prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What do dendritic spines contain?

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Context 1: JoVE | Peer Reviewed Scientific Video Journal - Methods and Protocols
A role for thrombospondin-1 deficits in astrocyte-mediated spine and synaptic pathology in Downs syndrome  Octavio Garcia, Maria Torres, Pablo Helguera, Pinar Coskun, Jorge Busciglio 
PUBLISHED: 07-02-2010	Downs syndrome (DS) is the most common genetic cause of mental retardation  Reduced number and aberrant architecture of dendritic spines are common features of DS neuropathology  However, the mechanisms involved in DS spine alterations are not known  In addition to a relevant role in synapse formation and maintenance, astrocytes can regulate spine dynamics by releasing soluble factors or by physical contact with neurons  We have previously shown impaired mitochondrial function in DS astrocytes leading to metabolic alterations in protein processing and secretion  In this study, we investigated whether deficits in astrocyte function contribute to DS spine pathology 
Analysis of Dendritic Spine Morphology in Cultured CNS Neurons Authors: Deepak P  Srivastava, Kevin M  Woolfrey, Peter Penzes  Published: 07-13-2011 JoVE Neuroscience
Dendritic spines are the sites of the majority of excitatory connections within the brain, and form the post-synaptic compartment of synapses  These structures are rich in actin and have been shown to be highly dynamic  In response to classical Hebbian plasticity as well as neuromodulatory signals, dendritic spines can change shape and number, which is thought to be critical for the refinement of neural circuits and the processing and storage of information within the brain  Within dendritic spines, a complex network of proteins link extracellular signals with the actin cyctoskeleton allowing for control of dendritic spine morphology and number  Neuropathological studies have demonstrated that a number of disease states, ranging from schizophrenia to autism spectrum disorders, display abnormal dendritic spine morphology or numbers  Moreover, recent genetic studies have identified mutations in numerous genes that encode synaptic proteins, leading to suggestions that these proteins may contribute to aberrant spine plasticity that, in part, underlie the pathophysiology of these disorders  In order to study the potential role of these proteins in controlling dendritic spine morphologies/number, the use of cultured cortical neurons offers several advantages  Firstly, this system allows for high-resolution imaging of dendritic spines in fixed cells as well as time-lapse imaging of live cells  Secondly, this in vitro system allows for easy manipulation of protein function by expression of mutant proteins, knockdown by shRNA constructs, or pharmacological treatments  These techniques allow researchers to begin to dissect the role of disease-associated proteins and to predict how mutations of these proteins may function in vivo 
Play ButtonIsolation and Culture of Mouse Cortical AstrocytesAuthors: Sebastian Schildge, Christian Bohrer, Kristina Beck, Christian Schachtrup  Institutions: University of Freiburg , University of Freiburg  Astrocytes are an abundant cell type in the mammalian brain, yet much remains to be learned about their molecular and functional characteristics  In vitro astrocyte cell culture systems can be used to study the biological functions of these glial cells in detail  This video protocol shows how to obtain pure astrocytes by isolation and culture of mixed cortical cells of mouse pups  The method is based on the absence of viable neurons and the separation of astrocytes, oligodendrocytes and microglia, the three main glial cell populations of the central nervous system, in culture  Representative images during the first days of culture demonstrate the presence of a mixed cell population and indicate the timepoint, when astrocytes become confluent and should be separated from microglia and oligodendrocytes  Moreover, we demonstrate purity and astrocytic morphology of cultured astrocytes using immunocytochemical stainings for well established and newly described astrocyte markers  This culture system can be easily used to obtain pure mouse astrocytes and astrocyte-conditioned medium for studying various aspects of astrocyte biology Neuroscience, Issue 71, Neurobiology, Cellular Biology, Medicine, Molecular Biology, Anatomy, Physiology, brain, mouse, astrocyte culture, astrocyte, fibroblast, fibrinogen, chondroitin sulfate proteoglycan, neuronal regeneration, cell culture, animal model50079Play ButtonImaging Dendritic Spines of Rat Primary Hippocampal Neurons using Structured Illumination MicroscopyAuthors: Marijn Schouten, Giulia M  R  De Luca, Diana K  Alatriste González, Babette E  de Jong, Wendy Timmermans, Hui Xiong, Harm Krugers, Erik M  M  Manders, Carlos P  Fitzsimons  Institutions: University of Amsterdam, University of Amsterdam Dendritic spines are protrusions emerging from the dendrite of a neuron and represent the primary postsynaptic targets of excitatory inputs in the brain  Technological advances have identified these structures as key elements in neuron connectivity and synaptic plasticity  The quantitative analysis of spine morphology using light microscopy remains an essential problem due to technical limitations associated with light's intrinsic refraction limit  Dendritic spines can be readily identified by confocal laser-scanning fluorescence microscopy  However, measuring subtle changes in the shape and size of spines is difficult because spine dimensions other than length are usually smaller than conventional optical resolution fixed by light microscopy's theoretical resolution limit of 200 nm 
Several recently developed super resolution techniques have been used to image cellular structures smaller than the 200 nm, including dendritic spines  These techniques are based on classical far-field operations and therefore allow the use of existing sample preparation methods and to image beyond the surface of a specimen  Described here is a working protocol to apply super resolution structured illumination microscopy (SIM) to the imaging of dendritic spines in primary hippocampal neuron cultures  Possible applications of SIM overlap with those of confocal microscopy  However, the two techniques present different applicability  SIM offers higher effective lateral resolution, while confocal microscopy, due to the usage of a physical pinhole, achieves resolution improvement at the expense of removal of out of focus light  In this protocol, primary neurons are cultured on glass coverslips using a standard protocol, transfected with DNA plasmids encoding fluorescent proteins and imaged using SIM  The whole protocol described herein takes approximately 2 weeks, because dendritic spines are imaged after 16-17 days in vitro, when dendritic development is optimal  After completion of the protocol, dendritic spines can be reconstructed in 3D from series of SIM image stacks using specialized software Neuroscience, Issue 87, Dendritic Spine, Microscopy, Confocal, Fluorescence, Neurosciences, hippocampus, primary neuron, super resolution microscopy, structured illumination microscopy (SIM), neuroscience, dendrite51276Play ButtonSetting-up an In Vitro Model of Rat Blood-brain Barrier (BBB): A Focus on BBB Impermeability and Receptor-mediated TransportAuthors: Yves Molino, Françoise Jabès, Emmanuelle Lacassagne, Nicolas Gaudin, Michel Khrestchatisky  Institutions: VECT-HORUS SAS, CNRS, NICN UMR 7259 The blood brain barrier (BBB) specifically regulates molecular and cellular flux between the blood and the nervous tissue  Our aim was to develop and characterize a highly reproducible rat syngeneic in vitro model of the BBB using co-cultures of primary rat brain endothelial cells (RBEC) and astrocytes to study receptors involved in transcytosis across the endothelial cell monolayer  Astrocytes were isolated by mechanical dissection following trypsin digestion and were frozen for later co-culture  RBEC were isolated from 5-week-old rat cortices  The brains were cleaned of meninges and white matter, and mechanically dissociated following enzymatic digestion  Thereafter, the tissue homogenate was centrifuged in bovine serum albumin to separate vessel fragments from nervous tissue  The vessel fragments underwent a second enzymatic digestion to free endothelial cells from their extracellular matrix  The remaining contaminating cells such as pericytes were further eliminated by plating the microvessel fragments in puromycin-containing medium  They were then passaged onto filters for co-culture with astrocytes grown on the bottom of the wells  RBEC expressed high levels of tight junction (TJ) proteins such as occludin, claudin-5 and ZO-1 with a typical localization at the cell borders  The transendothelial electrical resistance (TEER) of brain endothelial monolayers, indicating the tightness of TJs reached 300 ohm·cm2 on average  The endothelial permeability coefficients (Pe) for lucifer yellow (LY) was highly reproducible with an average of 0 26 ± 0 11 x 10-3 cm/min  Brain endothelial cells organized in monolayers expressed the efflux transporter P-glycoprotein (P-gp), showed a polarized transport of rhodamine 123, a ligand for P-gp, and showed specific transport of transferrin-Cy3 and DiILDL across the endothelial cell monolayer  In conclusion, we provide a protocol for setting up an in vitro BBB model that is highly reproducible due to the quality assurance methods, and that is suitable for research on BBB transporters and receptors Medicine, Issue 88, rat brain endothelial cells (RBEC), mouse, spinal cord, tight junction (TJ), receptor-mediated transport (RMT), low density lipoprotein (LDL), LDLR, transferrin, TfR, P-glycoprotein (P-gp), transendothelial electrical resistance (TEER),51278Play ButtonInducing Plasticity of Astrocytic Receptors by Manipulation of Neuronal Firing RatesAuthors: Alison X  Xie, Kelli Lauderdale, Thomas Murphy, Timothy L  Myers, Todd A  Fiacco  Institutions: University of California Riverside, University of California Riverside, University of California Riverside Close to two decades of research has established that astrocytes in situ and in vivo express numerous G protein-coupled receptors (GPCRs) that can be stimulated by neuronally-released transmitter  However, the ability of astrocytic receptors to exhibit plasticity in response to changes in neuronal activity has received little attention  Here we describe a model system that can be used to globally scale up or down astrocytic group I metabotropic glutamate receptors (mGluRs) in acute brain slices  Included are methods on how to prepare parasagittal hippocampal slices, construct chambers suitable for long-term slice incubation, bidirectionally manipulate neuronal action potential frequency, load astrocytes and astrocyte processes with fluorescent Ca2+ indicator, and measure changes in astrocytic Gq GPCR activity by recording spontaneous and evoked astrocyte Ca2+ events using confocal microscopy  In essence, a “calcium roadmap” is provided for how to measure plasticity of astrocytic Gq GPCRs  Applications of the technique for study of astrocytes are discussed  Having an understanding of how astrocytic receptor signaling is affected by changes in neuronal activity has important implications for both normal synaptic function as well as processes underlying neurological disorders and neurodegenerative disease Neuroscience, Issue 85, astrocyte, plasticity, mGluRs, neuronal Firing, electrophysiology, Gq GPCRs, Bolus-loading, calcium, microdomains, acute slices, Hippocampus, mouse51458Play ButtonInhibitory Synapse Formation in a Co-culture Model Incorporating GABAergic Medium Spiny Neurons and HEK293 Cells Stably Expressing GABAA ReceptorsAuthors: Laura E  Brown, Celine Fuchs, Martin W  Nicholson, F  Anne Stephenson, Alex M  Thomson, Jasmina N  Jovanovic  Institutions: University College London Inhibitory neurons act in the central nervous system to regulate the dynamics and spatio-temporal co-ordination of neuronal networks  GABA (γ-aminobutyric acid) is the predominant inhibitory neurotransmitter in the brain  It is released from the presynaptic terminals of inhibitory neurons within highly specialized intercellular junctions known as synapses, where it binds to GABAA receptors (GABAARs) present at the plasma membrane of the synapse-receiving, postsynaptic neurons  Activation of these GABA-gated ion channels leads to influx of chloride resulting in postsynaptic potential changes that decrease the probability that these neurons will generate action potentials  During development, diverse types of inhibitory neurons with distinct morphological, electrophysiological and neurochemical characteristics have the ability to recognize their target neurons and form synapses which incorporate specific GABAARs subtypes  This principle of selective innervation of neuronal targets raises the question as to how the appropriate synaptic partners identify each other  To elucidate the underlying molecular mechanisms, a novel in vitro co-culture model system was established, in which medium spiny GABAergic neurons, a highly homogenous population of neurons isolated from the embryonic striatum, were cultured with stably transfected HEK293 cell lines that express different GABAAR subtypes  Synapses form rapidly, efficiently and selectively in this system, and are easily accessible for quantification  Our results indicate that various GABAAR subtypes differ in their ability to promote synapse formation, suggesting that this reduced in vitro model system can be used to reproduce, at least in part, the in vivo conditions required for the recognition of the appropriate synaptic partners and formation of specific synapses  Here the protocols for culturing the medium spiny neurons and generating HEK293 cells lines expressing GABAARs are first described, followed by detailed instructions on how to combine these two cell types in co-culture and analyze the formation of synaptic contacts  Neuroscience, Issue 93, Developmental neuroscience, synaptogenesis, synaptic inhibition, co-culture, stable cell lines, GABAergic, medium spiny neurons, HEK 293 cell line52115Play ButtonTwo-Photon in vivo Imaging of Dendritic Spines in the Mouse Cortex Using a Thinned-skull PreparationAuthors: Xinzhu Yu, Yi Zuo  Institutions: University of California, Santa Cruz In the mammalian cortex, neurons form extremely complicated networks and exchange information at synapses  Changes in synaptic strength, as well as addition/removal of synapses, occur in an experience-dependent manner, providing the structural foundation of neuronal plasticity  As postsynaptic components of the most excitatory synapses in the cortex, dendritic spines are considered to be a good proxy of synapses  Taking advantages of mouse genetics and fluorescent labeling techniques, individual neurons and their synaptic structures can be labeled in the intact brain  Here we introduce a transcranial imaging protocol using two-photon laser scanning microscopy to follow fluorescently labeled postsynaptic dendritic spines over time in vivo  This protocol utilizes a thinned-skull preparation, which keeps the skull intact and avoids inflammatory effects caused by exposure of the meninges and the cortex  Therefore, images can be acquired immediately after surgery is performed  The experimental procedure can be performed repetitively over various time intervals ranging from hours to years  The application of this preparation can also be expanded to investigate different cortical regions and layers, as well as other cell types, under physiological and pathological conditions Neuroscience, Issue 87, dendritic spine, mouse cortex, in vivo, two-photon microscopy, thinned-skull, imaging51520Play ButtonModeling Astrocytoma Pathogenesis In Vitro and In Vivo Using Cortical Astrocytes or Neural Stem Cells from Conditional, Genetically Engineered MiceAuthors: Robert S  McNeill, Ralf S  Schmid, Ryan E  Bash, Mark Vitucci, Kristen K  White, Andrea M  Werneke, Brian H  Constance, Byron Huff, C  Ryan Miller  Institutions: University of North Carolina School of Medicine, University of North Carolina School of Medicine, University of North Carolina School of Medicine, University of North Carolina School of Medicine, University of North Carolina School of Medicine, Emory University School of Medicine, University of North Carolina School of Medicine Current astrocytoma models are limited in their ability to define the roles of oncogenic mutations in specific brain cell types during disease pathogenesis and their utility for preclinical drug development  In order to design a better model system for these applications, phenotypically wild-type cortical astrocytes and neural stem cells (NSC) from conditional, genetically engineered mice (GEM) that harbor various combinations of floxed oncogenic alleles were harvested and grown in culture  Genetic recombination was induced in vitro using adenoviral Cre-mediated recombination, resulting in expression of mutated oncogenes and deletion of tumor suppressor genes  The phenotypic consequences of these mutations were defined by measuring proliferation, transformation, and drug response in vitro  Orthotopic allograft models, whereby transformed cells are stereotactically injected into the brains of immune-competent, syngeneic littermates, were developed to define the role of oncogenic mutations and cell type on tumorigenesis in vivo  Unlike most established human glioblastoma cell line xenografts, injection of transformed GEM-derived cortical astrocytes into the brains of immune-competent littermates produced astrocytomas, including the most aggressive subtype, glioblastoma, that recapitulated the histopathological hallmarks of human astrocytomas, including diffuse invasion of normal brain parenchyma  Bioluminescence imaging of orthotopic allografts from transformed astrocytes engineered to express luciferase was utilized to monitor in vivo tumor growth over time  Thus, astrocytoma models using astrocytes and NSC harvested from GEM with conditional oncogenic alleles provide an integrated system to study the genetics and cell biology of astrocytoma pathogenesis in vitro and in vivo and may be useful in preclinical drug development for these devastating diseases Neuroscience, Issue 90, astrocytoma, cortical astrocytes, genetically engineered mice, glioblastoma, neural stem cells, orthotopic allograft51763Play ButtonPaired Whole Cell Recordings in Organotypic Hippocampal SlicesAuthors: Chantelle Fourie, Marianna Kiraly, Daniel V  Madison, Johanna M  Montgomery  Institutions: University of Auckland, Stanford University Pair recordings involve simultaneous whole cell patch clamp recordings from two synaptically connected neurons, enabling not only direct electrophysiological characterization of the synaptic connections between individual neurons, but also pharmacological manipulation of either the presynaptic or the postsynaptic neuron  When carried out in organotypic hippocampal slice cultures, the probability that two neurons are synaptically connected is significantly increased  This preparation readily enables identification of cell types, and the neurons maintain their morphology and properties of synaptic function similar to that in native brain tissue  A major advantage of paired whole cell recordings is the highly precise information it can provide on the properties of synaptic transmission and plasticity that are not possible with other more crude techniques utilizing extracellular axonal stimulation  Paired whole cell recordings are often perceived as too challenging to perform  While there are challenging aspects to this technique, paired recordings can be performed by anyone trained in whole cell patch clamping provided specific hardware and methodological criteria are followed  The probability of attaining synaptically connected paired recordings significantly increases with healthy organotypic slices and stable micromanipulation allowing independent attainment of pre- and postsynaptic whole cell recordings  While CA3-CA3 pyramidal cell pairs are most widely used in the organotypic slice hippocampal preparation, this technique has also been successful in CA3-CA1 pairs and can be adapted to any neurons that are synaptically connected in the same slice preparation  In this manuscript we provide the detailed methodology and requirements for establishing this technique in any laboratory equipped for electrophysiology Neuroscience, Issue 91, hippocampus, paired recording, whole cell recording, organotypic slice, synapse, synaptic transmission, synaptic plasticity51958Play ButtonImaging Intracellular Ca2+ Signals in Striatal Astrocytes from Adult Mice Using Genetically-encoded Calcium IndicatorsAuthors: Ruotian Jiang, Martin D  Haustein, Michael V  Sofroniew, Baljit S  Khakh  Institutions: University of California Los Angeles, University of California Los Angeles Astrocytes display spontaneous intracellular Ca2+ concentration fluctuations ([Ca2+]i) and in several settings respond to neuronal excitation with enhanced [Ca2+]i signals  It has been proposed that astrocytes in turn regulate neurons and blood vessels through calcium-dependent mechanisms, such as the release of signaling molecules  However, [Ca2+]i imaging in entire astrocytes has only recently become feasible with genetically encoded calcium indicators (GECIs) such as the GCaMP series  The use of GECIs in astrocytes now provides opportunities to study astrocyte [Ca2+]i signals in detail within model microcircuits such as the striatum, which is the largest nucleus of the basal ganglia  In the present report, detailed surgical methods to express GECIs in astrocytes in vivo, and confocal imaging approaches to record [Ca2+]i signals in striatal astrocytes in situ, are described  We highlight precautions, necessary controls and tests to determine if GECI expression is selective for astrocytes and to evaluate signs of overt astrocyte reactivity  We also describe brain slice and imaging conditions in detail that permit reliable [Ca2+]i imaging in striatal astrocytes in situ  The use of these approaches revealed the entire territories of single striatal astrocytes and spontaneous [Ca2+]i signals within their somata, branches and branchlets  The further use and expansion of these approaches in the striatum will allow for the detailed study of astrocyte [Ca2+]i signals in the striatal microcircuitry Neuroscience, Issue 93, astrocyte, calcium, striatum, GECI, GCaMP3, AAV2/5, stereotaxic injection, brain slice, imaging51972Play ButtonMethods to Assess Subcellular Compartments of Muscle in C  elegansAuthors: Christopher J  Gaffney, Joseph J  Bass, Thomas F  Barratt, Nathaniel J  Szewczyk  Institutions: University of Nottingham Muscle is a dynamic tissue that responds to changes in nutrition, exercise, and disease state  The loss of muscle mass and function with disease and age are significant public health burdens  We currently understand little about the genetic regulation of muscle health with disease or age  The nematode C  elegans is an established model for understanding the genomic regulation of biological processes of interest  This worm’s body wall muscles display a large degree of homology with the muscles of higher metazoan species  Since C  elegans is a transparent organism, the localization of GFP to mitochondria and sarcomeres allows visualization of these structures in vivo  Similarly, feeding animals cationic dyes, which accumulate based on the existence of a mitochondrial membrane potential, allows the assessment of mitochondrial function in vivo  These methods, as well as assessment of muscle protein homeostasis, are combined with assessment of whole animal muscle function, in the form of movement assays, to allow correlation of sub-cellular defects with functional measures of muscle performance  Thus, C  elegans provides a powerful platform with which to assess the impact of mutations, gene knockdown, and/or chemical compounds upon muscle structure and function  Lastly, as GFP, cationic dyes, and movement assays are assessed non-invasively, prospective studies of muscle structure and function can be conducted across the whole life course and this at present cannot be easily investigated in vivo in any other organism Developmental Biology, Issue 93, Physiology, C  elegans, muscle, mitochondria, sarcomeres, ageing52043Play ButtonImproved Preparation and Preservation of Hippocampal Mouse Slices for a Very Stable and Reproducible Recording of Long-term PotentiationAuthors: Agnès Villers, Laurence Ris  Institutions: University of Mons Long-term potentiation (LTP) is a type of synaptic plasticity characterized by an increase in synaptic strength and believed to be involved in memory encoding  LTP elicited in the CA1 region of acute hippocampal slices has been extensively studied  However the molecular mechanisms underlying the maintenance phase of this phenomenon are still poorly understood  This could be partly due to the various experimental conditions used by different laboratories  Indeed, the maintenance phase of LTP is strongly dependent on external parameters like oxygenation, temperature and humidity  It is also dependent on internal parameters like orientation of the slicing plane and slice viability after dissection 
The optimization of all these parameters enables the induction of a very reproducible and very stable long-term potentiation  This methodology offers the possibility to further explore the molecular mechanisms involved in the stable increase in synaptic strength in hippocampal slices  It also highlights the importance of experimental conditions in in vitro investigation of neurophysiological phenomena Neuroscience, Issue 76, Neurobiology, Anatomy, Physiology, Biomedical Engineering, Surgery, Memory Disorders, Learning, Memory, Neurosciences, Neurophysiology, hippocampus, long-term potentiation, mice, acute slices, synaptic plasticity, in vitro, electrophysiology, animal model50483Play ButtonIn Vivo Modeling of the Morbid Human Genome using Danio rerioAuthors: Adrienne R  Niederriter, Erica E  Davis, Christelle Golzio, Edwin C  Oh, I-Chun Tsai, Nicholas Katsanis  Institutions: Duke University Medical Center, Duke University, Duke University Medical Center Here, we present methods for the development of assays to query potentially clinically significant nonsynonymous changes using in vivo complementation in zebrafish  Zebrafish (Danio rerio) are a useful animal system due to their experimental tractability; embryos are transparent to enable facile viewing, undergo rapid development ex vivo, and can be genetically manipulated 1 These aspects have allowed for significant advances in the analysis of embryogenesis, molecular processes, and morphogenetic signaling  Taken together, the advantages of this vertebrate model make zebrafish highly amenable to modeling the developmental defects in pediatric disease, and in some cases, adult-onset disorders  Because the zebrafish genome is highly conserved with that of humans (~70% orthologous), it is possible to recapitulate human disease states in zebrafish  This is accomplished either through the injection of mutant human mRNA to induce dominant negative or gain of function alleles, or utilization of morpholino (MO) antisense oligonucleotides to suppress genes to mimic loss of function variants  Through complementation of MO-induced phenotypes with capped human mRNA, our approach enables the interpretation of the deleterious effect of mutations on human protein sequence based on the ability of mutant mRNA to rescue a measurable, physiologically relevant phenotype  Modeling of the human disease alleles occurs through microinjection of zebrafish embryos with MO and/or human mRNA at the 1-4 cell stage, and phenotyping up to seven days post fertilization (dpf)  This general strategy can be extended to a wide range of disease phenotypes, as demonstrated in the following protocol  We present our established models for morphogenetic signaling, craniofacial, cardiac, vascular integrity, renal function, and skeletal muscle disorder phenotypes, as well as others  Molecular Biology, Issue 78, Genetics, Biomedical Engineering, Medicine, Developmental Biology, Biochemistry, Anatomy, Physiology, Bioengineering, Genomics, Medical, zebrafish, in vivo, morpholino, human disease modeling, transcription, PCR, mRNA, DNA, Danio rerio, animal model50338Play ButtonDirect Imaging of ER Calcium with Targeted-Esterase Induced Dye Loading (TED)Authors: Samira Samtleben, Juliane Jaepel, Caroline Fecher, Thomas Andreska, Markus Rehberg, Robert Blum  Institutions: University of Wuerzburg, Max Planck Institute of Neurobiology, Martinsried, Ludwig-Maximilians University of Munich Visualization of calcium dynamics is important to understand the role of calcium in cell physiology  To examine calcium dynamics, synthetic fluorescent Ca2+ indictors have become popular  Here we demonstrate TED (= targeted-esterase induced dye loading), a method to improve the release of Ca2+ indicator dyes in the ER lumen of different cell types  To date, TED was used in cell lines, glial cells, and neurons in vitro  TED bases on efficient, recombinant targeting of a high carboxylesterase activity to the ER lumen using vector-constructs that express Carboxylesterases (CES)  The latest TED vectors contain a core element of CES2 fused to a red fluorescent protein, thus enabling simultaneous two-color imaging  The dynamics of free calcium in the ER are imaged in one color, while the corresponding ER structure appears in red  At the beginning of the procedure, cells are transduced with a lentivirus  Subsequently, the infected cells are seeded on coverslips to finally enable live cell imaging  Then, living cells are incubated with the acetoxymethyl ester (AM-ester) form of low-affinity Ca2+ indicators, for instance Fluo5N-AM, Mag-Fluo4-AM, or Mag-Fura2-AM  The esterase activity in the ER cleaves off hydrophobic side chains from the AM form of the Ca2+ indicator and a hydrophilic fluorescent dye/Ca2+ complex is formed and trapped in the ER lumen  After dye loading, the cells are analyzed at an inverted confocal laser scanning microscope  Cells are continuously perfused with Ringer-like solutions and the ER calcium dynamics are directly visualized by time-lapse imaging  Calcium release from the ER is identified by a decrease in fluorescence intensity in regions of interest, whereas the refilling of the ER calcium store produces an increase in fluorescence intensity  Finally, the change in fluorescent intensity over time is determined by calculation of ΔF/F0 Cellular Biology, Issue 75, Neurobiology, Neuroscience, Molecular Biology, Biochemistry, Biomedical Engineering, Bioengineering, Virology, Medicine, Anatomy, Physiology, Surgery, Endoplasmic Reticulum, ER, Calcium Signaling, calcium store, calcium imaging, calcium indicator, metabotropic signaling, Ca2+, neurons, cells, mouse, animal model, cell culture, targeted esterase induced dye loading, imaging50317Play ButtonPreparation of Dissociated Mouse Cortical Neuron CulturesAuthors: Lutz G  W  Hilgenberg, Martin A  Smith  Institutions: University of California, Irvine (UCI) This video will guide you through the process for generating cortical neuronal cultures from late embryo and early postnatal mouse brain  These cultures can be used for a variety of applications including immunocytochemistry, biochemistry, electrophysiology, calcium and sodium imaging, protein and/or RNA isolation  These cultures also provide a platform to study the neuronal development of transgenic animals that carry a late embryonic or postnatal lethal gene mutation  The procedure is relatively straight forward, requires some experience in tissue culture technique and should not take longer than two to three hours if you are properly prepared  Careful separation of the cortical rind from the thalamo-cortical fiber tract will reduce the number of unwanted non-neuronal cells  To increase yields of neuronal cells triturate the pieces of the cortical tissue gently after the enzyme incubation step  This is imperative as it prevents unnecessary injury to cells and premature neuronal cell death  Since these cultures are maintained in the absence of glia feeder cells, they also offer an added advantage of growing cultures enriched in neurons Neuroscience, Issue 10, cellular, molecular, neurobiology, neuron, calcium/sodium imaging, primary cultures, mouse562Play ButtonAnalysis of Schwann-astrocyte Interactions Using In Vitro AssaysAuthors: Fardad T  Afshari, Jessica C  Kwok, James W  Fawcett  Institutions: University of Cambridge Schwann cells are one of the commonly used cells in repair strategies following spinal cord injuries  Schwann cells are capable of supporting axonal regeneration and sprouting by secreting growth factors 1,2 and providing growth promoting adhesion molecules 3 and extracellular matrix molecules 4  In addition they myelinate the demyelinated axons at the site of injury 5 
However following transplantation, Schwann cells do not migrate from the site of implant and do not intermingle with the host astrocytes 6,7  This results in formation of a sharp boundary between the Schwann cells and astrocytes, creating an obstacle for growing axons trying to exit the graft back into the host tissue proximally and distally  Astrocytes in contact with Schwann cells also undergo hypertrophy and up-regulate the inhibitory molecules 8-13 
In vitro assays have been used to model Schwann cell-astrocyte interactions and have been important in understanding the mechanism underlying the cellular behaviour 
These in vitro assays include boundary assay, where a co-culture is made using two different cells with each cell type occupying different territories with only a small gap separating the two cell fronts  As the cells divide and migrate, the two cellular fronts get closer to each other and finally collide  This allows the behaviour of the two cellular populations to be analyzed at the boundary  Another variation of the same technique is to mix the two cellular populations in culture and over time the two cell types segregate with Schwann cells clumped together as islands in between astrocytes together creating multiple Schwann-astrocyte boundaries 
The second assay used in studying the interaction of two cell types is the migration assay where cellular movement can be tracked on the surface of the other cell type monolayer 14,15  This assay is commonly known as inverted coverslip assay  Schwann cells are cultured on small glass fragments and they are inverted face down onto the surface of astrocyte monolayers and migration is assessed from the edge of coverslip 
Both assays have been instrumental in studying the underlying mechanisms involved in the cellular exclusion and boundary formation  Some of the molecules identified using these techniques include N-Cadherins 15, Chondroitin Sulphate proteoglycans(CSPGs) 16,17, FGF/Heparin 18, Eph/Ephrins19 
This article intends to describe boundary assay and migration assay in stepwise fashion and elucidate the possible technical problems that might occur Cellular Biology, Issue 47, Schwann cell, astrocyte, boundary, migration, repulsion2214Play ButtonQuantifying Synapses: an Immunocytochemistry-based Assay to Quantify Synapse NumberAuthors: Dominic M  Ippolito, Cagla Eroglu  Institutions: Duke University, Duke University One of the most important goals in neuroscience is to understand the molecular cues that instruct early stages of synapse formation  As such it has become imperative to develop objective approaches to quantify changes in synaptic connectivity  Starting from sample fixation, this protocol details how to quantify synapse number both in dissociated neuronal culture and in brain sections using immunocytochemistry  Using compartment-specific antibodies, we label presynaptic terminals as well as sites of postsynaptic specialization  We define synapses as points of colocalization between the signals generated by these markers  The number of these colocalizations is quantified using a plug in Puncta Analyzer (written by Bary Wark, available upon request, c eroglu@cellbio duke edu) under the ImageJ analysis software platform  The synapse assay described in this protocol can be applied to any neural tissue or culture preparation for which you have selective pre- and postsynaptic markers  This synapse assay is a valuable tool that can be widely utilized in the study of synaptic development Neuroscience, Issue 45, synapse, immunocytochemistry, brain, neuron, astrocyte2270Play ButtonPreparation of Acute Hippocampal Slices from Rats and Transgenic Mice for the Study of Synaptic Alterations during Aging and Amyloid PathologyAuthors: Diana M  Mathis, Jennifer L  Furman, Christopher M  Norris  Institutions: University of Kentucky College of Public Health, University of Kentucky College of Medicine, University of Kentucky College of Medicine The rodent hippocampal slice preparation is perhaps the most broadly used tool for investigating mammalian synaptic function and plasticity  The hippocampus can be extracted quickly and easily from rats and mice and slices remain viable for hours in oxygenated artificial cerebrospinal fluid  Moreover, basic electrophysisologic techniques are easily applied to the investigation of synaptic function in hippocampal slices and have provided some of the best biomarkers for cognitive impairments  The hippocampal slice is especially popular for the study of synaptic plasticity mechanisms involved in learning and memory  Changes in the induction of long-term potentiation and depression (LTP and LTD) of synaptic efficacy in hippocampal slices (or lack thereof) are frequently used to describe the neurologic phenotype of cognitively-impaired animals and/or to evaluate the mechanism of action of nootropic compounds  This article outlines the procedures we use for preparing hippocampal slices from rats and transgenic mice for the study of synaptic alterations associated with brain aging and Alzheimer's disease (AD)1-3  Use of aged rats and AD model mice can present a unique set of challenges to researchers accustomed to using younger rats and/or mice in their research  Aged rats have thicker skulls and tougher connective tissue than younger rats and mice, which can delay brain extraction and/or dissection and consequently negate or exaggerate real age-differences in synaptic function and plasticity  Aging and amyloid pathology may also exacerbate hippocampal damage sustained during the dissection procedure, again complicating any inferences drawn from physiologic assessment  Here, we discuss the steps taken during the dissection procedure to minimize these problems  Examples of synaptic responses acquired in "healthy" and "unhealthy" slices from rats and mice are provided, as well as representative synaptic plasticity experiments  The possible impact of other methodological factors on synaptic function in these animal models (e g  recording solution components, stimulation parameters) are also discussed  While the focus of this article is on the use of aged rats and transgenic mice, novices to slice physiology should find enough detail here to get started on their own studies, using a variety of rodent models Neuroscience, Issue 49, aging, amyloid, hippocampal slice, synaptic plasticity, Ca2+, CA1, electrophysiology2330Play ButtonMesenteric Artery Contraction and Relaxation Studies Using Automated Wire MyographyAuthors: Lakeesha E  Bridges, Cicely L  Williams, Mildred A  Pointer, Emmanuel M  Awumey  Institutions: North Carolina Central University, Durham, North Carolina Central University, Durham, Wake Forest University School of Medicine Proximal resistance vessels, such as the mesenteric arteries, contribute substantially to the peripheral resistance  These small vessels of between 100-400 μm in diameter function primarily in directing blood flow to various organs according to the overall requirements of the body  The rat mesenteric artery has a diameter greater than 100 μm  The myography technique, first described by Mulvay and Halpern1, was based on the method proposed by Bevan and Osher2  The technique provides information about small vessels under isometric conditions, where substantial shortening of the muscle preparation is prevented  Since force production and sensitivity of vessels to different agonists is dependent on the extent of stretch, according to active tension-length relation, it is essential to conduct contraction studies under isometric conditions to prevent compliance of the mounting wires  Stainless steel wires are preferred to tungsten wires because of oxidation of the latter, which affects recorded responses3 The technique allows for the comparison of agonist-induced contractions of mounted vessels to obtain evidence for normal function of vascular smooth muscle cell receptors 
Medicine, Issue 55, cardiovascular, resistant arteries, contraction, relaxation, myography3119Play ButtonVisualization and Genetic Manipulation of Dendrites and Spines in the Mouse Cerebral Cortex and Hippocampus using In utero ElectroporationAuthors: Emilie Pacary, Matilda A  Haas, Hendrik Wildner, Roberta Azzarelli, Donald M  Bell, Djoher Nora Abrous, François Guillemot  Institutions: MRC National Institute for Medical Research, National Institute for Medical Research, Université de Bordeaux In utero electroporation (IUE) has become a powerful technique to study the development of different regions of the embryonic nervous system 1-5  To date this tool has been widely used to study the regulation of cellular proliferation, differentiation and neuronal migration especially in the developing cerebral cortex 6-8  Here we detail our protocol to electroporate in utero the cerebral cortex and the hippocampus and provide evidence that this approach can be used to study dendrites and spines in these two cerebral regions 
Finally, IUE provides a useful tool to identify functional interactions between genes involved in dendrite, spine and/or synapse development  Indeed, in contrast to other gene transfer methods such as virus, it is straightforward to combine multiple RNAi or transgenes in the same population of cells  In summary, IUE is a powerful method that has already contributed to the characterization of molecular mechanisms underlying brain function and disease and it should also be useful in the study of dendrites and spines Neuroscience, Issue 65, Developmental Biology, Molecular Biology, Neuronal development, In utero electroporation, dendrite, spines, hippocampus, cerebral cortex, gain and loss of function4163Play ButtonImaging Analysis of Neuron to Glia Interaction in Microfluidic Culture Platform (MCP)-based Neuronal Axon and Glia Co-culture SystemAuthors: Haruki Higashimori, Yongjie Yang  Institutions: Tufts University, Tufts Sackler School of Graduate Biomedical Sciences Proper neuron to glia interaction is critical to physiological function of the central nervous system (CNS)  This bidirectional communication is sophisticatedly mediated by specific signaling pathways between neuron and glia1,2   Identification and characterization of these signaling pathways is essential to the understanding of how neuron to glia interaction shapes CNS physiology  Previously, neuron and glia mixed cultures have been widely utilized for testing and characterizing signaling pathways between neuron and glia  What we have learned from these preparations and other in vivo tools, however, has suggested that mutual signaling between neuron and glia often occurred in specific compartments within neurons (i e , axon, dendrite, or soma)3  This makes it important to develop a new culture system that allows separation of neuronal compartments and specifically examines the interaction between glia and neuronal axons/dendrites  In addition, the conventional mixed culture system is not capable of differentiating the soluble factors and direct membrane contact signals between neuron and glia  Furthermore, the large quantity of neurons and glial cells in the conventional co-culture system lacks the resolution necessary to observe the interaction between a single axon and a glial cell 
In this study, we describe a novel axon and glia co-culture system with the use of a microfluidic culture platform (MCP)  In this co-culture system, neurons and glial cells are cultured in two separate chambers that are connected through multiple central channels  In this microfluidic culture platform, only neuronal processes (especially axons) can enter the glial side through the central channels  In combination with powerful fluorescent protein labeling, this system allows direct examination of signaling pathways between axonal/dendritic and glial interactions, such as axon-mediated transcriptional regulation in glia, glia-mediated receptor trafficking in neuronal terminals, and glia-mediated axon growth  The narrow diameter of the chamber also significantly prohibits the flow of the neuron-enriched medium into the glial chamber, facilitating probing of the direct membrane-protein interaction between axons/dendrites and glial surfaces Neuroscience, Issue 68, Molecular Biology, Cellular Biology, Biophysics, Microfluidics, Microfluidic culture platform, Compartmented culture, Neuron to glia signaling, neurons, glia, cell culture4448Play ButtonFluorescence Recovery After Photobleaching (FRAP) of Fluorescence Tagged Proteins in Dendritic Spines of Cultured Hippocampal NeuronsAuthors: Chan-Ying Zheng, Ronald S  Petralia, Ya-Xian Wang, Bechara Kachar  Institutions: National Institutes of Health, Bethesda FRAP has been used to quantify the mobility of GFP-tagged proteins  Using a strong excitation laser, the fluorescence of a GFP-tagged protein is bleached in the region of interest  The fluorescence of the region recovers when the unbleached GFP-tagged protein from outside of the region diffuses into the region of interest  The mobility of the protein is then analyzed by measuring the fluorescence recovery rate  This technique could be used to characterize protein mobility and turnover rate 
This FRAP protocol shows how to perform a basic FRAP experiment as well as how to analyze the data Neuroscience, Issue 50, Spine, FRAP, hippocampal neurons, live cell imaging, protein mobility2568Play ButtonPrimary Neuronal Cultures from the Brains of Late Stage Drosophila PupaeAuthors: Beatriz Sicaeros, Jorge M  Campusano, Diane K  O'Dowd  Institutions: University of California, Irvine (UCI) In this video, we demonstrate the preparation of primary neuronal cultures from the brains of late stage Drosophila pupae  The procedure begins with the removal of brains from animals at 70-78 hrs after puparium formation  The isolated brains are shown after brief incubation in papain followed by several washes in serum-free growth medium  The process of mechanical dissociation of each brain in a 5 ul drop of media on a coverslip is illustrated  The axons and dendrites of the post-mitotic neurons are sheered off near the soma during dissociation but the neurons begin to regenerate processes within a few hours of plating  Images show live cultures at 2 days  Neurons continue to elaborate processes during the first week in culture  Specific neuronal populations can be identified in culture using GAL4 lines to drive tissue specific expression of fluorescent markers such as GFP or RFP  Whole cell recordings have demonstrated the cultured neurons form functional, spontaneously active cholinergic and GABAergic synapses  A short video segment illustrates calcium dynamics in the cultured neurons using Fura-2 as a calcium indicator dye to monitor spontaneous calcium transients and nicotine evoked calcium responses in a dish of cultured neurons  These pupal brain cultures are a useful model system in which genetic and pharmacological tools can be used to identify intrinsic and extrinsic factors that influence formation and function of central synapses 
Context 2: \section{Introduction}
\label{sec:introduction}

Probabilistic models have proven to be very useful in a lot of applications in signal processing where signal estimation is needed \cite{rabiner1989tutorial,arulampalam2002tutorial,ji2008bayesian}  Some of their advantages are that 1) they force the designer to specify all the assumptions of the model, 2) they provide a clear separation between the model and the algorithm used to solve it, and 3) they usually provide some measure of uncertainty about the estimation 

On the other hand, adaptive filtering is a standard approach in estimation problems when the input is received as a stream of data that is potentially non-stationary  This approach is widely understood and applied to several problems such as echo cancellation \cite{gilloire1992adaptive}, noise cancellation \cite{nelson1991active}, and channel equalization \cite{falconer2002frequency} 

Although these two approaches share some underlying relations, there are very few connections in the literature  The first important attempt in the signal processing community to relate these two fields was the connection between a linear Gaussian state-space model (i e  Kalman filter) and the RLS filter, by Sayed and Kailath \cite{sayed1994state} and then by Haykin \emph{et al } \cite{haykin1997adaptive}  The RLS adaptive filtering algorithm emerges naturally when one defines a particular state-space model (SSM) and then performs exact inference in that model  This approach was later exploited in \cite{van2012kernel} to design a kernel RLS algorithm based on Gaussian processes 

A first attempt to approximate the LMS filter from a probabilistic perspective was presented in \cite{park2014probabilistic}, focusing on a kernel-based implementation  The algorithm of \cite{park2014probabilistic} makes use of a Maximum a Posteriori (MAP) estimate as an approximation for the predictive step  However, this approximation does not preserve the estimate of the uncertainty in each step, therefore degrading the performance of the algorithm 

In this work, we provide a similar connection between state-space models and least-mean-squares (LMS)  Our approach is based on approximating the posterior distribution with an isotropic Gaussian distribution  We show how the computation of this approximated posterior leads to a linear-complexity algorithm, comparable to the standard LMS  Similar approaches have already been developed for a variety of problems such as channel equalization using recurrent RBF neural networks \cite{cid1994recurrent}, or Bayesian forecasting \cite{harrison1999bayesian}  Here, we show the usefulness of this probabilistic approach for adaptive filtering 

The probabilistic perspective we adopt throughout this work presents two main advantages  Firstly, a novel LMS algorithm with adaptable step size emerges naturally with this approach, making it suitable for both stationary and non-stationary environments  The proposed algorithm has less free parameters than previous LMS algorithms with variable step size \cite{kwong1992variable,aboulnasr1997robust,shin2004variable}, and its parameters are easier to be tuned w r t  these algorithms and standard LMS  Secondly, the use of a probabilistic model provides us with an estimate of the error variance, which is useful in many applications 

Experiments with simulated and real data show the advantages of the presented approach with respect to previous works  However, we remark that the main contribution of this paper is that it opens the door to introduce more Bayesian machine learning techniques, such as variational inference and Monte Carlo sampling methods \cite{barber2012bayesian}, to adaptive filtering \\


\section{Probabilistic Model}

Throughout this work, we assume the observation model to be linear-Gaussian with the following distribution,

\begin{equation}
p(y_k|{\bf w}_k) = \mathcal{N}(y_k;{\bf x}_k^T {\bf w}_k , \sigma_n^2),
\label{eq:mess_eq}
\end{equation}
where  $\sigma_n^2$ is the variance of the observation noise, ${\bf x}_k$ is the regression vector and ${\bf w}_k$ is the parameter vector to be sequentially estimated, both $M$-dimensional column vectors 


In a non-stationary scenario, ${\bf w}_k$ follows a dynamic process  In particular, we consider a diffusion process (random-walk model) with variance $\sigma_d^2$ for this parameter vector:


\begin{equation}
p({\bf w}_k|{\bf w}_{k-1})= \mathcal{N}({\bf w}_k;{\bf w}_{k-1}, \sigma_d^2 {\bf I}),
\label{eq:trans_eq}
\end{equation}
where $\bf I$ denotes the identity matrix  In order to initiate the recursion, we assume the following prior distribution on ${\bf w}_k$

\begin{equation}
p({\bf w}_0)= \mathcal{N}({\bf w}_0;0, \sigma_d^2{\bf I}) \nonumber
\end{equation}

\section{Exact inference in this model: Revisiting the RLS filter}

Given the described probabilistic SSM, we would like to infer the posterior probability distribution $p({\bf w}_k|y_{1:k})$ 
Since all involved distributions are Gaussian, one can perform exact inference, leveraging the probability rules in a straightforward manner  The resulting probability distribution is
\begin{equation}
p({\bf w}_k|y_{1:k}) =  \mathcal{N}({\bf w}_k;{\bf\boldsymbol\mu}_{k}, \boldsymbol\Sigma_{k}), \nonumber
\end{equation}
in which the mean vector ${\bf\boldsymbol\mu}_{k}$ is given by
\begin{equation}
{\bf\boldsymbol\mu}_k = {\bf\boldsymbol\mu}_{k-1} + {\bf K}_k (y_k - {\bf x}_k^T {\bf\boldsymbol\mu}_{k-1}){\bf x}_k, \nonumber
\end{equation}
where we have introduced the auxiliary variable
\begin{equation}
{\bf K}_k = \frac{ \left(\boldsymbol\Sigma_{k-1} + \sigma_d^2 {\bf I}\right)}{{\bf x}_k^T  \left(\boldsymbol\Sigma_{k-1} + \sigma_d^2 {\bf I}\right)  {\bf x}_k + \sigma_n^2}, \nonumber
\end{equation}
and the covariance matrix $\boldsymbol\Sigma_k$ is obtained as
\begin{equation}
\boldsymbol\Sigma_k = \left( {\bf I} -  {\bf K}_k{\bf x}_k {\bf x}_k^T \right) ( \boldsymbol\Sigma_{k-1} +\sigma_d^2), \nonumber
\end{equation}
Note that the mode of $p({\bf w}_k|y_{1:k})$, i e  the maximum-a-posteriori estimate (MAP), coincides with the RLS adaptive rule
\begin{equation}
{{\bf w}}_k^{(RLS)} = {{\bf w}}_{k-1}^{(RLS)} + {\bf K}_k (y_k - {\bf x}_k^T {{\bf w}}_{k-1}^{(RLS)}){\bf x}_k  
\label{eq:prob_rls}
\end{equation}
This rule is similar to the one introduced in \cite{haykin1997adaptive} 

Finally, note that the covariance matrix $\boldsymbol\Sigma_k$ is a measure of the uncertainty of the estimate ${\bf w}_k$ conditioned on the observed data $y_{1:k}$  Nevertheless, for many applications a single scalar summarizing the variance of the estimate could prove to be sufficiently useful  In the next section, we show how such a scalar is obtained naturally when $p({\bf w}_k|y_{1:k})$ is approximated with an isotropic Gaussian distribution  We also show that this approximation leads to an LMS-like estimation 
 


\section{Approximating the posterior distribution: LMS filter }

The proposed approach consists in approximating the posterior distribution $p({\bf w}_k|y_{1:k})$, in general a multivariate Gaussian distribution with a full covariance matrix, by an isotropic spherical Gaussian distribution 

\begin{equation}
\label{eq:aprox_post}
\hat{p}({\bf w}_{k}|y_{1:k})=\mathcal{N}({\bf w}_{k};{\bf \hat{\boldsymbol\mu}}_{k}, \hat{\sigma}_{k}^2 {\bf I} ) 
\end{equation}

In order to estimate the mean and covariance of the approximate distribution $\hat{p}({\bf w}_{k}|y_{1:k})$, we propose to select those that minimize the Kullback-Leibler divergence with respect to the original distribution, i e , 

\begin{equation}
\{\hat{\boldsymbol\mu}_k,\hat{\sigma}_k\}=\arg \displaystyle{  \min_{\hat{\boldsymbol\mu}_k,\hat{\sigma}_k}} \{ D_{KL}\left(p({\bf w}_{k}|y_{1:k}))\| \hat{p}({\bf w}_{k}|y_{1:k})\right) \}  \nonumber
\end{equation}

The derivation of the corresponding minimization problem can be found in Appendix A  In particular, the optimal mean and the covariance are found as
\begin{equation}
{\hat{\boldsymbol\mu}}_{k} = {\boldsymbol\mu}_{k};~~~~~~ \hat{\sigma}_{k}^2 = \frac{{\sf Tr}\{ \boldsymbol\Sigma_k\} }{M} 
\label{eq:sigma_hat}
\end{equation}


We now show that by using \eqref{eq:aprox_post} in the recursive predictive and filtering expressions we obtain an LMS-like adaptive rule  First, let us assume that we have an approximate posterior distribution at $k-1$, $\hat{p}({\bf w}_{k-1}|y_{1:k-1}) =  \mathcal{N}({\bf w}_{k-1};\hat{\bf\boldsymbol\mu}_{k-1}, \hat{\sigma}_{k-1}^2 {\bf I} )$  Since all involved distributions are Gaussian, the predictive distribution
is obtained as %
\begin{eqnarray}
\hat{p}({\bf w}_k|y_{1:k-1}) &=& \int p({\bf w}_k|{\bf w}_{k-1}) \hat{p}({\bf w}_{k-1}|y_{1:k-1}) d{\bf w}_{k-1} \nonumber\\
&=& \mathcal{N}({\bf w}_k;{\bf\boldsymbol\mu}_{k|k-1}, \boldsymbol\Sigma_{k|k-1}), 
\label{eq:approx_pred}
\end{eqnarray}
where the mean vector and covariance matrix are given by
\begin{eqnarray}
\hat{\bf\boldsymbol\mu}_{k|k-1} &=& \hat{\bf\boldsymbol\mu}_{k-1} \nonumber \\
\hat{\boldsymbol\Sigma}_{k|k-1} &=& (\hat{\sigma}_{k-1}^2 + \sigma_d^2 ){\bf I}\nonumber 
\end{eqnarray}

From \eqref{eq:approx_pred}, the posterior distribution at time $k$ can be computed using Bayes' Theorem and standard Gaussian manipulations (see for instance \cite[Ch  4]{murphy2012machine})  Then, we approximate the posterior $p({\bf w}_k|y_{1:k})$ with an isotropic Gaussian,
\begin{equation}
\hat{p}({\bf w}_k|y_{1:k}) =  \mathcal{N}({\bf w}_k ; {\hat{\boldsymbol\mu}}_{k}, \hat{\sigma}_k^2 {\bf I} ),\nonumber
\end{equation}
where 
\begin{eqnarray}
{\hat{\boldsymbol\mu}}_{k} &= & {\hat{\boldsymbol\mu}}_{k-1}+ \frac{ (\hat{\sigma}_{k-1}^2+ \sigma_d^2)  }{(\hat{\sigma}_{k-1}^2+ \sigma_d^2)  \|{\bf x}_k\|^2 + \sigma_n^2} (y_k - {\bf x}_k^T {\hat{\boldsymbol\mu}}_{k-1}){\bf x}_k  \nonumber  \\
&=& {\hat{\boldsymbol\mu}}_{k-1}+ \eta_k (y_k - {\bf x}_k^T {\hat{\boldsymbol\mu}}_{k-1}){\bf x}_k   
\label{eq:prob_lms}
\end{eqnarray}
Note that, instead of a gain matrix ${\bf K}_k$ as in Eq ~\eqref{eq:prob_rls}, we now have a scalar gain $\eta_k$ that operates as a variable step size 


Finally, to obtain the posterior variance, which is our measure of uncertainty, we apply \eqref{eq:sigma_hat} and the trick ${\sf Tr}\{{\bf x}_k{\bf x}_k^T\}= {\bf x}_k^T{\bf x}_k= \|{\bf x}_k \|^2$,

\begin{eqnarray}
\hat{\sigma}_k^2 &=& \frac{{\sf Tr}(\boldsymbol\Sigma_k)}{M} \\
&=& \frac{1}{M}{\sf Tr}\left\{ \left( {\bf I} -  \eta_k {\bf x}_k {\bf x}_k^T \right) (\hat{\sigma}_{k-1}^2 +\sigma_d^2)\right\} \\
&=& \left(1 - \frac{\eta_k \|{\bf x}_k\|^2}{M}\right)(\hat{\sigma}_{k-1}^2 +\sigma_d^2) 
\label{eq:sig_k}
\end{eqnarray}
If MAP estimation is performed, we obtain  an adaptable step-size LMS estimation

\begin{equation}
{\bf w}_{k}^{(LMS)} = {\bf w}_{k-1}^{(LMS)} + \eta_k (y_k - {\bf x}_k^T {\bf w}_{k-1}^{(LMS)}){\bf x}_k, 	
\label{eq:lms}
\end{equation}
with
\begin{equation}
\eta_k = \frac{ (\hat{\sigma}_{k-1}^2+ \sigma_d^2)  }{(\hat{\sigma}_{k-1}^2+ \sigma_d^2)  \|{\bf x}_k\|^2 + \sigma_n^2} \nonumber
\end{equation}
At this point, several interesting remarks can be made:

\begin{itemize}

\item The adaptive rule \eqref{eq:lms} has linear complexity since it does not require us to compute the full matrix $\boldsymbol\Sigma_k$ 

\item For a stationary model, we have $\sigma_d^2=0$ in \eqref{eq:prob_lms} and \eqref{eq:sig_k}  In this case, the algorithm remains valid and both the step size and the error variance, $\hat{\sigma}_{k}$, vanish over time $k$  

\item Finally, the proposed adaptable step-size LMS has only two parameters, $\sigma_d^2$ and $\sigma_n^2$, (and only one, $\sigma_n^2$, in stationary scenarios) in contrast to other variable step-size algorithms \cite{kwong1992variable,aboulnasr1997robust,shin2004variable}  More interestingly, both $\sigma_d^2$ and $\sigma_n^2$ have a clear underlying physical meaning, and they can be estimated in many cases  We will comment more about this in the next section  
\end{itemize}



\section{Experiments}
\label{sec:experiments}

We evaluate the performance of the proposed algorithm in both stationary and tracking experiments  In the first experiment, we estimate a fixed vector ${\bf w}^{o}$ of dimension $M=50$  The entries of the vector are independently and uniformly chosen in the range $[-1,1]$  Then, the vector is normalized so that $\|{\bf w}^o\|=1$  Regressors $\boldsymbol{x}_{k}$ are zero-mean Gaussian vectors with identity covariance matrix  The additive noise variance is such that the SNR is $20$ dB
Context 3: A special tribute to Del Bigtree (pictured) and his team at ICAN for his stunning 88 page letter to the HHS regarding vaccine safety  As Del reported - in the latest edition of Highwire - the letter, in response to an earlier reply from the then acting Director National Vaccine Program Office, Melinda Wharton, took virtually a year to compile, and is a meticulous piece of research  Most sensationally they researched the HHS claim through US government archives that at least some pediatric vaccines had been trialed against genuine placebo, and came to a negative conclusion  Not only that, they established that none of the vaccines those vaccines had been trialed against had ever been trialed against genuine placebo either  At the end of the line the toxic products were only being compared with other toxic products, rather than against saline 
Leave aside the sceptics, for any believer in the vaccine program as a necessary intervention in public health, this should be a devastating finding  Fundamentally, the research into the safety of any of the products before marketing was simply not there  The manufacturers apparently had no faith that their proto-products could withstand this scrutiny, and for the rest they just did not care: under the alleged imperative of protecting the population it seems anything went  So even before all the sham monitoring procedures and reviews which Del and his team dismantle in forensic detail we are left with the proposition that none of the present products being given to US children – and frequently other children across most of the developed world – have any meaningful pre-marketing safety data all  If you are believer in the program you have been let down: if you wanted a program with any pretensions to safety - supposing such a thing to be possible - it looks like you would have to start from scratch  The manufacturers did this: the governments, the politicians and the regulators (internationally) let it happen 
This damning document is published simultaneously with a demand in the UK from the Royal Society for Public Health (which I had never heard of) to shut down comment about vaccines on the web  It echoes calls from Seth Berkley of GAVI, Heidi Larson of the Vaccine Confidence Project and the European Parliament  The pamphlet airily dismisses concerns that vaccines have side effects or that you could possibly have too many  It is pure public relations, and if the RSPH claims to be "independent" it also admits that the publication was paid for by Merck, a detail which was reported by British Medical Journal and the Guardian, but not true to form by the BBC  We have, in truth, been building to this moment for two decades: as the evidence piles up that every single aspect of the program lacks integrity or is simply rotten to the core all the perpetrators can do is call for the silencing of their critics, and maintain the products are safe because they say so 
Please help give the ICAN letter the widest possible distribution, particularly to politicians 
"The outcome of disease always depends both on the virulence of the pathogen and the health of the individual immune system "
Nope  This makes no sense  Lots of people who seemed vibrant will get a very severe case of the same illness that a vulnerable baby overcomes in a day 
And under the germ theory it doesn't matter how strong your immune system *was*  Once it's been overcome by the pathogen it is every bit as weak as anybody else's with that pathogen 
What you say makes no sense  There's no reason for me to reply to you again 
"Why do you think that within a few years (not many) of the introduction of the vaccines for them, pertussis, measles, mumps, rubella, tetanus, diphtheria, Hib disease, and chickenpox (and others) almost entirely disappeared?"
Why do you keep asking this question when I've already provided the answer hundreds of times? Why are you so desperate to believe the people who you already recognize are harming our children?
Why would Walter Reed be any more trustworthy than Paul Offit or Senator Pan? Why would Jenner or Pasteur?
And you went no way to explaining my arguments against germ theory  If we are attacked by billions of viruses every day then if even a tiny fraction of them are pathogenic then we couldn't possibly survive  And even if we could, we would already be immune rendering every vaccine pointless  Once we had survived our first few days on earth, then we could never get sick again 
If that's wrong then we must conclude that precisely 0% of germs are pathogenic 
Plus your comment about the immune system completely misunderstood my point  The immune system does not allow us to overcome our math problem  In fact, it makes it worse 
You did provide one solitary example of a patient with what are presumably yellow fever symptoms but you didn't say whether they had been given any toxic medical treatments 
And like I said before, the whole "incubation period" is more than a little suspicious  Clearly they never found what they thought they would and just rigged the results to tell them what they want to hear 
Like every other germ theorist/vaccine promoter in history 
Many kinds of bacteria are constantly evolving and changing, like flu viruses  Others are more stable over time, like the yellow fever virus  Those that change develop new ways of infiltrating the cells of the organism being attacked (from our point of view, from its unconscious point of view, it's just carrying out its need to replicate, which it can only do inside the cells of its host)  The changes which allow it to better infiltrate are more successful and result in more viruses with those traits 
Our immune system is designed to detect and destroy potentially dangerous invading pathogens  Many bacteria are usually harmless and absolutely necessary  The minority are dangerous, and most people's immune systems do a good job of analyzing them and killing them, often with no signs of disease  Others experience a clinical infection, and the immune system usually mounts a successful attack on them 
The outcome of disease always depends both on the virulence of the pathogen and the health of the individual immune system  Vaccines are usually effective in giving immunity to the targeted diseases  They also have many dangers which everyone should be aware of, and vaccines should be avoided whenever possible  But in the case of the most dangerous diseases, everyone should learn about them and think about what he wants to do to protect himself and his children from them, considering all the factors involved  And no one can have 100% certainty that he has made the right decision, but that's life  But if you live in the Congo and many people around you are currently dying of yellow fever, then that means that you yourself are at risk of being bitten by a loaded mosquito and getting, often dying, of yellow fever  The yellow fever vaccine is very effective at preventing yellow fever  From there, each person must make a choice 
At the end of this stage there is a remission of two or three days  About 80% of those with clinical disease recover at this point, with permanent immunity



ground_truth: They are rich in actin and have been shown to be highly dynamic.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the proposed approach in this research paper?

Read the following text and answer briefly.

Context 2:  We compare our algorithm with standard RLS and three other LMS-based algorithms: LMS, NLMS \cite{sayed2008adaptive}, VSS-LMS \cite{shin2004variable} \footnote{The used parameters for each algorithm are: for RLS $\lambda=1$, $\epsilon^{-1}=0 01$; for LMS $\mu=0 01$; for NLMS $\mu=0 5$; and for VSS-LMS $\mu_{max}=1$, $\alpha=0 95$, $C=1e-4$ } The probabilistic LMS algorithm in \cite{park2014probabilistic} is not simulated because it is not suitable for stationary environments 

In stationary environments, the proposed algorithm has only one parameter, $\sigma^2_n$  We simulate both the scenario where we have perfectly knowledge of the amount of noise (probLMS1) and the case where the value $\sigma^2_n$ is $100$ times smaller than the actual value (probLMS2)  The Mean-Square Deviation (${\sf MSD} = {\mathbb E} \| {\bf w}_0 - {\bf w}_k \|^2$), averaged out over $50$ independent simulations, is presented in Fig  \ref{fig:msd_statationary} 



\begin{figure}[htb]
\centering
\begin{minipage}[b]{\linewidth}
  \centering
  \centerline{\includegraphics[width=\textwidth]{results_stationary_MSD}}
\end{minipage}
\caption{Performance in terms of MSD of probabilistic LMS with both optimal (probLMS1) and suboptimal (probLMS2) compared to LMS, NLMS, VS-LMS, and RLS }
\label{fig:msd_statationary}
\end{figure}

The performance of probabilistic LMS is close to RLS (obviously at a much lower computational cost) and largely outperforms previous variable step-size LMS algorithms proposed in the literature  Note that, when the model is stationary, i e  $\sigma^2_d=0$ in \eqref{eq:trans_eq},  both the uncertainty $\hat{\sigma}^2_k$, and the adaptive step size $\eta_k$, vanish over time  This implies that the error tends to zero when $k$ goes to infinity  Fig  \ref{fig:msd_statationary} also shows that the proposed approach is not very sensitive to a bad choice of its only parameter, as demonstrated by the good results of probLMS2, which uses a $\sigma^2_n$ that is $100$ times smaller than the optimal value  


\begin{figure}[htb]
\centering
\begin{minipage}[b]{\linewidth}
  \centering
  \centerline{\includegraphics[width=\textwidth]{fig2_final}}
\end{minipage}
\caption{Real part of one coefficient of the measured and estimated channel in experiment two  The shaded area represents two standard deviations from the prediction {(the mean of the posterior distribution)} }
\label{fig_2}
\end{figure}


\begin{table}[ht]
\begin{footnotesize}
\setlength{\tabcolsep}{2pt}
\def1 5mm{1 5mm}
\begin{center}
\begin{tabular}{|l@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|}
\hline
Method &  LMS &  NLMS & LMS-2013 & VSSNLMS & probLMS & RLS \\
\hline
\hline
MSD (dB) &-28 45 &-21 07 &-14 36 &-26 90 &-28 36 &-25 97\\
\hline                                                                     
\end{tabular}
\end{center}
\caption{Steady-state MSD of the different algorithms for the tracking of a real MISO channel }
\label{tab:table_MSD}
\end{footnotesize}

\end{table}
\newpage
In a second experiment, we test the tracking capabilities of the proposed algorithm with {real} data of a wireless MISO channel acquired in a realistic indoor scenario  More details on the setup can be found in \cite{gutierrez2011frequency}  Fig  \ref{fig_2} shows the real part of one of the channels, and the estimate of the proposed algorithm  The shaded area represents the estimated uncertainty for each prediction, i e  $\hat{\mu}_k\pm2\hat{\sigma}_k$  Since the experimental setup does not allow us to obtain the optimal values for the parameters, we fix these parameters to their values that optimize the steady-state mean square deviation (MSD)  \hbox{Table \ref{tab:table_MSD}} shows this steady-state MSD of the estimate of the MISO channel with different methods  As can be seen, the best tracking performance is obtained by standard LMS and the proposed method  





\section{Conclusions and Opened Extensions}
\label{sec:conclusions}

{We have presented a probabilistic interpretation of the least-mean-square filter  The resulting algorithm is an adaptable step-size LMS that performs well both in stationary and tracking scenarios  Moreover, it has fewer free parameters than previous approaches and these parameters have a clear physical meaning  Finally, as stated in the introduction, one of the advantages of having a probabilistic model is that it is easily extensible:}

\begin{itemize}
\item If, instead of using an isotropic Gaussian distribution in the approximation, we used a Gaussian with diagonal covariance matrix, we would obtain a similar algorithm with different step sizes and measures of uncertainty, for each component of ${\bf w}_k$  Although this model can be more descriptive, it needs more parameters to be tuned, and the parallelism with LMS vanishes 
\item Similarly, if we substitute the transition model of \eqref{eq:trans_eq} by an Ornstein-Uhlenbeck process, 

\begin{equation}
p({\bf w}_k|{\bf w}_{k-1})= \mathcal{N}({\bf w}_k;\lambda {\bf w}_{k-1}, \sigma_d^2), \nonumber
\label{eq:trans_eq_lambda}
\end{equation}
a similar algorithm is obtained but with a forgetting factor $\lambda$ multiplying ${\bf w}_{k-1}^{(LMS)}$ in \eqref{eq:lms}  This algorithm may have improved performance under such a kind of autoregresive dynamics of ${\bf w}_{k}$, though, again, the connection with standard LMS becomes dimmer 

\item As in \cite{park2014probabilistic}, the measurement model \eqref{eq:mess_eq} can be changed to obtain similar adaptive algorithms for classification, ordinal regression, and Dirichlet regression for compositional data  

\item A similar approximation technique could be applied to more complex dynamical models, i e  switching dynamical models \cite{barber2010graphical}  The derivation of efficient adaptive algorithms that explicitly take into account a switch in the dynamics of the parameters of interest is a non-trivial and open problem, though the proposed approach could be useful 

\item Finally, like standard LMS, this algorithm can be kernelized for its application in estimation under non-linear scenarios 

\end{itemize}


\begin{appendices}

\section{KL divergence between a general gaussian distribution and an isotropic gaussian}
\label{sec:kl}

 We want to approximate  $p_{{\bf x}_1}(x) = \mathcal{N}({\bf x}; \boldsymbol\mu_1,\boldsymbol\Sigma_1)$ by $p_{{\bf x}_2}({\bf x}) = \mathcal{N}({\bf x}; \boldsymbol\mu_2,\sigma_2^2 {\bf I})$  In order to do so, we have to compute the parameters of $p_{{\bf x}_2}({\bf x})$, $\boldsymbol\mu_2$ and $\sigma_2^2$, that minimize the following Kullback-Leibler divergence,

\begin{eqnarray}
D_{KL}(p_{{\bf x}_1}\| p_{{\bf x}_2}) &=&\int_{-\infty}^{\infty} p_{{\bf x}_1}({\bf x}) \ln{\frac{p_{{\bf x}_1}({\bf x})}{p_{{\bf x}_2}({\bf x})}}d{\bf x} \nonumber  \\
&= &  \frac{1}{2} \{ -M + {\sf Tr}(\sigma_2^{-2} {\bf I}\cdot \boldsymbol\Sigma_1^{-1})  \nonumber \\
  & &  + (\boldsymbol\mu_2 - \boldsymbol\mu_1 )^T \sigma^{-2}_2{\bf I} (\boldsymbol\mu_2 - \boldsymbol\mu_1 )  \nonumber \\
 & &   +  \ln \frac{{\sigma_2^2}^M}{\det\boldsymbol\Sigma_1} \}   
\label{eq:divergence}
\end{eqnarray}
Using symmetry arguments, we obtain 
\begin{equation}
\boldsymbol\mu_2^{*} =\arg \displaystyle{  \min_{\boldsymbol\mu_2}} \{ D_{KL}(p_{{\bf x}_1}\| p_{{\bf x}_2}) \} = \boldsymbol\mu_1 
\end{equation}
Then, \eqref{eq:divergence} gets simplified into 

\begin{eqnarray}
D_{KL}(p_{{\bf x}_1}\| p_{{\bf x}_2}) = \frac{1}{2}\lbrace { -M + {\sf Tr}(\frac{\boldsymbol\Sigma_1}{\sigma_2^{2}}) + \ln \frac{\sigma_2^{2M}}{\det\boldsymbol\Sigma_1}}\rbrace 
\end{eqnarray}
The variance $\sigma_2^2$ is computed in order to minimize this Kullback-Leibler divergence as

\begin{eqnarray}
\sigma_2^{2*} &=& \arg\min_{\sigma_2^2} D_{KL}(P_{x_1}\| P_{x_2}) \nonumber \\
 &=& \arg\min_{\sigma_2^2}\{ \sigma_2^{-2}{\sf Tr}\{\boldsymbol\Sigma_1\} + M\ln \sigma_2^{2} \}  
\end{eqnarray}
Deriving and making it equal zero leads to

\begin{equation}
\frac{\partial}{\partial \sigma_2^2} \left[ \frac{{\sf Tr}\{\boldsymbol\Sigma_1\}}{\sigma_2^{2}} + M \ln \sigma_2^{2} \right] = \left  {\frac{M}{\sigma_2^{2}}-\frac{{\sf Tr}\{\boldsymbol\Sigma_1\}}{(\sigma_2^{2})^2}}\right|_{\sigma_2^{2}=\sigma_2^{2*}}\left  =0 \right   
\nonumber
\end{equation}
Finally, since the divergence has a single extremum in $R_+$,
\begin{equation}
\sigma_2^{2*} = \frac{{\sf Tr}\{\boldsymbol\Sigma_1\}}{M} 
\end{equation}




\end{appendices}

\vfill
\clearpage

\bibliographystyle{IEEEbib}

Context 3:  The other 20% enter the toxic stage, with a return of the fever, black vomit (coffee-ground emesis), diarrhea, a slowing of the pulse (Faget's sign), jaundice, yellow eyes, yellow skin, and failure of the kidneys, liver, and heart  The patient gets a strange hiccup (like with Ebola, a related disease), falls into a coma, and dies  About half of those patients who enter the toxic stage dies, even now, even with the best of hospital care  The Faget's sign can also occur at the end of the first stage 
You asked specifically about the symptoms of the Americans on Dr  Reed's team who got yellow fever in Cuba in 1900  I'll give the passage from The American Plague (162-5), which describes the course of Jesse Lazear's illness  "In his logbook, Lazear wrote an unusual entry on September 13  In all cases before those, page after page of records, Lazear had used the soldier's name and simply the date he was bitten, with no other attention to the mosquito  A one-line entry with a name and a date  On that day, however, in his elegant hand, Lazear did not write the soldier's name, but instead wrote 'Guinea Pig No  1 ' He went on to write that this guinea pig had been bitten by a mosquito that developed from an egg laid by a mosquito that developed from an egg laid by a mosquito that fed on a number of yellow fever cases: Suarez, Hernández, De Long, Ferández  It was a precise, detailed history that proved beyond doubt that the mosquito was loaded with the virus when it bit a healthy soldier   (If he had entered his name, then his death would have been considered medical suicide by the insurance company, and his wife and two children would not have gotten any payment ) For the next few days, Lazear's life continued much as it had over the last few months in Cuba  He fed and cared for the mosquitoes in the lab    Then he began to lose his appetite  He skipped a few meals in the mess hall  He didn't mention it to anyone, nor did he ask to see one of the yellow fever doctors; instead, he worked hard in the lab trying to ignore the oncoming headache 
"On September 18, he complained of feeling 'out of sorts,' and stayed in his officer's quarters  His head pounded and L  decided to write a letter    (he wrote to his mother, and referred to his one-year old son Houston and the baby his wife Mabel was about to have: they were staying with his mother in the US)    That night, L  started to feel chilled as the fever came on  He never went to sleep but worked at his desk all through the night, trying to get all the information about the mosquitoes organized  By morning, he showed all the signs of a severe attack of yellow fever  The camp doctors made the diagnosis, and L  agreed to go to the yellow fever ward    L  was carried by litter out of the two-room, white pine board house in which he had lived since he and Mabel first arrived in Cuba    (In the yellow fever ward, in a separate one-room building), Lena Warner (the immune nurse who had survived the yellow fever in 1878, when she was nine, and was found in her boarded-up house by a former slave who first thought she was dead, and carried her to safety) nursed J L , recording his vitals  (I put up a link to his case record and vital signs last week  The surgeon general required that this record be made for every yellow fever patient )    (On September 25,) Lena Warner braced L's arms with all of her weight, shouting for help  Still he bolted from the bed, darting around the small frame-wood room as wildly as a trapped insect beating against glass  Two soldiers ran into the ward, pinning L to his bed, tying restraints around his wrists and elbows



ground_truth: This research paper proposed an approach based on approximating the posterior distribution with an isotropic Gaussian distribution.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Who compiled the 88-page letter to the HHS regarding vaccine safety?

Read the following text and answer briefly.

Context 3:    Warner sponged his body with iced whiskey and water  She recorded his temperature, which had held at 104 degrees for days, on the chart beside his bed    (Warner watched him sleep ) But the quiet did not last  L's body began to lurch, and black vomit rolled from his mouth; through the bar hanging above his hospital cot  He writhed in the bed, and his skin grew deep yellow  His 104 temperature slowly fell, leveling out 99 degrees, and JL died at 8:45 p m  at the age of thirty-four "
As is obvious, there are many problems with vaccines  But, that being said, most of them usually work for a period of time to prevent the targeted diseases  The basic science behind vaccines is correct  Why do you think that within a few years (not many) of the introduction of the vaccines for them, pertussis, measles, mumps, rubella, tetanus, diphtheria, Hib disease, and chickenpox (and others) almost entirely disappeared? In the case of the routine childhood diseases, this was a bad thing, but it is a true thing 
Vaccines usually don't cause any obvious reactions  While they usually prevent the diseases, and that's why people continue to get them  With the increasing vaccination schedule, more and more are severely and permanently damaged, and it is immoral to mandate any vaccine for anyone for this reason  But it would also be immoral to prohibit vaccines for those who want them enough to take the risk 
Your article said as though it had any probative value that 90% of those who get pertussis had been vaxxed  The old DPT vaccine was MUCH more effective at preventing pertussis, but it was so dangerous (again, not to most, but to many), that developed countries replaced it with the acellular version, DTaP  From the beginning about twenty years ago, it was clear that it was not very effective and that huge numbers of vaxxed people got pertussis anyway, including my daughter who got pertussis at eight month old after having gotten three DTaPs  The pertussis vaccine continues to be very dangerous, and I do not recommend that anyone get it  It used to be a killer disease, but evolved to become much milder, to the extent that the disease is very rarely dangerous (usually only to newborns under three months old), while the vaccine is very dangerous  And they're trying to see how they can go back to the old DPT  This does not show that vaccine science has collapsed, but rather that the vaccine they developed to replace the DPT turned out to be much less effective than they first thought, while continuing to be much more dangerous than they first thought 
Your article extrapolated from that that modern medical science in general has collapsed, but that, again, is going too far  A older woman in Mexico City who is like my mother to me had a pacemaker inserted about two months ago to aid her failing heart, and it has restored her to optimism and energy, when she was despondent, weak, and close to death  I took my daughter to the dentist yesterday, who said she has three wisdom teeth coming in and that she said that the lower right one was sore  So, although I am cautious about X-rays, I made an appointment for a panoramic X-ray in a month to assess the wisdom teeth, and, if it seems appropriate, I'll take her to an oral surgeon to have one or more extracted under IV sedation, in his office, if possible (the dentist thought that it would be)  And I am confident that there will be no serious problems, but this is thanks to technology and training in modern medicine that haven't been available for that long 
I think that everyone should inform himself on all medical procedures before agreeing to anything, but I also think that he should have access to any medical procedure which is reasonable (and opinions can differ as to that) 
One problem is that you have not said how you think people should protect themselves against tetanus, bacterial meningitis, and yellow fever in the relevant cases, for example  These are diseases which healthy, well-nourished people used to die from very readily 
If most people stopped vaxxing and the mortality from these diseases rose to something like pre-vaccine levels, do you think they should just accept dying from them?
I put that in a separate paragraph because it is the crucial issue 
balinaheuchter Air Traffic Control You Tube - Colin Campbell example of - How to "Fudge a Nudge" -"Deal" or "No Deal" "Not in a month of Sundays" "No exceptions/no compromise?" -make a trade off -do an exception- everyone get's a good deal /good outcome!
Hans, you are right that we are looking at one of the biggest crimes in all history  When I read the story of that poor girl who was so healthy and is now confined to a wheelchair after getting her third Gardasil shot I could not believe that Merck could produce such a toxic vaccine and give it out to girls like it was something they absolutely had to have only to be mislead and made into cripples  Merck should be prosecuted for the damage they have done to so many girls who got the Gardasil vaccine and were physically debilitated for life  There is a place for the people who perpetrated this crime on young girls and women and it is called hell  They have destroyed people's lives and gotten away with it  My heart goes out to those who have suffered this damage for no damn good reason except to help make huge profits for Merck!
Here is the reason that the germ theory is nonsense 
1) Everyday we are bombarded with billions of germs  Presumably at least some of them are of the kind that germ theorists believe are dangerous (otherwise we would have to conclude that none of them are dangerous)  So how do we survive?
2) Let's just say that we ignore 1 and imagine that, by way of magic, none of the billions of viruses we get bombarded with are pathogenic but all those that are are tucked away somewhere  Ok  But presumably they reside in sick people right? So where are there lots of sick people? Doctor offices and hospitals! So everybody must be dying the moment they enter these places right?
3) I love this one because I have never seen anybody else ever raise it  Under the germ theory there are no negative feedbacks  This makes a stable biological system by definition impossible  The immune system is *not* a negative feedback it is the opposite  It actually reinforces our math problem because the immune system will weaken as the number of pathogens increase 
There is no way of resolving this problem without a discontinuity  A Deus ex Machina as The Almighty Pill so beautifully put it  So the germ theory is quite literally, mathematically impossible 
There is as much chance of it being true as 2+2 = 5 
There are plenty of other massive problems with germ theory such as why did things like SARS and bird flu magically disappear? Why do we have the symptoms that we do? Is our body controlling the symptoms to help fight the germs and if so, why would suppressing the symptoms with antibiotics or Tamiflu be considered a good idea? If the virus is causing the symptoms then why would it cause these kinds of things?



ground_truth: Del Bigtree and his team at ICAN.