William L. Kath

ORCID: 0000-0003-3867-4783
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About
Contact & Profiles
Research Areas
  • Optical Network Technologies
  • Advanced Fiber Laser Technologies
  • Photonic Crystal and Fiber Optics
  • Advanced Photonic Communication Systems
  • Neural dynamics and brain function
  • Neuroscience and Neuropharmacology Research
  • Photonic and Optical Devices
  • Nonlinear Photonic Systems
  • Nonlinear Waves and Solitons
  • Circadian rhythm and melatonin
  • Laser-Matter Interactions and Applications
  • Nonlinear Dynamics and Pattern Formation
  • Neurobiology and Insect Physiology Research
  • Gene Regulatory Network Analysis
  • Advanced Fiber Optic Sensors
  • Neuroscience and Neural Engineering
  • Photoreceptor and optogenetics research
  • Semiconductor Lasers and Optical Devices
  • Retinal Development and Disorders
  • Advanced Memory and Neural Computing
  • Evolution and Genetic Dynamics
  • Theoretical and Computational Physics
  • Memory and Neural Mechanisms
  • Quantum chaos and dynamical systems
  • Stochastic processes and statistical mechanics

Northwestern University
2013-2024

Physical Sciences (United States)
2002-2015

Applied Mathematics (United States)
2001-2013

McCormick (United States)
1991-2009

The Ohio State University
2004

University of Maryland, Baltimore County
1997-2003

University of California, Santa Barbara
2002

Northeastern University
2002

University of Edinburgh
1995

California Institute of Technology
1982-1985

Overexpression of the histone methyltransferase MMSET in t(4;14)+ multiple myeloma patients is believed to be driving factor pathogenesis this subtype myeloma. catalyzes dimethylation lysine 36 on H3 (H3K36me2), and its overexpression causes a global increase H3K36me2, redistributing mark broad, elevated level across genome. Here, we demonstrate that an increased also induces reduction 27 trimethylation (H3K27me3). Despite net decrease H3K27 methylation, specific genomic loci exhibit...

10.1371/journal.pgen.1004566 article EN cc-by PLoS Genetics 2014-09-04

In hippocampal CA1 pyramidal neurons, action potentials are typically initiated in the axon and backpropagate into dendrites, shaping integration of synaptic activity influencing induction plasticity. Despite previous reports describing action-potential propagation proximal apical extent to which invade distal dendrites neurons remains controversial. Using paired somatic dendritic whole cell recordings, we find that 280 μm from soma, single backpropagating exhibit <50% attenuation their...

10.1152/jn.2001.86.6.2998 article EN Journal of Neurophysiology 2001-12-01

We performed simultaneous patch-electrode recordings from the soma and apical dendrite of CA1 pyramidal neurons in hippocampal slices, order to determine degree voltage attenuation along dendrites. Fifty per cent steady-state somatic changes occurred at a distance 238 microm control 409 after blocking hyperpolarization-activated (H) conductance. The morphology three was reconstructed used generate computer models, which were adjusted fit dendritic responses. These models identify several...

10.1113/jphysiol.2005.086793 article EN The Journal of Physiology 2005-07-08

Circadian clocks play a key role in regulating vast array of biological processes, with significant implications for human health. Accurate assessment physiological time using transcriptional biomarkers found blood can significantly improve diagnosis circadian disorders and optimize the delivery therapeutic treatments. To be useful, such test must accurate, minimally burdensome to patient, readily generalizable new data. A major obstacle development gene expression biomarker tests is...

10.1073/pnas.1800314115 article EN cc-by-nc-nd Proceedings of the National Academy of Sciences 2018-09-10

The gain of signaling in primary sensory circuits is matched to the stimulus intensity by process adaptation. Retinal neural adapt visual scene statistics, including mean (background adaptation) and temporal variance (contrast light stimulus. intrinsic properties retinal bipolar cells synapses contribute background contrast adaptation, but it unclear whether both forms adaptation depend on same cellular mechanisms. Studies cell identified synaptic mechanisms control, relevance these...

10.1523/jneurosci.2631-11.2011 article EN Journal of Neuroscience 2011-07-27

A system of coupled nonlinear Schr\"odinger equations (NLS) governs the interaction propagating pulses in two-mode optical fibers and directional couplers. Using NLS solitons as trial functions an averaged Lagrangian formulation, ordinary-differential-equation (ODE) approximations for pulse dynamics are derived. These ODE's give a criterion two to attract one another form bound state; they also describe complicated oscillations these undergo this state. In addition, ODE show that collisions...

10.1103/physreva.42.563 article EN Physical Review A 1990-07-01

The transient evolution of general initial pulses into solitons for the nonlinear Schr\"odinger (NLS) equation is considered. By employing a trial function which consists solitonlike pulse with variable parameters plus linear dispersive term in an averaged Lagrangian, ordinary differential equations (ODE's) are derived approximate this evolution. These take account effect generated radiation upon Specifically, ODE's acts as damping causes to decay steady soliton. solutions compared numerical...

10.1103/physreve.51.1484 article EN Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 1995-02-01

In many forms of retinal degeneration, photoreceptors die but inner circuits remain intact. the rd1 mouse, an established model for blinding diseases, spontaneous activity in coupled network AII amacrine and ON cone bipolar cells leads to rhythmic bursting ganglion cells. Since such could impair and/or cortical responses restored photoreceptor function, understanding its nature is important developing treatments pathologies. Here we analyzed a compartmental wild-type mouse cell predict that...

10.1152/jn.00437.2014 article EN Journal of Neurophysiology 2014-07-09

Noise caused by fluctuations at the molecular level is a fundamental part of intracellular processes. While response biological systems to noise has been studied extensively, there limited understanding how exploit it induce desired cell state. Here we present scalable, quantitative method based on Freidlin-Wentzell action predict and control noise-induced switching between different states in genetic networks that, conveniently, can also transitions stable absence noise. We apply this...

10.1103/physrevx.5.031036 article EN cc-by Physical Review X 2015-09-16

We analyze pulse propagation in an optical fiber employing a periodic dispersion map. Second-order averaging is used to determine general evolution equation valid for both return-to-zero and non-return-to-zero pulses dispersion-managed systems. The then applied the case of solitons, analytic expression power enhancement arising from management obtained.

10.1364/ol.22.000985 article EN Optics Letters 1997-07-01

We describe the application of importance sampling to Monte-Carlo simulations polarization-mode dispersion (PMD) in optical fibers. The method allows rare differential group delay (DGD) events be simulated much more efficiently than with standard methods and, thus, it can used assess PMD-induced system outage probabilities at realistic bit-error rates. demonstrate technique by accurately calculating tails DGD probability distribution a relatively small number trials.

10.1109/68.986796 article EN IEEE Photonics Technology Letters 2002-03-01

We present a novel linearization method to calculate accurate eye diagrams and bit error rates (BERs) for arbitrary optical transmission systems apply it dispersion-managed soliton (DMS) system. In this approach, we the full nonlinear evolution using Monte Carlo methods. However, analyze data at receiver assuming that interaction of noise with itself in an appropriate basis set is negligible during transmission. Noise-noise beating due quadratic nonlinearity kept. approach highly DMS system,...

10.1109/50.988987 article EN Journal of Lightwave Technology 2002-03-01

A model equation containing a memory integral is posed. The extent of the memory, relaxation time $\lambda $, controls bifurcation behavior as control parameter R increased. Small (large) $ gives steady (periodic) bifurcation. There double eigenvalue at = \lambda _1 separating purely $(\lambda < _{1} )$ from combined steady/T-periodic > states with $T \to \infty _1^ + $. Analysis leads to co-existence stable steady/periodic and increased, periodic give way states. Numerical solutions show...

10.1137/0146013 article EN SIAM Journal on Applied Mathematics 1986-04-01

Homeostatic and circadian processes collaborate to appropriately time consolidate sleep wake. To understand how these are integrated, we scheduled brief deprivation at different times of day in

10.7554/elife.74327 article EN cc-by eLife 2022-06-23

Single-cell "omics"-based measurements are often high dimensional so that dimensionality reduction (DR) algorithms necessary for data visualization and analysis. The lack of methods separating signal from noise in DR outputs has limited their utility generating data-driven discoveries single-cell data. In this work we present EMBEDR, which assesses the output any algorithm to distinguish evidence structure algorithm-induced outputs. We apply EMBEDR DR-generated representations omics several...

10.1016/j.patter.2022.100443 article EN cc-by-nc-nd Patterns 2022-02-08
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