Hemant Bokil | Boston Scientific Corporation (original) (raw)
Papers by Hemant Bokil
Physical Review B, 1997
We study the problem of flux penetration into type-I superconductors with a high demagnetization ... more We study the problem of flux penetration into type-I superconductors with a high demagnetization factor (slab geometry). Assuming that the interface between the normal and superconducting regions is sharp, that flux diffuses rapidly in the normal regions, and that thermal effects are negligible, we analyze the process by which flux invades the sample as the applied field is increased slowly from zero. We find that flux does not penetrate gradually. Rather there is an instability in the process and the flux penetrates from the boundary in a series of bursts, accompanied by the formation of isolated droplets of the normal phase, leading to a multiply connected flux domain structure similar to that seen in experiments. 74.55.+h, 05.70.Ln,
Physical Review Letters, 1995
We study the gauge glass model for the vortex glass transition in type-II superconductors, includ... more We study the gauge glass model for the vortex glass transition in type-II superconductors, including screening of the interaction between vortices.
Journal of Physics A-mathematical and General, 1996
We study the chirality in the Villain form of the XY spin glass in two-dimensions by Monte Carlo ... more We study the chirality in the Villain form of the XY spin glass in two-dimensions by Monte Carlo simulations. We calculate the chiral-glass correlation length exponent νCG and find that νCG = 1.8 ± 0.3 in reasonable agreement with earlier studies. This indicates that the chiral and phase variables are decoupled on long length scales and diverge as T → 0 with different exponents, since the spin-glass correlation length exponent was found, in earlier studies, to be about 1.0.
Recent work has suggested the existence of glassy behavior in a ferromagnetic model with a foursp... more Recent work has suggested the existence of glassy behavior in a ferromagnetic model with a fourspin interaction. Motivated by these findings, we have studied the dynamics of this model using Monte Carlo simulations with particular attention being paid to two-time quantities. We find that the system shares many features in common with glass forming liquids. In particular, the model exhibits: (i) a very long-lived metastable state, (ii) autocorrelation functions that show stretched exponential relaxation, (iii) a non-equilibrium timescale that appears to diverge at a well defined temperature, and (iv) low temperature aging behaviour characteristic of glasses.
Physical Review Letters, 1999
Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. ... more Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment [1] on our paper [2] the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling between the replicas. They claim that the results of the MCS indicate replica symmetry breaking (RSB), while those of the MKA are trivial, and that moderate size lattices display the true low temperature behavior. Here we show that these claims are incorrect, and that the results of MCS and MKA both can be explained within the droplet picture.
Physical Review Letters, 1999
A Reply to the Comment by E. Marinari et al.
Physical Review Letters, 1999
A Comment on the Letter by E. Marinari et al., Phys. Rev. Lett. 81, 1698 (1998). The authors of t... more A Comment on the Letter by E. Marinari et al., Phys. Rev. Lett. 81, 1698 (1998). The authors of the Letter offer a Reply.
European Physical Journal B, 2000
We study the link overlap between two replicas of an Ising spin glass in three dimensions using t... more We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link overlap shows the asymmetric shape and large sample-to-sample variations found in Monte Carlo simulations and usually attributed to replica symmetry breaking. However, the scaling of the width of the distribution, and the link overlap in the presence of a weak coupling between the two replicas are in agreement with the droplet picture. We also discuss why it is impossible to see the asymptotic droplet-like behaviour for moderate system sizes and temperatures not too far below the critical temperature.
Physical Review E, 2000
We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approxima... more We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behaviour for strong values of the couplings. We also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For the spin glass in a field the maximum of non-self-averaging follows for given system size a line that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte-Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica-symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the one-step replica symmetry approach breaking predicts two transitions, the first transition being dynamical and the second thermodynamical. Our results suggest that in real finite dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.
Physical Review B, 2000
Recent work has suggested the existence of glassy behavior in a ferromagnetic model with a foursp... more Recent work has suggested the existence of glassy behavior in a ferromagnetic model with a fourspin interaction. Motivated by these findings, we have studied the dynamics of this model using Monte Carlo simulations with particular attention being paid to two-time quantities. We find that the system shares many features in common with glass forming liquids. In particular, the model exhibits: (i) a very long-lived metastable state, (ii) autocorrelation functions that show stretched exponential relaxation, (iii) a non-equilibrium timescale that appears to diverge at a well defined temperature, and (iv) low temperature aging behaviour characteristic of glasses.
Physical Review Letters, 1999
In a recent letter Marinari et al. introduced a new method to study spin glass transitions and ar... more In a recent letter Marinari et al. introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method unambiguously shows that replica symmetry breaking (RSB) occurs in shortrange spin glasses. In this comment we show that while the method introduced in [1] is indeed useful for studying transitions in systems where TRS is absent (such as the p-spin model studied by them), the conclusion that it shows the existence of RSB in short-range spin glasses is wrong.
We have studied the Parisi overlap distribution for the three-dimensional Ising spin glass in the... more We have studied the Parisi overlap distribution for the three-dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T ≃ 0.7Tc and system sizes up to L = 32, we found a P (q) as expected for full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behavior in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that system sizes larger than the correlation length have not been achieved.
Physical Review Letters, 1999
ABSTRACT
Physical Review B, 2000
We have argued in recent papers that the Monte Carlo results for the equilibrium properties of th... more We have argued in recent papers that the Monte Carlo results for the equilibrium properties of the Edwards-Anderson spin glass in three dimensions, which had been interpreted earlier as providing evidence for replica symmetry breaking, can be explained quite simply within the droplet model once finite size effects and proximity to the critical point are taken into account. In this paper we show that similar considerations are sufficient to explain the Monte Carlo data in four dimensions. In particular, we study the Parisi overlap and the link overlap for the four-dimensional Ising spin glass in the Migdal-Kadanoff approximation. Similar to what is seen in three dimensions, we find that temperatures well below those studied in the Monte Carlo simulations have to be reached before the droplet model predictions become apparent. We also show that the double-peak structure of the link overlap distribution function is related to the difference between domain-wall excitations that cross the entire system and droplet excitations that are confined to a smaller region.
European Physical Journal B, 2000
We study the link overlap between two replicas of an Ising spin glass in three dimensions using t... more We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link overlap shows the asymmetric shape and large sample-to-sample variations found in Monte-Carlo simulations and usually attributed to replica symmetry breaking. However, the scaling of the width of the distribution, and the link overlap in the presence of a weak coupling between the two replicas are in agreement with the droplet picture. We also discuss why it is impossible to see the asymptotic droplet-like behaviour for moderate system sizes and temperatures not too far below the critical temperature.
Physical Review Letters, 1998
We have studied the Parisi overlap distribution for the three-dimensional Ising spin glass in the... more We have studied the Parisi overlap distribution for the three-dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T ≃ 0.7Tc and system sizes up to L = 32, we found a P (q) as expected for full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behavior in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that system sizes larger than the correlation length have not been achieved.
PLOS One, 2009
Many neuroscientific reports reference discrete macro-anatomical regions of the brain which were ... more Many neuroscientific reports reference discrete macro-anatomical regions of the brain which were delineated according to a brain atlas or parcellation protocol. Currently, however, no widely accepted standards exist for partitioning the cortex and subcortical structures, or for assigning labels to the resulting regions, and many procedures are being actively used. Previous attempts to reconcile neuroanatomical nomenclatures have been largely qualitative, focusing on the development of thesauri or simple semantic mappings between terms. Here we take a fundamentally different approach, discounting the names of regions and instead comparing their definitions as spatial entities in an effort to provide more precise quantitative mappings between anatomical entities as defined by different atlases. We develop an analytical framework for studying this brain atlas concordance problem, and apply these methods in a comparison of eight diverse labeling methods used by the neuroimaging community. These analyses result in conditional probabilities that enable mapping between regions across atlases, which also form the input to graph-based methods for extracting higher-order relationships between sets of regions and to procedures for assessing the global similarity between different parcellations of the same brain. At a global scale, the overall results demonstrate a considerable lack of concordance between available parcellation schemes, falling within chance levels for some atlas pairs. At a finer level, this study reveals spatial relationships between sets of defined regions that are not obviously apparent; these are of high potential interest to researchers faced with the challenge of comparing results that were based on these different anatomical models, particularly when coordinate-based data are not available. The complexity of the spatial overlap patterns revealed points to problems for attempts to reconcile anatomical parcellations and nomenclatures using strictly qualitative and/or categorical methods. Detailed results from this study are made available via an interactive web site at http://obart.info.
Spectra and coherences are standard measures of association within and between time series. These... more Spectra and coherences are standard measures of association within and between time series. These measures have several advantages over their time-domain counterparts, not the least of which is the ability to derive and estimate confidence intervals. However, comparing spectra and coherences between two groups of observation is a problem that has not received much attention. This problem is important in neuroscience since it is often of great interest to determine whether the estimates differ between distinct experimental/behavioral conditions. Here we propose one approach to this problem. Based on the known distributional properties of spectral and coherence estimates, we derive a test for equality of two spectral or coherence estimates. The test is applicable to unequal sample sizes. We also derive jackknifed estimates of the variance of the proposed test statistic. We suggest that comparing the estimates obtained from the jackknife procedure with the theoretical estimates provides a robust means of determining whether the data in question shows non-Gaussian or non-stationary behavior. Finally, we present applications of the method to simulated and real data.
Physical Review B, 1997
We study the problem of flux penetration into type-I superconductors with a high demagnetization ... more We study the problem of flux penetration into type-I superconductors with a high demagnetization factor (slab geometry). Assuming that the interface between the normal and superconducting regions is sharp, that flux diffuses rapidly in the normal regions, and that thermal effects are negligible, we analyze the process by which flux invades the sample as the applied field is increased slowly from zero. We find that flux does not penetrate gradually. Rather there is an instability in the process and the flux penetrates from the boundary in a series of bursts, accompanied by the formation of isolated droplets of the normal phase, leading to a multiply connected flux domain structure similar to that seen in experiments. 74.55.+h, 05.70.Ln,
Physical Review Letters, 1995
We study the gauge glass model for the vortex glass transition in type-II superconductors, includ... more We study the gauge glass model for the vortex glass transition in type-II superconductors, including screening of the interaction between vortices.
Journal of Physics A-mathematical and General, 1996
We study the chirality in the Villain form of the XY spin glass in two-dimensions by Monte Carlo ... more We study the chirality in the Villain form of the XY spin glass in two-dimensions by Monte Carlo simulations. We calculate the chiral-glass correlation length exponent νCG and find that νCG = 1.8 ± 0.3 in reasonable agreement with earlier studies. This indicates that the chiral and phase variables are decoupled on long length scales and diverge as T → 0 with different exponents, since the spin-glass correlation length exponent was found, in earlier studies, to be about 1.0.
Recent work has suggested the existence of glassy behavior in a ferromagnetic model with a foursp... more Recent work has suggested the existence of glassy behavior in a ferromagnetic model with a fourspin interaction. Motivated by these findings, we have studied the dynamics of this model using Monte Carlo simulations with particular attention being paid to two-time quantities. We find that the system shares many features in common with glass forming liquids. In particular, the model exhibits: (i) a very long-lived metastable state, (ii) autocorrelation functions that show stretched exponential relaxation, (iii) a non-equilibrium timescale that appears to diverge at a well defined temperature, and (iv) low temperature aging behaviour characteristic of glasses.
Physical Review Letters, 1999
Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. ... more Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment [1] on our paper [2] the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling between the replicas. They claim that the results of the MCS indicate replica symmetry breaking (RSB), while those of the MKA are trivial, and that moderate size lattices display the true low temperature behavior. Here we show that these claims are incorrect, and that the results of MCS and MKA both can be explained within the droplet picture.
Physical Review Letters, 1999
A Reply to the Comment by E. Marinari et al.
Physical Review Letters, 1999
A Comment on the Letter by E. Marinari et al., Phys. Rev. Lett. 81, 1698 (1998). The authors of t... more A Comment on the Letter by E. Marinari et al., Phys. Rev. Lett. 81, 1698 (1998). The authors of the Letter offer a Reply.
European Physical Journal B, 2000
We study the link overlap between two replicas of an Ising spin glass in three dimensions using t... more We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link overlap shows the asymmetric shape and large sample-to-sample variations found in Monte Carlo simulations and usually attributed to replica symmetry breaking. However, the scaling of the width of the distribution, and the link overlap in the presence of a weak coupling between the two replicas are in agreement with the droplet picture. We also discuss why it is impossible to see the asymptotic droplet-like behaviour for moderate system sizes and temperatures not too far below the critical temperature.
Physical Review E, 2000
We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approxima... more We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behaviour for strong values of the couplings. We also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For the spin glass in a field the maximum of non-self-averaging follows for given system size a line that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte-Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica-symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the one-step replica symmetry approach breaking predicts two transitions, the first transition being dynamical and the second thermodynamical. Our results suggest that in real finite dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.
Physical Review B, 2000
Recent work has suggested the existence of glassy behavior in a ferromagnetic model with a foursp... more Recent work has suggested the existence of glassy behavior in a ferromagnetic model with a fourspin interaction. Motivated by these findings, we have studied the dynamics of this model using Monte Carlo simulations with particular attention being paid to two-time quantities. We find that the system shares many features in common with glass forming liquids. In particular, the model exhibits: (i) a very long-lived metastable state, (ii) autocorrelation functions that show stretched exponential relaxation, (iii) a non-equilibrium timescale that appears to diverge at a well defined temperature, and (iv) low temperature aging behaviour characteristic of glasses.
Physical Review Letters, 1999
In a recent letter Marinari et al. introduced a new method to study spin glass transitions and ar... more In a recent letter Marinari et al. introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method unambiguously shows that replica symmetry breaking (RSB) occurs in shortrange spin glasses. In this comment we show that while the method introduced in [1] is indeed useful for studying transitions in systems where TRS is absent (such as the p-spin model studied by them), the conclusion that it shows the existence of RSB in short-range spin glasses is wrong.
We have studied the Parisi overlap distribution for the three-dimensional Ising spin glass in the... more We have studied the Parisi overlap distribution for the three-dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T ≃ 0.7Tc and system sizes up to L = 32, we found a P (q) as expected for full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behavior in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that system sizes larger than the correlation length have not been achieved.
Physical Review Letters, 1999
ABSTRACT
Physical Review B, 2000
We have argued in recent papers that the Monte Carlo results for the equilibrium properties of th... more We have argued in recent papers that the Monte Carlo results for the equilibrium properties of the Edwards-Anderson spin glass in three dimensions, which had been interpreted earlier as providing evidence for replica symmetry breaking, can be explained quite simply within the droplet model once finite size effects and proximity to the critical point are taken into account. In this paper we show that similar considerations are sufficient to explain the Monte Carlo data in four dimensions. In particular, we study the Parisi overlap and the link overlap for the four-dimensional Ising spin glass in the Migdal-Kadanoff approximation. Similar to what is seen in three dimensions, we find that temperatures well below those studied in the Monte Carlo simulations have to be reached before the droplet model predictions become apparent. We also show that the double-peak structure of the link overlap distribution function is related to the difference between domain-wall excitations that cross the entire system and droplet excitations that are confined to a smaller region.
European Physical Journal B, 2000
We study the link overlap between two replicas of an Ising spin glass in three dimensions using t... more We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link overlap shows the asymmetric shape and large sample-to-sample variations found in Monte-Carlo simulations and usually attributed to replica symmetry breaking. However, the scaling of the width of the distribution, and the link overlap in the presence of a weak coupling between the two replicas are in agreement with the droplet picture. We also discuss why it is impossible to see the asymptotic droplet-like behaviour for moderate system sizes and temperatures not too far below the critical temperature.
Physical Review Letters, 1998
We have studied the Parisi overlap distribution for the three-dimensional Ising spin glass in the... more We have studied the Parisi overlap distribution for the three-dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T ≃ 0.7Tc and system sizes up to L = 32, we found a P (q) as expected for full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behavior in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that system sizes larger than the correlation length have not been achieved.
PLOS One, 2009
Many neuroscientific reports reference discrete macro-anatomical regions of the brain which were ... more Many neuroscientific reports reference discrete macro-anatomical regions of the brain which were delineated according to a brain atlas or parcellation protocol. Currently, however, no widely accepted standards exist for partitioning the cortex and subcortical structures, or for assigning labels to the resulting regions, and many procedures are being actively used. Previous attempts to reconcile neuroanatomical nomenclatures have been largely qualitative, focusing on the development of thesauri or simple semantic mappings between terms. Here we take a fundamentally different approach, discounting the names of regions and instead comparing their definitions as spatial entities in an effort to provide more precise quantitative mappings between anatomical entities as defined by different atlases. We develop an analytical framework for studying this brain atlas concordance problem, and apply these methods in a comparison of eight diverse labeling methods used by the neuroimaging community. These analyses result in conditional probabilities that enable mapping between regions across atlases, which also form the input to graph-based methods for extracting higher-order relationships between sets of regions and to procedures for assessing the global similarity between different parcellations of the same brain. At a global scale, the overall results demonstrate a considerable lack of concordance between available parcellation schemes, falling within chance levels for some atlas pairs. At a finer level, this study reveals spatial relationships between sets of defined regions that are not obviously apparent; these are of high potential interest to researchers faced with the challenge of comparing results that were based on these different anatomical models, particularly when coordinate-based data are not available. The complexity of the spatial overlap patterns revealed points to problems for attempts to reconcile anatomical parcellations and nomenclatures using strictly qualitative and/or categorical methods. Detailed results from this study are made available via an interactive web site at http://obart.info.
Spectra and coherences are standard measures of association within and between time series. These... more Spectra and coherences are standard measures of association within and between time series. These measures have several advantages over their time-domain counterparts, not the least of which is the ability to derive and estimate confidence intervals. However, comparing spectra and coherences between two groups of observation is a problem that has not received much attention. This problem is important in neuroscience since it is often of great interest to determine whether the estimates differ between distinct experimental/behavioral conditions. Here we propose one approach to this problem. Based on the known distributional properties of spectral and coherence estimates, we derive a test for equality of two spectral or coherence estimates. The test is applicable to unequal sample sizes. We also derive jackknifed estimates of the variance of the proposed test statistic. We suggest that comparing the estimates obtained from the jackknife procedure with the theoretical estimates provides a robust means of determining whether the data in question shows non-Gaussian or non-stationary behavior. Finally, we present applications of the method to simulated and real data.