Academic literature on the topic 'Spike Train Distance'

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Journal articles on the topic "Spike Train Distance"

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Rusu, Cătălin V., and Răzvan V. Florian. "A New Class of Metrics for Spike Trains." Neural Computation 26, no. 2 (February 2014): 306–48. http://dx.doi.org/10.1162/neco_a_00545.

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The distance between a pair of spike trains, quantifying the differences between them, can be measured using various metrics. Here we introduce a new class of spike train metrics, inspired by the Pompeiu-Hausdorff distance, and compare them with existing metrics. Some of our new metrics (the modulus-metric and the max-metric) have characteristics that are qualitatively different from those of classical metrics like the van Rossum distance or the Victor and Purpura distance. The modulus-metric and the max-metric are particularly suitable for measuring distances between spike trains where information is encoded in bursts, but the number and the timing of spikes inside a burst do not carry information. The modulus-metric does not depend on any parameters and can be computed using a fast algorithm whose time depends linearly on the number of spikes in the two spike trains. We also introduce localized versions of the new metrics, which could have the biologically relevant interpretation of measuring the differences between spike trains as they are perceived at a particular moment in time by a neuron receiving these spike trains.
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Ciba, Manuel, Robert Bestel, Christoph Nick, Guilherme Ferraz de Arruda, Thomas Peron, Comin César Henrique, Luciano da Fontoura Costa, Francisco Aparecido Rodrigues, and Christiane Thielemann. "Comparison of Different Spike Train Synchrony Measures Regarding Their Robustness to Erroneous Data From Bicuculline-Induced Epileptiform Activity." Neural Computation 32, no. 5 (May 2020): 887–911. http://dx.doi.org/10.1162/neco_a_01277.

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As synchronized activity is associated with basic brain functions and pathological states, spike train synchrony has become an important measure to analyze experimental neuronal data. Many measures of spike train synchrony have been proposed, but there is no gold standard allowing for comparison of results from different experiments. This work aims to provide guidance on which synchrony measure is best suited to quantify the effect of epileptiform-inducing substances (e.g., bicuculline, BIC) in in vitro neuronal spike train data. Spike train data from recordings are likely to suffer from erroneous spike detection, such as missed spikes (false negative) or noise (false positive). Therefore, different timescale-dependent (cross-correlation, mutual information, spike time tiling coefficient) and timescale-independent (Spike-contrast, phase synchronization (PS), A-SPIKE-synchronization, A-ISI-distance, ARI-SPIKE-distance) synchrony measures were compared in terms of their robustness to erroneous spike trains. For this purpose, erroneous spike trains were generated by randomly adding (false positive) or deleting (false negative) spikes (in silico manipulated data) from experimental data. In addition, experimental data were analyzed using different spike detection threshold factors in order to confirm the robustness of the synchrony measures. All experimental data were recorded from cortical neuronal networks on microelectrode array chips, which show epileptiform activity induced by the substance BIC. As a result of the in silico manipulated data, Spike-contrast was the only measure that was robust to false-negative as well as false-positive spikes. Analyzing the experimental data set revealed that all measures were able to capture the effect of BIC in a statistically significant way, with Spike-contrast showing the highest statistical significance even at low spike detection thresholds. In summary, we suggest using Spike-contrast to complement established synchrony measures because it is timescale independent and robust to erroneous spike trains.
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Kreuz, Thomas, Daniel Chicharro, Conor Houghton, Ralph G. Andrzejak, and Florian Mormann. "Monitoring spike train synchrony." Journal of Neurophysiology 109, no. 5 (March 1, 2013): 1457–72. http://dx.doi.org/10.1152/jn.00873.2012.

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Recently, the SPIKE-distance has been proposed as a parameter-free and timescale-independent measure of spike train synchrony. This measure is time resolved since it relies on instantaneous estimates of spike train dissimilarity. However, its original definition led to spuriously high instantaneous values for eventlike firing patterns. Here we present a substantial improvement of this measure that eliminates this shortcoming. The reliability gained allows us to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. Additional new features include selective and triggered temporal averaging as well as the instantaneous comparison of spike train groups. In a second step, a causal SPIKE-distance is defined such that the instantaneous values of dissimilarity rely on past information only so that time-resolved spike train synchrony can be estimated in real time. We demonstrate that these methods are capable of extracting valuable information from field data by monitoring the synchrony between neuronal spike trains during an epileptic seizure. Finally, the applicability of both the regular and the real-time SPIKE-distance to continuous data is illustrated on model electroencephalographic (EEG) recordings.
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Kreuz, Thomas, Mario Mulansky, and Nebojsa Bozanic. "SPIKY: a graphical user interface for monitoring spike train synchrony." Journal of Neurophysiology 113, no. 9 (May 2015): 3432–45. http://dx.doi.org/10.1152/jn.00848.2014.

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Techniques for recording large-scale neuronal spiking activity are developing very fast. This leads to an increasing demand for algorithms capable of analyzing large amounts of experimental spike train data. One of the most crucial and demanding tasks is the identification of similarity patterns with a very high temporal resolution and across different spatial scales. To address this task, in recent years three time-resolved measures of spike train synchrony have been proposed, the ISI-distance, the SPIKE-distance, and event synchronization. The Matlab source codes for calculating and visualizing these measures have been made publicly available. However, due to the many different possible representations of the results the use of these codes is rather complicated and their application requires some basic knowledge of Matlab. Thus it became desirable to provide a more user-friendly and interactive interface. Here we address this need and present SPIKY, a graphical user interface that facilitates the application of time-resolved measures of spike train synchrony to both simulated and real data. SPIKY includes implementations of the ISI-distance, the SPIKE-distance, and the SPIKE-synchronization (an improved and simplified extension of event synchronization) that have been optimized with respect to computation speed and memory demand. It also comprises a spike train generator and an event detector that makes it capable of analyzing continuous data. Finally, the SPIKY package includes additional complementary programs aimed at the analysis of large numbers of datasets and the estimation of significance levels.
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Paiva, António R. C., Il Park, and José C. Príncipe. "A Reproducing Kernel Hilbert Space Framework for Spike Train Signal Processing." Neural Computation 21, no. 2 (February 2009): 424–49. http://dx.doi.org/10.1162/neco.2008.09-07-614.

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This letter presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical description as point processes. Moreover, because many inner products can be formulated, a particular definition can be crafted to best fit an application. These ideas are illustrated by the definition of a number of spike train inner products. To further elicit the advantages of the RKHS framework, a family of these inner products, the cross-intensity (CI) kernels, is analyzed in detail. This inner product family encapsulates the statistical description from the conditional intensity functions of spike trains. The problem of their estimation is also addressed. The simplest of the spike train kernels in this family provide an interesting perspective to others' work, as will be demonstrated in terms of spike train distance measures. Finally, as an application example, the RKHS framework is used to derive a clustering algorithm for spike trains from simple principles.
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Adamatzky, Andrew, Alessandro Chiolerio, and Georgios Sirakoulis. "Electrical Resistive Spiking of Fungi." Biophysical Reviews and Letters 16, no. 01 (January 21, 2021): 1–7. http://dx.doi.org/10.1142/s1793048021500016.

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We study long-term electrical resistance dynamics in mycelium and fruit bodies of oyster fungi P. ostreatus. A nearly homogeneous sheet of mycelium on the surface of a growth substrate exhibits trains of resistance spikes. The average width of spikes is c. 23[Formula: see text]min and the average amplitude is c. 1[Formula: see text]k[Formula: see text]. The distance between neighboring spikes in a train of spikes is c. 30[Formula: see text]min. Typically, there are 4–6 spikes in a train of spikes. Two types of electrical resistance spikes trains are found in fruit bodies: low frequency and high amplitude (28[Formula: see text]min spike width, 1.6[Formula: see text]k[Formula: see text] amplitude, 57[Formula: see text]min distance between spikes) and high frequency and low amplitude (10[Formula: see text]min width, 0.6[Formula: see text]k[Formula: see text] amplitude, 44[Formula: see text]min distance between spikes). The findings could be applied in monitoring of physiological states of fungi and future development of living electronic devices and sensors.
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Houghton, Conor, and Kamal Sen. "A New Multineuron Spike Train Metric." Neural Computation 20, no. 6 (June 2008): 1495–511. http://dx.doi.org/10.1162/neco.2007.10-06-350.

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The Victor-Purpura spike train metric has recently been extended to a family of multineuron metrics and used to analyze spike trains recorded simultaneously from pairs of proximate neurons. The metric is one of the two metrics commonly used for quantifying the distance between two spike trains; the other is the van Rossum metric. Here, we suggest an extension of the van Rossum metric to a multineuron metric. We believe this gives a metric that is both natural and easy to calculate. Both types of multineuron metric are applied to simulated data and are compared.
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Chen, Yan, Vitaliy Marchenko, and Robert F. Rogers. "Joint Probability-Based Neuronal Spike Train Classification." Computational and Mathematical Methods in Medicine 10, no. 3 (2009): 229–39. http://dx.doi.org/10.1080/17486700802448615.

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Neuronal spike trains are used by the nervous system to encode and transmit information. Euclidean distance-based methods (EDBMs) have been applied to quantify the similarity between temporally-discretized spike trains and model responses. In this study, using the same discretization procedure, we developed and applied a joint probability-based method (JPBM) to classify individual spike trains of slowly adapting pulmonary stretch receptors (SARs). The activity of individual SARs was recorded in anaesthetized, paralysed adult male rabbits, which were artificially-ventilated at constant rate and one of three different volumes. Two-thirds of the responses to the 600 stimuli presented at each volume were used to construct three response models (one for each stimulus volume) consisting of a series of time bins, each with spike probabilities. The remaining one-third of the responses where used as test responses to be classified into one of the three model responses. This was done by computing the joint probability of observing the same series of events (spikes or no spikes, dictated by the test response) in a given model and determining which probability of the three was highest. The JPBM generally produced better classification accuracy than the EDBM, and both performed well above chance. Both methods were similarly affected by variations in discretization parameters, response epoch duration, and two different response alignment strategies. Increasing bin widths increased classification accuracy, which also improved with increased observation time, but primarily during periods of increasing lung inflation. Thus, the JPBM is a simple and effective method performing spike train classification.
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Brasselet, Romain, Roland S. Johansson, and Angelo Arleo. "Quantifying Neurotransmission Reliability Through Metrics-Based Information Analysis." Neural Computation 23, no. 4 (April 2011): 852–81. http://dx.doi.org/10.1162/neco_a_00099.

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We set forth an information-theoretical measure to quantify neurotransmission reliability while taking into full account the metrical properties of the spike train space. This parametric information analysis relies on similarity measures induced by the metrical relations between neural responses as spikes flow in. Thus, in order to assess the entropy, the conditional entropy, and the overall information transfer, this method does not require any a priori decoding algorithm to partition the space into equivalence classes. It therefore allows the optimal parameters of a class of distances to be determined with respect to information transmission. To validate the proposed information-theoretical approach, we study precise temporal decoding of human somatosensory signals recorded using microneurography experiments. For this analysis, we employ a similarity measure based on the Victor-Purpura spike train metrics. We show that with appropriate parameters of this distance, the relative spike times of the mechanoreceptors’ responses convey enough information to perform optimal discrimination—defined as maximum metrical information and zero conditional entropy—of 81 distinct stimuli within 40 ms of the first afferent spike. The proposed information-theoretical measure proves to be a suitable generalization of Shannon mutual information in order to consider the metrics of temporal codes explicitly. It allows neurotransmission reliability to be assessed in the presence of large spike train spaces (e.g., neural population codes) with high temporal precision.
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Itskov, Vladimir, Carina Curto, and Kenneth D. Harris. "Valuations for Spike Train Prediction." Neural Computation 20, no. 3 (March 2008): 644–67. http://dx.doi.org/10.1162/neco.2007.3179.

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The ultimate product of an electrophysiology experiment is often a decision on which biological hypothesis or model best explains the observed data. We outline a paradigm designed for comparison of different models, which we refer to as spike train prediction. A key ingredient of this paradigm is a prediction quality valuation that estimates how close a predicted conditional intensity function is to an actual observed spike train. Although a valuation based on log likelihood (L) is most natural, it has various complications in this context. We propose that a quadratic valuation (Q) can be used as an alternative to L. Q shares some important theoretical properties with L, including consistency, and the two valuations perform similarly on simulated and experimental data. Moreover, Q is more robust than L, and optimization with Q can dramatically improve computational efficiency. We illustrate the utility of Q for comparing models of peer prediction, where it can be computed directly from cross-correlograms. Although Q does not have a straightforward probabilistic interpretation, Q is essentially given by Euclidean distance.
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Dissertations / Theses on the topic "Spike Train Distance"

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Chicharro, Raventós Daniel. "Characterization of information and causality measures for the study of neuronal data." Doctoral thesis, Universitat Pompeu Fabra, 2011. http://hdl.handle.net/10803/22658.

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We study two methods of data analysis which are common tools for the analysis of neuronal data. In particular, we examine how causal interactions between brain regions can be investigated using time series reflecting the neural activity in these regions. Furthermore, we analyze a method used to study the neural code that evaluates the discrimination of the responses of single neurons elicited by different stimuli. This discrimination analysis is based on the quantification of the similarity of the spike trains with time scale parametric spike train distances. In each case we describe the methods used for the analysis of the neuronal data and we characterize their specificity using simulated or exemplary experimental data. Taking into account our results, we comment the previous studies in which the methods have been applied. In particular, we focus on the interpretation of the statistical measures in terms of underlying neuronal causal connectivity and properties of the neural code, respectively.
Estudiem dos mètodes d'anàlisi de dades que són eines habituals per a l'anàlisi de dades neuronals. Concretament, examinem la manera en què les interaccions causals entre regions del cervell poden ser investigades a partir de sèries temporals que reflecteixen l'activitat neuronal d'aquestes regions. A més a més, analitzem un mètode emprat per estudiar el codi neuronal que avalua la discriminació de les respostes de neurones individuals provocades per diferents estímuls. Aquesta anàlisi de la discriminació es basa en la quantificació de la similitud de les seqüències de potencials d'acció amb distàncies amb un paràmetre d'escala temporal. Tenint en compte els nostres resultats, comentem els estudis previs en els quals aquests mètodes han estat aplicats. Concretament, ens centrem en la interpretació de les mesures estadístiques en termes de connectivitat causal neuronal subjacent i propietats del codi neuronal, respectivament.
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BOZANIC, NEBOJSA. "Measures of spike train synchrony." Doctoral thesis, 2016. http://hdl.handle.net/2158/1043650.

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In experimental neuroscience techniques for recording large-scale neuronal spiking activity are developing very fast. This leads to an increasing demand for algorithms capable of analyzing large amounts of spike train data. One of the most crucial and demanding tasks is the identification of similarity patterns with a very high temporal resolution and across different spatial scales. To address this task, in recent years time-resolved measures of spike train synchrony such as the ISI-distance and the SPIKE-distance have been proposed. Here we add the complementary measure SPIKE-synchronization, a sophisticated multivariate coincidence detector with a very intuitive interpretation. In the first Results chapter we present SPIKY, an interactive graphical user interface that facilitates the application of these three time-resolved measures of spike train synchrony to both simulated and real data. SPIKY, which has been optimized with respect to computation speed and memory demand, also comprises a spike train generator and an event detector that makes it capable of analyzing continuous data. Finally, the SPIKY package includes additional complementary programs aimed at the analysis of large numbers of datasets and the estimation of significance levels. In the second Results chapter we deal with the very important problem of latency variations in real data. By means of a validated setup we can show that the parameter-free SPIKE-distance outperforms two time-scale dependent standard measures. In summary, in this thesis we provide several important measures and corrections that when applied to the right experimental datasets could potentially lead to an increased understanding of the neural code - the ultimate goal of neuroscience.
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SATUVUORI, EERO ANTERO. "Spike train distances and neuronal coding." Doctoral thesis, 2019. http://hdl.handle.net/2158/1153169.

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The thesis is from the field of data-analysis and computational neuroscience. In the thesis I improved existing spike train distance measures and developed new ones. The main methods used are ISI-distance, SPIKE-distance and SPIKE-Synchronization.
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Books on the topic "Spike Train Distance"

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Mason, Peggy. Electrical Communication Within a Neuron. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190237493.003.0010.

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Postsynaptic potentials integrate across time and space within a single neuron. The influence of the length constant on spatial summation and of the time constant on temporal summation is described. Whereas passive properties give rise to graded potentials, the voltage-gated sodium channel (VGSC) supports the all-or-none action potential. The action potential can be used to conduct information across long distances and is therefore used in the majority of neurons that have axons. How the inactivated state of VGSCs gives rise to the refractory period and dynamic polarization is described. The meaning of the action potential threshold is fully considered and then applied to understand the clinical condition of hyperkalemic periodic paralysis. Trains of action potentials carry information, and degradation of the spike train compromises the message. The speed of action potential conduction along both unmyelinated and myelinated axons is explored. In closing, an overview of demyelinating diseases is offered.
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Book chapters on the topic "Spike Train Distance"

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Victor, Jonathan D. "Spike Train Distance." In Encyclopedia of Computational Neuroscience, 2808–14. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4614-6675-8_409.

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Victor, Jonathan D. "Spike Train Distance." In Encyclopedia of Computational Neuroscience, 1–8. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-7320-6_409-1.

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Kreuz, Thomas, Conor Houghton, and Jonathan D. Victor. "Spike Train Distance." In Encyclopedia of Computational Neuroscience, 1–14. New York, NY: Springer New York, 2019. http://dx.doi.org/10.1007/978-1-4614-7320-6_409-2.

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"Measuring Representational Distances: The Spike-Train Metrics Approach." In Visual Population Codes. The MIT Press, 2011. http://dx.doi.org/10.7551/mitpress/8404.003.0012.

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Conference papers on the topic "Spike Train Distance"

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Shekhar, Shubhanshu, and Kaushik Majumdar. "A new spike train distance measure." In 2012 International Conference on Data Science & Engineering (ICDSE). IEEE, 2012. http://dx.doi.org/10.1109/icdse.2012.6281906.

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Iskarous, Mark M., Sriramana Sankar, Qianwei Li, Christopher L. Hunt, and Nitish V. Thakor. "A scalable algorithm based on spike train distance to select stimulation patterns for sensory feedback." In 2021 10th International IEEE/EMBS Conference on Neural Engineering (NER). IEEE, 2021. http://dx.doi.org/10.1109/ner49283.2021.9441155.

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Ande, Sathish, Jayanth R. Regatti, Neha Pandey, Ajith Karunarathne, Lopamudra Giri, and Soumya Jana. "Heterogeneity in Neuronal Calcium Spike Trains based on Empirical Distance." In 2021 10th International IEEE/EMBS Conference on Neural Engineering (NER). IEEE, 2021. http://dx.doi.org/10.1109/ner49283.2021.9441175.

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Nolasco Jauregui, Oralia. "A Machine Learning approach to Neural Information Decoding of Spike Train Distances in the Peripheral Nervous System." In LatinX in AI at Neural Information Processing Systems Conference 2019. Journal of LatinX in AI Research, 2019. http://dx.doi.org/10.52591/lxai2019120817.

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Decoding the neural signal has proved to be an elusive goal. We explore the use of sequence analysis algorithms to identify repeating patterns of spike train distances and found that they could be associated to the stimulus in the rat peripheral system with good results. The use of these algorithms is very common in genomics and proteomics for genetic sequence analysis but rarely applied to neural systems analysis. We are convinced that with proper tuning they could yield useful results.
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Jetti, Siddhartha, and Vahid Motevalli. "A System Level Analysis of the Framework and Feasibility for Dual Air and Road Mode Vehicle." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89205.

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The dual mode air-road vehicle is one of those concepts that have intrigued travelers and inventors for a long time. The quest for a vehicle that can be driven on the roads and flown in the sky started as early as the development of airplane by Wright brothers in 1906. With the ever growing traffic and congestion on the roads, increased security procedures at airports and airline hub-spoke system, the travel times for certain range of distances have increased in recent times creating a need for a dual mode vehicle. In the US, for the mid-range distances (200–500 mile), travel options available are limited for other than large population centers. Transportation by train or bus is often limited and involves multi-stops between desired destinations. Therefore, the mid-range travel is more likely accomplished by a car or an airline or sometimes both. Travel by car or airline for this ranged can consumes considerable time because of road, airport and air traffic congestions, security procedures and wait times. A survey published in 2004 by Bureau of Transportation Statistics [1] reveals that 200–500 mile trips account for about 31.8% of the total trips taken in the US. With the premise that a dual mode vehicle could be a potential solution for mid-range travel, particularly around a 300 mile distance, the present work aims at establishing a frame-work and performance envelope for this type vehicle, In other words, the roadable aircraft or the flying car. These vehicles are neither a high performance car nor a high performance aircraft. They are vehicles that have the capability to be driven on the roads and flown in the sky. The present study focuses on identifying the technical, operational and acceptability challenges that have to be overcome to build a dual mode vehicle. This paper also covers some preliminary design aspects like power-fuel requirements, wing-airfoil parameters and an approach to address the road mode issues arising due to the wing.
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Lawrence, George N. "Integration of geometrical and physical optics concepts in optical modeling." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.we1.

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Geometrical optics, in spite of its relatively simple treatment of the properties of light, has proved to be extraordinarily useful for many types of system. Physical optics analysis using a complex amplitude description of the wavefront can, in principle, more accurately calculate the properties of many types of system. The greater power comes with greater complexity and increased cost of calculation. By artfully including paraxial and exact geometrical principles, physical optics calculations can more readily be applied to a variety of simple and complex optical systems. The series of diffraction operations needed to propagate through an optical train can be associated with the paraxial properties plus the addition of aberration. Conventional lenses and mirrors as well as unconventional elements such as GRIN elements may be treated in this fashion. The concepts of optical path lengths and reduced distances also play an important role in characterizing diffraction effects.
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Western, Laura T., Kuldeepsinh Rana, and Michael R. King. "Flow-Based Isolation and Neutralization of Circulating Tumor Cells." In ASME 2009 7th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2009. http://dx.doi.org/10.1115/icnmm2009-82137.

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Circulating tumor cells (CTC) have the potential to be used clinically as a diagnostic tool and a treatment tool in the field of oncology. As a diagnostic tool, CTC may be used to indicate the presence of a tumor before the tumor is large enough to cause noticeable symptoms. As a treatment tool, CTC isolated from patients may be used to test the efficacy of chemotherapy options to personalize patient treatment. One way for tumors to spread is through metastasis via the circulatory system. CTC are able to exploit the natural leukocyte recruitment process that is initially mediated by rolling on transient selectin bonds. Our capture devices take advantage of this naturally occurring recruitment step to isolate CTC from whole blood by flowing samples through selectin and antibody-coated microtubes. Whole blood was spiked with a known concentration of labeled cancer cells and then perfused through pre-coated microtubes. Microtubes were then rinsed to remove unbound cells and the number of labeled cells captured on the lumen was assessed. CTC were successfully captured from whole blood at a clinically relevant level on the order of 10 cells per mL. Combination tubes with selectin and antibody coated surface exhibited higher capture rate than tubes coated with selectin alone or antibody alone. Additionally, CTC capture was demonstrated with the KG1a hematopoietic cell line and the Du145 epithelial cell line. Thus, the in vivo process of selectin-mediated CTC recruitment to distant vessel walls can be used in vitro to target CTC to a tube lumen. The microtube device can also be used to capture CTC of hematopoietic and epithelial tumor origin and is demonstrated sensitivity down to the order of 10 CTC per mL. In a related study aimed at reducing the blood borne metastatic cancer load, we have shown that cells captured to a surface can be neutralized by a receptor-mediated biochemical signal (Rana et al. 2008). In the proposed method we have shown that using a combined selecting and TRAIL (TNF Related Apoptosis Inducing Ligand or Apo 2L) functionalized surface we are able to kill about 30% of the captured cells in a short duration of 1 hour whereas it took about 4 hours to kill the same proportion of cells without flow on a similarly functionalized. Here we have taken the approach a step further by showing that with very small doses of chemotherapeutic agents like Bortezomib, we can increase the kill rate of CTCs., thus allowing the device to function in senarios where the patient is undergoing treatment. We show here with leukemic cells that are treated with Bortezomib that we are able kill about 41% of the captured cells.
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