consumption and cost effectiveness of the breeding process.

Influence of climate variability on seasonal and interannual variations of ecosystem CO2 exchange in flooded and non-flooded rice fields in the Philippines

Field Crops Research, 2012

Seasonal rainfall in the Philippines is known to be modulated by ENSO phenomenon, with El Niño fr... more Seasonal rainfall in the Philippines is known to be modulated by ENSO phenomenon, with El Niño frequently contributing to reduced rainfall and drought while La Niña resulting in excessive rainfalls, floods and more intense typhoons. The alterations in rainfall patterns can have considerable feedback on solar radiation, air temperature, and soil moisture which can affect the ecosystem CO 2 exchange. In this paper, we assessed the effects of the ENSO events (2008-mid 2010) on the seasonal climate conditions and determined how it affected the gross primary production (GPP), ecosystem respiration (Re), and net ecosystem production (NEP) of two contrasting rice environments: flooded and non-flooded. The 2008 dry season (DS) was under a La Niña event while the 2008 wet season (WS) was a neutral one with strong tropical cyclones associated during the wet season. The 2009DS was also La Niña while the 2009WS was El Niño; however, the northern part of the Philippines experienced strong tropical cyclones. The 2010DS was under an El Niño event. The La Niña in 2008DS resulted in about 15% lower solar radiation (SR), 0.3 • C lower air temperature (T a) and 60% higher precipitation compared to the 28-year climate normal patterns. Both flooded and non-flooded rice fields had lower NEP in 2008 DS (164 and 14 g C m −2 , respectively) than in 2008 WS (295 and 82 g C m −2 , respectively) because the climate anomaly resulted in SR-driven decrease in GPP. The La Niña in 2009DS even resulted in 0.2 • C lower air temperature and 40% more precipitation than the 2008DS La Niña. This cooler temperature resulted in lower Re in flooded rice fields while the higher precipitation resulted in higher GPP in non-flooded fields since the climate was favorable for the growth of the aerobic rice, the ratoon crops and the weeds. This climate anomaly benefitted both flooded and non-flooded rice fields by increasing NEP (351 and 218 g C m −2 , respectively). However, NEP decreased in 2009WS in both flooded and non-flooded rice fields (225 and 39 g C m −2 , respectively) due to the devastating effects of the strong tropical cyclones that hit the northern part of the Philippines. On the other hand, the El Niño event during 2010DS resulted in about 6% higher solar radiation, 0.4 • C higher air temperature and 67% lower precipitation than the 28-year climate normal pattern. The NEP of flooded and non-flooded rice fields were closely similar at 187 and 174 g C m −2 , respectively. This climate anomaly resulted in T a-driven increase in Re, as well as vapor pressure deficit (VPD)-driven decrease in GPP in flooded rice fields. The GPP and Re in non-flooded rice fields were less sensitive to higher VPD and higher T a , respectively. It appears that the net ecosystem CO 2 exchange in non-flooded rice field was less sensitive to an El Niño event.

Shaping corticostriatal connectivity with STDP

BMC Neuroscience, 2011

Modification of the Gum Elastic Bougie

Anesthesia & Analgesia, 2006

The heat and humidity in tropical countries causes the bougie to lose its stiffness (Fig. 1), mak... more

Comparisons of energy balance and evapotranspiration between flooded and aerobic rice fields in the Philippines

Agricultural Water Management, 2011

The seasonal and annual variability of sensible heat flux (H), latent heat flux (LE), evapotransp... more The seasonal and annual variability of sensible heat flux (H), latent heat flux (LE), evapotranspiration (ET), crop coefficient (K c) and crop water productivity (WP ET) were investigated under two different rice environments, flooded and aerobic soil conditions, using the eddy covariance (EC) technique during 2008-2009 cropping periods. Since we had only one EC system for monitoring two rice environments, we had to move the system from one location to the other every week. In total, we had to gap-fill an average of 50-60% of the missing weekly data as well as those values rejected by the quality control tests in each rice field in all four cropping seasons. Although the EC method provides a direct measurement of LE, which is the energy used for ET, we needed to correct the values of H and LE to close the energy balance using the Bowen ratio closure method before we used LE to estimate ET. On average, the energy balance closure before correction was 0.72 ± 0.06 and it increased to 0.99 ± 0.01 after correction. The G in both flooded and aerobic fields was very low. Likewise, the energy involved in miscellaneous processes such as photosynthesis, respiration and heat storage in the rice canopy was not taken into consideration. Average for four cropping seasons, flooded rice fields had 19% more LE than aerobic fields whereas aerobic rice fields had 45% more H than flooded fields. This resulted in a lower Bowen ratio in flooded fields (0.14 ± 0.03) than in aerobic fields (0.24 ± 0.01). For our study sites, evapotranspiration was primarily controlled by net radiation. The aerobic rice fields had lower growing season ET rates (3.81 ± 0.21 mm d −1) than the flooded rice fields (4.29 ± 0.23 mm d −1), most probably due to the absence of ponded water and lower leaf area index of aerobic rice. Likewise, the crop coefficient, K c , of aerobic rice was significantly lower than that of flooded rice. For aerobic rice, K c values were 0.95 ± 0.01 for the vegetative stage, 1.00 ± 0.01 for the reproductive stage, 0.97 ± 0.04 for the ripening stage and 0.88 ± 0.03 for the fallow period, whereas, for flooded rice, K c values were 1.04 ± 0.04 for the vegetative stage, 1.11 ± 0.05 for the reproductive stage, 1.04 ± 0.05 for the ripening stage and 0.93 ± 0.06 for the fallow period. The average annual ET was 1301 mm for aerobic rice and 1440 mm for flooded rice. This corresponds to about 11% lower total evapotranspiration in aerobic fields than in flooded fields. However, the crop water productivity (WP ET) of aerobic rice (0.42 ± 0.03 g grain kg −1 water) was significantly lower than that of flooded rice (1.26 ± 0.26 g grain kg −1 water) because the grain yields of aerobic rice were very low since they were subjected to water stress. The results of this investigation showed significant differences in energy balance and evapotranspiration between flooded and aerobic rice ecosystems. Aerobic rice is one of the promising water-saving technologies being developed to lower the water requirements of the rice crop to address the issues of water scarcity. This information should be taken into consideration in evaluating alternative water-saving technologies for environmentally sustainable rice production systems.

CO2/heat fluxes in rice fields: Comparative assessment of flooded and non-flooded fields in the Philippines

Agricultural and Forest Meteorology, 2009

The seasonal fluxes of heat, moisture and CO 2 were investigated under two different rice environ... more The seasonal fluxes of heat, moisture and CO 2 were investigated under two different rice environments: flooded and aerobic soil conditions, using the eddy covariance technique during 2008 dry season. The fluxes were correlated with the microclimate prevalent in each location. This study was intended to monitor the environmental impact, in terms of C budget and heat exchange, of shifting from lowland rice production to aerobic rice cultivation as an alternative to maintain crop productivity under water scarcity. The aerobic rice fields had higher sensible heat flux (H) and lower latent heat flux (LE) compared to flooded fields. On seasonal average, aerobic rice fields had 48% more sensible heat flux while flooded rice fields had 20% more latent heat flux. Consequently, the aerobic rice fields had significantly higher Bowen ratio (0.25) than flooded fields (0.14), indicating that a larger proportion of the available net radiation was used for sensible heat transfer or for warming the surrounding air. The total C budget integrated over the cropping period showed that the net ecosystem exchange (NEE) in flooded rice fields was about three times higher than in aerobic fields while gross primary production (GPP) and ecosystem respiration (R e) were 1.5 and 1.2 times higher, respectively. The high GPP of flooded rice ecosystem was evident because the photosynthetic capacity of lowland rice is naturally large. The R e of flooded rice fields was also relatively high because it was enhanced by the high photosynthetic activities of lowland rice as manifested by larger above-ground plant biomass. The NEE, GPP, and R e values for flooded rice fields were À258, 778, and 521 g C m À2 , respectively. For aerobic rice fields, values were À85, 515, and 430 g C m À2 for NEE, GPP, and R e , respectively. The ratio of R e /GPP in flooded fields was 0.67 while it was 0.83 for aerobic rice fields. This short-term data showed significant differences in C budget and heat exchange between flooded and aerobic rice ecosystems. Further investigation is needed to clarify seasonal and inter-annual variations in microclimate, carbon and water budget of different rice production systems.

Solid-State Conversion of Processable 3,4-Ethylenedioxythiophene (EDOT) Containing Poly(arylsilane) Precursors toπ-Conjugated Conducting Polymers

Advanced Materials, 2008