# Lawrence SirovichThe Rockefeller University | Rockefeller · Center for Physics and Biology

Lawrence Sirovich

Ph. D

## About

249

Publications

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29,395

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Citations since 2017

## Publications

Publications (249)

A fresh approach to the dynamics of gene assemblies is presented. Central to the exposition are the concepts of: high value genes; correlated activity; and the orderly unfolding of gene dynamics; and especially dynamic mode decomposition, DMD, a remarkable new tool for dissecting dynamics. This program is carried out, in detail, for the Orlando et...

Many gene array studies of the yeast cell cycle have been performed (1–4). Largely, these studies contain elements drawn from laboratory experiments. The present investigation determines cell division cycle (CDC) genes solely from the data (2).
It is shown by simple reasoning that the dynamics of the ∼ 6000 yeast genes are described by a ∼6 dimensi...

Under realistic estimates of geophysical conditions, two procedures are presented for diminishing the intensity of a hurricane: before it reaches landfall; or quenching it in its incipient stage. We demonstrate that within present-day technology, it is possible to mix the cold deep ocean with the warm surface layer sufficiently, and in a timely man...

Application of concepts from information theory have revealed new features of Single Nucleotide Polymorphism (SNP) organization.. These features lead to effective classifiers by which to distinguish genomic sequences of contrasting phenotypes; as in case/control cohorts.
When applied to a disease/control database, a disease classifier results; a pa...

This paper reports on an investigation of disease discovery from genomic data, by methods which depart substantially from customary practices found in the investigation of genome-wide association studies. Such data in general are composed of the genomic content from two contrasting phenotypes, e.g., disease versus control populations, and the analy...

A general approach is presented for the extraction of a classifier of disease risk that is latent in large scale disease/control databases. Novel features are the following: (1) a data reorganization into a regularized standard form that emphasizes individual alleles instead of the single nucleotide polymorphism (Snp) allele pair to which they belo...

Theoretical and experimental evidence is presented for the presence in nervous tissue of neurons whose firing rate faithfully follow their input stimulus. Such neurons are shown to deliver their spikes with minimum dissipation per spike. This optimal performance is likely accomplished by use of local circuitry that adjusts conductances to match inp...

This Teaching Resource provides lecture notes, slides, and a student assignment for a lecture on probabilistic reasoning in the analysis of biological data. General probabilistic frameworks are introduced, and a number of standard probability distributions are described using simple intuitive ideas. Particular attention is focused on random arrival...

We derive a model of a neuron's interspike interval probability density through analysis of the first passage problem. The fit of our expression to retinal ganglion cell laboratory data extracts three physiologically relevant parameters, with which our model yields input-output features that conform to laboratory results. Preliminary analysis sugge...

Large, recently-available genomic databases cover a wide range of life forms, suggesting opportunity for insights into genetic structure of biodiversity. In this study we refine our recently-described technique using indicator vectors to analyze and visualize nucleotide sequences. The indicator vector approach generates correlation matrices, dubbed...

Comparative DNA sequence analysis provides insight into evolution and helps construct a natural classification reflecting the Tree of Life. The growing numbers of organisms represented in DNA databases challenge tree-building techniques and the vertical hierarchical classification may obscure relationships among some groups. Approaches that can inc...

The essential midline symmetry of human faces is shown to play a key role in facial coding and recognition. This also has deep and important connections with recent explorations of the organization of primate cortex, as well as human psychophysical experiments. Evidence is presented that the dimension of face recognition space for human faces is dr...

The kidneys perform two major functions. First, they excrete most of the end prod ucts of bodily metabolism, and second, they control the concentrations of most of the constituents of the body fluids. The main goal of this chapter is to gain some under standing of the processes by which the urine is formed and waste products removed from the bloods...

The circulatory system forms a closed loop for the flow of blood that carries oxygen from the lungs to the tissues of the body and carries carbon dioxide from the tissues back to the lungs (Figs. 11.1 and 11.2). There are two pumps to overcome the resistance and maintain a constant flow. The left heart receives oxygen-rich blood from the lungs and...

Given an arbitrary standardized (zero mean and unit variance) prob-ability density, we measure its departure from the standard nor-mal density by the L 2 distance between the two density functions. In particular, we consider three different L 2 norms, each distin-guished by their weight functions. We investigate the reciprocal Gaussian, uniform, an...

A mathematical model, of general character for the dynamic description of coupled neural oscillators is presented. The population approach that is employed applies equally to coupled cells as to populations of such coupled cells. The formulation includes stochasticity and preserves details of precisely firing neurons. Based on the generally accepte...

The dimensionality of face space is measured objectively in a psychophysical study. Within this framework, we obtain a measurement of the dimension for the human visual system. Using an eigenface basis, evidence is presented that talented human observers are able to identify familiar faces that lie in a space of roughly 100 dimensions and the avera...

We present a mathematical model which includes TNF-alpha initiated survival and apoptotic cascades, as well as nuclear transcription of IkappaB. These pathways play a crucial role in deciding cell fate in response to inflammation and infection. Our model incorporates known specific protein-protein interactions as identified by experiments. Using th...

We introduce a method of accurately and efficiently modeling a large population of participants in a financial market. Each participant is modeled as having an internal preference state affected by the continual arrival of exogenous information and by the behavior of others. In order to describe a community of traders, we introduce a population equ...

A population formulation of neuronal activity is employed to study an excitatory network of (spiking) neurons receiving external input as well as recurrent feedback. At relatively low levels of feedback, the network exhibits time stationary asynchronous behavior. A stability analysis of this time stationary state leads to an analytical criterion fo...

In optical imaging experiments of primary visual cortex, visual stimuli evoke a complicated dynamics. Typically, any stimulus with sufficient contrast evokes a response. Much of the response is the same regardless of which stimulus is presented. For instance, when oriented drifting gratings are presented to the visual system, over 90% of the respon...

Many studies have demonstrated that the primary visual cortex contains multiple functional maps of visual properties (e.g., ocular dominance, orientation preference, and spatial-frequency preference), but as yet no consistent picture has emerged as to how these maps are related to one another. Three divergent, prior optical-imaging studies of spati...

In Chapter 10, we examined finite element methods for the numerical solution of Laplace's equation. In this chapter, we propose an alternative approach. We introduce the idea of reformulating Laplace's equation as a boundary integral equation (BIE), and then we consider the numerical solution of Laplace's equation by numerically solving its reformu...

In many experimental circumstances, heart dynamics are, to a good approximation, periodic. For this reason, it makes sense to use high-resolution methods in the frequency domain to visualize the spectrum of imaging data of the heart and to estimate the deterministic signal content and extract the periodic signal from background noise in experimenta...

The second Rehnquist Court has remained unchanged in composition for 8 yr, resulting in a large temporally stable database. This paper reports on a mathematically objective analysis of this ensemble of rulings aimed at extracting key patterns and latent information. Although the rulings of a nine-justice Court require representation in nine dimensi...

A novel approach to cortical modelling was introduced by Knight and co-workers in 1996. In their presentation cortical dynamics is formulated in terms of interacting populations of neurons, a perspective that is in part motivated by modern cortical imaging. The approach may be regarded as the application of statistical mechanics to neuronal populat...

Previous methods for analyzing optical imaging data have relied heavily on temporal averaging. However, response dynamics are rich sources of information. Here, we develop and present a method that combines principal component analysis and multitaper harmonic analysis to extract the statistically significant spatial and temporal response from optic...

The dynamical equations for the energy in a turbulent channel flow have been developed by using the Karhunen-Loéve modes to represent the velocity field. The energy balance equations show that all the energy in the flow originates from the applied pressure gradient acting on the mean flow. Energy redistribution occurs through triad interactions, wh...

A novel approach to cortical modeling was introduced by Knight et al. (1996). In their presentation cortical dynamics is formulated in terms of in- teracting populations of neurons, a perspective that is in part motivated by modern cortical imaging (For a review see Sirovich and Kaplan (2002)).

Any realistic model of the neuronal pathway from the retina to the visual cortex (V1) must account for the bursting behavior of neurons in the lateral geniculate nucleus (LGN). A robust but minimal model, the integrate-and-fire-or-burst (IFB) model, has recently been proposed for individual LGN neurons. Based on this, we derive a dynamic population...

We consider a problem of blind signal extraction from noisy multivariate data, in which each datum represents a system's response, observed under a particular experimental condition. Our prototype example is multipixel functional images of brain activity in response to a set of prescribed experimental stimuli. We present a novel multivariate analys...

A typical functional region in cortex contains thousands of neurons, therefore direct neuronal simulation of the dynamics of such a region necessarily involves massive computation. A recent efficient alternative formulation is in terms of kinetic equations that describe the collective activity of the whole population of similar neurons. A previous...

Citation
Ehud Kaplan, A. K. Prashanth, Cameron Brennan, and Lawrence Sirovich, "Optical Imaging: A Review," Optics & Photonics News 11(7), 26-30 (2000)
http://www.opticsinfobase.org/opn/abstract.cfm?URI=opn-11-7-26

The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upward shift in voltage in response to each synaptic e...

Low-dimensional representations of sensory signals are key to solving many of the computational problems encountered in high-level vision. Principal Component Analysis (PCA) has been used in the past to derive such compact representations for the object class of human faces. Here, with an interpretation of PCA as a probabilistic model, we employ tw...

We present a novel analysis technique for the extraction of neuronal activity patterns from functional imaging data. We illustrate this technique on data from optical imaging. Optical imaging of the mammalian visual cortex probe the patterns in which the neuronal responses to various aspects of the visual world, such as orientation and color, are s...

The behavior of an aggregate of neurons is followed by means of a population equation which describes the probability density of neurons as a function of membrane potentials. The model is based on integrate-and-fire membrane dynamics and a synaptic dynamics which produce a fixed potential jump in response to stimulation. In spite of the simplicity...

The dynamics of an orientation hypercolumn in visual cortex is investigated by means of kinetic equations that describe the dynamics of interacting populations of neurons. The derivation of these follows rigorously from consideration of individual neuron membrane dynamics. In previous work it has been shown that these equations produce results that...

A low-dimensional representation of sensory signals is the key to
solving many of the computational problems encountered in high-level
vision. Principal component analysis (PCA) has been used in the past to
derive such compact representations for the object class of human faces.
Here, with an interpretation of PCA as a probabilistic model, we emplo...

The dynamics of large populations of interacting neurons is investigated. Redundancy present in subpopulations of cortical networks is exploited through the introduction of a probabilistic description. A derivation of the kinetic equations for such subpopulations, under general transmembrane dynamics, is presented.
The particular case of integrate...

A typical functional region in cortex contains thousands of neurons, therefore direct neuronal simulation of the dynamics of such a region necessarily involves massive computation. A recent efficient alternative formulation is in terms of kinetic equations that describe the collective activity of the whole population of similar neurons. A previous...

We investigate a sequence of low-dimensional models of turbulent channel flows. These models are based on the extraction of the Karhunen–Loève (KL) eigenfunctions from a large-scale simulation in a wide channel with R
*=180 (based on the friction velocity). KL eigenfunctions provide an optimal coordinate system in which to represent the dynamics of...

In vivo optical imaging of the visual cortex (both of intrinsic signals as well as with voltagesensitive dyes) makes the activity of entire neuronal assemblies accessible for the first time. However, the magnitude of the data collected (?1 Gbyte/minute) as well as the tiny signal-tonoise ratio (O(10 Gamma4 )) necessitate the development of optimize...

Turbulent solutions of the one-dimensional complex Ginzburg-Landau equation when the dissipation is very small are considered. It is found that probability distributions are strictly Gaussian, implying hard turbulence does not occur. Also, no inertial range is observed in the wavenumber spectrum. As expected a linear relation between the attractor...

Knowledge of the response of the primary visual cortex to the various spatial frequencies and orientations in the visual scene should help us understand the principles by which the brain recognizes patterns. Current information about the cortical layout of spatial frequency response is still incomplete because of difficulties in recording and inter...

The Empirical Orthogonal Function (EOF) decomposition is used to analyze time records of AVHRR sea surface temperature observations of the Western North Atlantic from 32.9 ffi to 43.6 ffi N and from 62.7 ffi to 76.3 ffi W. A manually declouded dataset covering the spring of 1985 is analyzed. The majority (80%) of the variance about the mean is acco...

Experimental datasets from a variety of mixing flows are analyzed to assess the degree of mixing and the rate of mixing. The concentration field of an axisymmetric jet is measured at ten downstream locations by optical imaging of Rayleigh scattering from a laser sheet. A new measure of mixedness, based on entropy considerations, and a related mixin...

This paper addresses the problem of using the Karhunen-Lo`eve transform with partial data. Given a set of empirical eigenfunctions we show how to recover the modal coefficients for each gappy snapshot by a least-squares procedure. This method gives an unbiased estimate of the data that lay in the gaps and permits gaps to be filled in a reasonable m...

Extensions to the Karhunen-Loève transform applied to complicated phenomena are demonstrated on Rayleigh-Benard thermal convection phenomena. The extensions deal with the role of the mean flow, and with the enhancement of the robustness of the Karhunen-Loève basis when used for a range of parameter values, such as Rayleigh number, other than the pa...

We consider the problem of estimating a small stimulus-induced response to stimulation that is masked by a fluctuating background when measurements of the background in the absence of stimulation are available, as is common in optical imaging of the cortex and in many other experimental situations. Two related methods based on the Karhunen-Loève pr...

In many situations involving flows of high Reynolds number (where inertial forces dominate over viscous forces), such as aircraft flight and the pipeline transportation of fuels, turbulent drag is an important factor limiting performance. This has led to an extensive search for both active and passive methods for drag reduction. Here we report the...

Minimal channel flow is analyzed by means of the Karhunen–Loe´ve (KL) decomposition. It is shown that the most energetic modes are streamwise rollers followed by outward tilted quasi-streamwise vortices. Both of these mode types have a strong similarity to structures seen in physical experiments. Temporal plots of roll energy, propagating energy, b...

In the ensuing period we were able to demonstrate that the origin of these filamentous patterns resulted from the action of synoptic-scale vortical velocity field on the global-scale background gradient of ozone concentration in the meridional direction. Hyperbolic flow patterns between long-lived atmospheric vortices bring together air parcels fro...

Roughly speaking, homogenization is a mathematical method that allows us to “upscale” differential equations. This method not only offers formulas for up-scaling but also provides tools for producing rigorous mathematical convergence proofs.

This report contains a critical account of recent and current developments in the study and treatment of wall bounded turbulence. Special attention is given to those modalities which are regarded as instrumental in the self-sustaining nature of wall turbulence. A careful study of computational simulations reveals that a stereotypical cycle of event...

The Karhunen‐Loève decomposition is used to analyze time records of AVHRR sea surface temperature observations of the Western North Atlantic. A manually declouded dataset covering the spring of 1985 is analyzed. The majority (80%) of the variance about the mean is accounted for by an empirical eigenfunction which is identified with seasonal warming...

In a previous paper we discussed the spectral properties of the Earth{close_quote}s ozone layer, obtained using Empirical Orthogonal Function decomposition of the Total Ozone Mapping Spectrometer (TOMS) database. Here we present other aspects of the analysis, including the EOF method adapted for incomplete datasets, analysis of spatial structure an...

While many models of the dynamics and interactions of single neurons are extant, analogous constructs which attempt to describe large-scale (_>O(108)) neuronal activity are few and far between. Optical imaging of the visual cortex makes such macroscopic neuronal activity accessible. Symmetries latent in the cortical architecture are used here to de...

In this work, we study a blinking vortex-uniform stream map. This map arises as an idealized, but essential, model of time-dependent convection past concentrated vorticity in a number of fluid systems. The map exhibits a rich variety of phenomena, yet it is simple enough so as to yield to extensive analytical investigation. The map's dynamics is do...

An immersed boundary technique is used to model a riblet covered surface on one wall of a channel bounding fully developed turbulent flow. The conjecture that the beneficial drag reduction effect of riblets is a result of the damping of cross-flow velocity fluctuations is then examined. This possibility has been discussed by others but is unverifie...

Streamwise high vorticity rolls and streaks in the turbulent channel flows have been the subject of many studies due to their important role in turbulence production, as a result of sweeping, ejection, and bursting of these structures. Understanding the physics of these streamwise structures is important in controlling drag producing events. Invest...

The problem of using the Karhunen–Loève transform with partial data is addressed. Given a set of empirical eigenfunctions, we show how to recover the modal coefficients for each gappy snapshot by a least-squares procedure. This method gives an unbiased estimate of the data that lie in the gaps and permits gaps to be filled in a reasonable manner. I...

We present a split-step method for integration of the complex Ginzburg- Landau equation in any number of spatial dimensions. The novel aspect of the method lies in the fact that each portion of the splitting is explicitly integrable. This leads to an extremely fast, stable, and efficient procedure. A comparison is made with spectral and pseudospect...

Probability density functions (PDFs) of the fluctuating velocity components, as well as their first and second derivatives, are calculated using data from the direct numerical simulations (DNS) of fully developed turbulent channel flow. It is observed that, beyond the buffer region, the PDF of each of these quantities (except for u,y), is independe...