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What is oscillating? The electromagnetic field caused by (1) certain types of nerve cells(neurons) that can generate rhythmic firing/spiking on their own without any input or by (2) dynamically assembled groups of connected neurons that individually spike irregularly in response to input, but collectively generate an oscillating field due to synchronization mechanisms driven largely by their connectivity.[ 20 , 25 , 30, 37,38 , 40]Oscillations have been observed at different frequency ranges and have been given different names such as delta (1-4Hz), theta (4-8 Hz), alpha (8-12Hz), beta (12-30Hz), gamma (>30 Hz) etc. Figures 1 and 2 [30]Understanding these oscillatory patterns particularly by correlating with animal behavior, including humans, is serving as a valuable tool to reverse engineer mechanisms of brain function.[30]Several basic questions regarding oscillations remain unanswered requiring further study such as the details of their role, the neuronal mechanisms of their sources, how to interpret them, how to standardize measuring them etc.[44,46]What brain functions do these oscillations correlate with?Neurons fire in the backdrop of neighboring neurons, some of which may also be firing while the others listening, and they influence each other with excitatory and inhibitory connections. Figures 3,4 and 5. [20 , 25 ,30]The firing activity of neurons can be measured at different population scales - (1) individual neuron spiking, (2) activity of tens of thousands of neurons, (3) several millions and (4) the consolidated activity of multiple brain areas. The measurements can range from electric voltage recordings done inside neurons or outside in the space between them, to noninvasive measurement of the magnetic field registered outside the head. [ 26, 43]By measuring individual neuron firing spikes along with the background voltage oscillations in healthy/impaired humans and animals, oscillatory patterns with characteristic properties of frequency, modulation/coupling type etc. (Figure 6, 7 and 8) are beginning to emerge that correlate with different information/memory related activities such asCommunication across anatomically different regions of the brain.[7]Transient encoding, maintenance, and manipulation of memory (volatile/working memory, processing) [ 27, 35 ,42]Consolidating memory into long term storage (persistent memory) [41]Recall/Retrieval of memory from long term storage [41]What is an example of oscillations correlating with real life experience?Even though oscillations are present in all states of the brain, the example below highlights individual aspects where oscillations with different characteristics correlate with cognition,behavior, and memory.[14,7,8]Imagine the first time perception of a Ferrari sports car. The information about its color (red), the stimulus category (car) and its motion (moving fast) is processed in anatomically different regions in the brain, but simultaneously perceived together.These representations need to be linked by some mechanism to ensure that the brain assigns them to the same object. This binding function is made possible by communication across these different regions through coherent wave patterns.If this experience seemed so fantastic(novel experience), then we may also remember other details such as where we saw it (location) and even the minute detail of the aroma of a cheeseburger (smell) from a nearby restaurant as the Ferrari zips by.We may then immediately recall the experience internally (processing,working memory) reliving the experience or talk about it others.If the experience was so novel, the experience may be played in “fast forward” mode while we are asleep and consolidated into long term memory. Our recalling the experience to others over the course of next few days aids this consolidation and strengthening of this long term memory even further.A few months/years later, we may still recall that experience with all the minute detail including the aroma of cheeseburgers wafting in the air as the Ferrari zipped by.Of course, if one had little to no interest in cars, the memory would be transiently held, if at all it is, only to fade away soon or during the course of the day.Oscillations with characteristic properties of frequency, modulation and coupling type(multiple frequencies coupled in phase, amplitude etc.) correlate with each of the key aspects of this example – communication, processing,volatile memory, consolidation into persistent memory, and retrieval.What do we know so far about the role of oscillations?The firing of a neuron is driven by its input except for those special neurons that have intrinsic mechanisms to generate firing on their own.[30,37,38 ]Certain physical,electrical and chemical properties of a neuron dictate the time length of the sampling window of its input from other neurons, to be in the range of 10-30 msecs. A neuron will fire based on the input it samples in this time window. If an input spike to a neuron comes slightly later than this 10-30 msec time window, it will be sampled in the next time window - so it will be part of the next "event" as far as this neuron is concerned. Figure 2 [30, 34 ,45]Memory of events is encoded in the connection strengths between neurons. The altering of connection strengths between a pair of neurons also requires the participating neuron pair to be in certain activity states within a time window of 10-30 msecs.[30, 35 ,39]The 10-30 msec time constraint for the input sampling window and the same time constraint for the encoding of memory mandates a synchronization mechanism to make neurons fire in this short time window to constitute an event and to potentially store it, despite the individual irregular spiking behavior. [ 27, 32]For example, while information can be encoded quite sparsely in a small set of connected neurons for an aspect of sensory stimulus (e.g. the concept of a celebrity like Jennifer Aniston evoked by a photograph of her), it still requires sufficient number of neurons in this sparse set to fire synchronously to both constitute that information and subsequently recall that information. [ 17 , 18 , 21 , 35 , 41]This synchronous firing is made possible largely by the inhibitory actions of intermediate neurons that connect this sparse set, generating a local oscillating field. These inhibitory neurons help collectively time the spiking of these neurons to millisecond precision within certain phases of the oscillation field. Inhibitory neurons appear to also play a key role in containing the size of oscillating sparse group of neurons. This containment avoids an explosive growth in the group size of spiking neurons due to connectivity with other neurons Figure 11.[50, 20 ,40]The field oscillations that emerge from the synchronizing action of inhibitory neurons on the collective firing of the excitatory neurons satisfy the 10-30 msec constraint and hence have a frequency greater than 30 Hz ( 1000/30 = 33). Each oscillation conceptually frames spikes into time window slots with slot widths determined by the frequency. The spiking group of neurons that fire within a time slot may vary with each slot creating a temporal sequence of events [ 19] Figure 14The power in these high frequency oscillations ( > 30 Hz) is not much, given only a sparse set of neurons are typically involved. So these oscillations, on their own cannot transmit information across different anatomical regions of the brain, other than rare instances where direct wiring between distant regions have enabled synchronous oscillations across those regions Figure 13.[ 2 ,6 ,8]There are slower frequency oscillations involving larger number of neurons and hence with more power in their oscillations. The lower power high frequency oscillations that encapsulate information spikes "ride on" these higher power lower frequency oscillations by different modulation schemes. The longer time windows of these low frequency oscillations serve to nest and temporally serialize the higher frequency oscillations that encapsulate episodic events Figures 13 and 14.[11, 12 , 13 , 14 , 15 , 16 , 19 , 22 , 23 , 24 , 28 , 29 ,36 , 42,8]This appears to be the general mechanism behind communication of information between different parts of the brain. The saving of Ferrari sports car into persistent memory appears to be facilitated by similar coupling between higher and slower frequency oscillations. [ 43, 47, 48, 49 ,50]Humans and other mammals have a working memory store that is anatomically distinct from a long term memory store. While sleeping, a high frequency oscillating wave form ( ~ 200 Hz) has been observed in the working memory region that appears to perform a fast replay of memories encoded during the day and this replay is coordinated by a slower oscillation to consolidate some of those memories into the long term memory store. Figures 9,10 and 15. [31, 33 , 52 , 53]In the Ferrari car example, the simultaneous perception of different aspects of the car stored in different anatomical regions appear to be made possible by phase synchronized oscillations across these regions- communication through coherence. Figure 7 (image Ba) and Figure 12 [7, 13]FiguresFigure 1. Oscillatory classes in the cortex. State of the art Buzsaki Lab [Open]Figure 2. a, Location of the recording electrodes. b, c, Raster plots of 25 pyramidal cells that were active during a 1-s period of spatial exploration out of 68 simultaneously recorded neurons. b, Neurons are arranged in order of physical position in the CA1 pyramidal layer (colour-code refers to locations in a). Vertical lines indicate troughs of theta waves (bottom trace). Location-specific synchrony is not apparent in the population activity. c, The same spike rasters shown in b, reordered by stochastic search over all possible orderings to highlight synchrony between anatomically distributed populations. 'Cell assembly' organization is now visible, with repeatedly synchronous firing of some subpopulations (circled). Organization of cell assemblies in the hippocampus, Nature 2003Figure 3. Pacemaker neuron network that drives breathing. The top left figure shows a collection of pacemaker neurons in brainstem that drive breathing under normal conditions. The red and the blue circles are excitatory pacemaker neurons - the grey circles are the inhibitory non-pacemaker neurons.These red and blue pacemaker neurons generate spikes without any input. The figure to its right shows a red pacemaker neuron functioning alone under low oxygen conditions (hypoxia) generating the gasping response - the other pacemakers ( white circles labeled E) and inhibitory neurons (white circles labeled I) have gone silent. Pacemaker neurons and neuronal network: an integrative view, Current Opinion in Neurobiology, 2004Figure 4. Central pattern generators. (a) Early work suggested two hypotheses for the generation of rhythmic and alternating movements. In the reflex chain model (left) sensory neurons innervating a muscle fire and excite interneurons that activate motor neurons to the antagonist muscle. Right, in a central pattern generator (CPG) model a central circuit generates rhythmic patterns of activity in the motor neurons to antagonist muscles. (b) Fictive motor patterns resemble those recorded in vivo. Top left, picture of a lobster with electromyographic recording (EMG) wires implanted to measure stomach motor patterns in the behaving animal. Top right, EMG recordings showing that triphasic motor pattern generated by the LP, PY, and PD neurons. Modified from [34]. Bottom left, in vitro preparation, showing the dissected stomatogastric nervous system in a saline-filled dish with extracellular recording electrodes on the motor nerves and intracellular recordings from the somata of the stomatogastric ganglion motor neurons. Bottom right, unpublished recordings by V. Thirumalai made in vitro from the stomatogastric ganglion of the lobster, Homarus americanus. The top three traces are simultaneous intracellular recordings from the somata of the LP, PY, and PD neurons, and the bottom trace is an extracellular recording from the motor nerve that carries the axons of these neurons. Note the similarity of the in vivo recordings and the fictive motor patterns produced in vitro in the absence of sensory inputs. STG, stomatogastric ganglion; OG, esophageal ganglion; CoG, commissural ganglion; lvn, lateral ventricular nerve. Central pattern generators and the control of rhythmic movements, Cell 2001Figure 5. Cellular mechanisms underlying pattern generation. (a) Neurons have different intrinsic properties. Some neurons fire bursts of action potentials endogenously (panel 1). In some neurons depolarizing current pulses trigger plateau potentials that outlast the duration of the depolarization but that can be terminated by hyperpolarizing current pulses (panel 2). Some neurons respond to inhibition with rebound firing (panel 3), and others show spike frequency adaptation (panel 4). (b)Rhythms can be generated by endogenous bursters, or can be an emergent property of synaptic coupling between non-bursting neurons. In pacemaker driven networks a pacemaker neuron or neuron (red) can synaptically drive an antagonist (green) to fire in alternation. The simplest example of a network oscillator is one formed between two neurons that fire non-rhythmically in isolation, but fire in alternating bursts as a consequence of reciprocal inhibition.Central pattern generators and the control of rhythmic movements, Cell 2001Figure 6. Oscillatory coupling mechanisms. (a) Schematic view of the human brain showing hot spots of transient gamma oscillations (i–iv) andtheta oscillation in the hippocampus (HI); entorhinal cortex (EC). Oscillators of the same and different kind (e.g., theta, gamma) caninfluence each other in the same and different structures, thereby modulating the phase, amplitude, or both. (b) Phase-phase coupling ofgamma oscillations between two areas. Synthetic data used for illustration purposes. Coherence spectrum (or other, more specific,phase-specific measures) between the two signals can determine the strength of phase coupling. (c) Cross-frequency phase-amplitudecoupling. Although phase coupling between gamma waves is absent, the envelope of gamma waves at the two cortical sites is modulatedby the common theta rhythm. This can be revealed by the power-power correlation (comodugram; right). (d) Gamma phase-phasecoupling between two cortical sites, whose powers are modulated by the common theta rhythm. Both gamma coherence and gammapower-power coupling are high. (e) Cross-frequency phase-phase coupling. Phases of theta and gamma oscillations are correlated, asshown by the phase-phase plot of the two frequencies. (f) Hippocampal theta oscillation can modulate gamma power by its duty cycleat multiple neocortical areas so that the results of the local computations are returned to the hippocampus during the accrual(‘‘readiness’’) phase of the slow oscillation. Mechanisms of gamma oscillations, Annual review Neurosciance 2012 [Open]Figure 7.Putative functions of phase synchronization. A | Neural oscillations may show phase synchronization (left; stable phase relationships) or may show no phase synchronization (right; variable phase relationships). Methods for the quantification of phase synchronization have been described extensively elsewhere116, 142. B | Potential roles of phase synchronization in neural processing. Blue curves represent oscillations of neural assemblies in two brain regions, arrows denote interregional information transfer. Ba | Phase synchronization of neural assemblies coordinates the timing of synaptic inputs to a common target region. Coincident activity (indicated by the box surrounding two coinciding spikes) thus reliably induces action potentials. Bb | Phase synchronization between multiple brain regions allows for efficient information transfer (indicated by the arrows) during excitable periods (the box indicates the first such period). Bc | Precise timing of action potentials resulting from phase synchronization between two regions can induce spike timing-dependent plasticity of the synaptic connections (depicted on the right) between these regions. Consequently, communication is facilitated further (indicated by thicker arrows). Bd | The putative function of theta phase synchronization between two regions. The propensity of action potentials that are propagated from region 2 to region 1 (indicated by the arrows) to induce synaptic plasticity in region 1 depends on the theta phase in region 1 during which the action potentials arrive. Therefore, phase synchronization in the theta range may serve to recruit memory-related regions (for example, the hippocampus) during periods of high susceptibility to synaptic potentiation (solid arrows). LTD, long-term depression; LTP, long-term potentiation. The role of phase synchronization in memory processes, Nature reviews 2011Figure 8. Phase amplitude Cross Frequency Coupling (CFC) occurs between distinct brain rhythms, but varies as a function of cortical area and task demands... The functional role of cross-frequency coupling, Cell, 2010 [Open]Figure 9. Reactivation of spike sequences. This figure shows a schematic illustration of how CA1 pyramidal cells tend to fire in the same order during sleep as during a prior track running session [37,38]. Upper panel: firing probability of six hippocampal pyramidal cells A–F as a function of the location of the rat as it traverses the linear track.Bottom panels: spike times of the same cells during sleep before and after the track running. Note that in the first sleep (the sleep before track running), cells fire in an order that is unrelated to ensemble firing patterns during subsequent track running. However, in sleep after exploration, the order of cell firing during an SWR reflects the order in which the cells fired during track running.Play it again:reactivation of waking experience and memory, Cell 2010 [Open]Figure 10. Proposed roles of the prefrontal cortex (PFC) in the formation and recall of remote memories. Initially, memories are encoded in hippocampal–neocortical networks (A, thick lines). At this early time point, the hippocampus is crucial for integrating information from distributed cortical modules, each representing individual components of a memory. However, over time direct projections from the hippocampus are thought to transfer a high-order representation of the memory to the PFC (B), which then uses this information to facilitate the transfer of information from the hippocampus to the neocortex, via the entorhinal and perirhinal cortices. As initially proposed for the hippocampus, the PFC may also use this version of the memory to strengthen the connections between the distributed cortical modules involved in the memory (thick lines), and to integrate the memory within related preexisting memories. Later, the PFC may also use this memory to identify and recall context-relevant information from remote memory stores. Finally, during recall of remote memories, the PFC appears to inhibit hippocampal activity (blue line), thereby preventing the encoding of redundant information. Nature Reviews Neuroscience, Frankland & Bontempi, 2005. Hippocampal memory consolidation during sleep: a comparison of mammals and birds. biol Rev Camb Philos Soc. 2011[Open]Figure 11. Segregation of cell assemblies by inhibition. A. A ring of pyramidal neurons (1–6), mutually innervating an interneuron (i). The synaptic strength between the interneuron and pyramidal cell 4 is stronger than between other pairs. When pyramidal cell one receives an input (arrow), cells 1 to 3 are activiated while 4 to 6 remain silent (segregated).... Neural syntax: cell assemblies, synapsembles, and Readers[Open]Figure 12. Individual subdural recording sites from the patients studied by Watrous et al.1 (blue, prefrontal; green, parietal; orange, precuneus; yellow, parahippocampal).The red oscillation (1–4 Hz) represents coherence between brain regions during spatial memory. The orange oscillation (7–10 Hz) represents coherence between these regions during temporal memory. Multiplexed memories:a view from human cortex, Nature Neuroscience 2013[Open]Figure 13. Power spectrum of EEG from the right temporal lobe in a sleeping human subject. Subdural recording. Note the near-linear decrease of log power with increasing log frequency from .5 to 100 Hz. Neuronal oscillations in cortical networks, Science 2004[Open]Figure 14. Schematic of a neural code. The ovals at top represent states of the same network during two gamma cycles (active cells are black and constitute the ensemble that codes for a particular item). Different ensembles are active in different gamma cycles. The Theta-Gamma Neural Code, Neuron 2013Figure 15. Three phenomena that occur during sleep have been linked to memory enhancement—slow-wave oscillations in brain electrical activity, reactivation of recent experiences, and changes in synaptic connectivity but the strength of the evidence (indicated by arrow thickness) varies. As shown in red, Yang et al. link both reactivation and slow-wave sleep to changes in synaptic connectivity that enhance learning. Memories-getting wired during sleep, Science 6, June 2014ReferencesSome of the references below require subscription for viewing while others have open access. The ones that have open access are marked "[Open]".State of the art, Buzsaki lab [Open]Neuronal oscillations in cortical networks - Science, 2004 [Open]Organization of cell assemblies in hippocampus, Nature 2003Pacemaker neurons and neuronal network: an integrative view, Current Opinion in Neurobiology, 2004Central pattern generators and the control of rhythmic movements, Cell 2001 [Open]Mechanisms of gamma oscillations, Annual review Neuroscience 2012 [Open]The role of phase synchronization in memory processes, Nature reviews 2011The functional role of cross-frequency coupling, Cell, 2010 [Open]Play it again:reactivation of waking experience and memory, Cell 2010 [Open]Hippocampal memory consolidation during sleep: a comparison of mammals and birds. biol Rev Camb Philos Soc. 2011[Open]Membrane Resonance Enables Stable and Robust Gamma Oscillations,Cerebral cortex, 2012Multifaceted roles for low-frequency oscillations in bottom-up and top-down processing during navigation and memory, NeuroImage 2014Multiplexed memories: a view from human cortex, Nature Neuroscience 2013 [Open] This is a review of the paper cited below [14]. A hypothesis called the 'spectral fingerprint' proposes that frequency band-specific inter-regional coherence subserves many cognitive processes. This hypothesis does not state that information is being encoded in low frequency oscillations. Rather, the idea is that setting two or more regions in phase coherence facilitates information transfer in single-unit volleys by local adjustments in likelihood of spiking.Frequency-specific network connectivity increases underlie accurate spatiotemporal memory retrieval, Nature Neuroscience, 2013 [Open]Gamma Oscillatory Firing Reveals Distinct Populations of Pyramidal Cells in the CA1 Region of the Hippocampus, Journal of Neuroscience, 2008 [Open]Recognition memory and theta-gamma interactions in the hippocampus, Hippocampus 2013Modulation of theta phase sync during a recognition memory task, Cognitive neuroscience and neuropsychology, 2012[Open]Phase-dependent neuronal coding of objects in short-term memory, PNAS 2009 [Open]Segmentation of spatial experience by hippocampal theta sequences, Nature Neuroscience 2012 [Open] This paper suggests based on encoding of spatial paths in rats, a mechanism for cognitive chunking of experience. When a rat navigates its environment, ongoing experiences are compressed into theta sequences. The spatial paths represented by theta sequences extend ahead of the animal while accelerating and begin farther behind the animal during deceleration.Spontaneous synchronization in nature IEEE 1997 [ Open] Discusses the prevalence of mutual synchronization of oscillators in nature such as the synchronized flashing on an off by Southeast Asian fireflies. When they begin to congregate in the early hours of night, their flickerings are uncoordinated. But as the night goes on, they build up synchrony and eventually whole treefuls pulsate in silent concert. Steven Strogatz, the author of this paper also mentioned Winfree's work on the nonlinear dynamics of large systems of coupled oscillators. Coupled oscillators are one of models used to explain the the emergence of synchronized oscillations among neurons.Concept cells: the building blocks of declarative memory functions, Nature reviews 2012 [Open]The Theta-Gamma Neural Code, Neuron 2013. This paper proposes a “neural code” of information processing/memory storage in the brain of rats though it remains to be seen if this code or a variant of it is ubiquitous across speciesFast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates, Neural computation 1999 [ Open]The theta/gamma discrete phase code occuring during the hippocampal phase precession may be a more general brain coding scheme, Hippocampus 2005Layer and frequency dependencies of phase response properties of pyramidal neurons in rat motor cortex, European Journal of Neuroscience 2007Local field potentials, BOLD and spiking activity - relationships and physiological mechanisms, Nature 2010Theta-alpha cross-frequency synchronization facilitates working memory control - a modeling study, SpringerPlus 2013Analytical Insights on Theta-Gamma Coupled Neural Oscillators, Journal of mathematicl Neuroscience, 2013The principle of coherence in multi-level brain information processing, Progress in Biophysics and molecular biology 2013Neurophysiological and computational principles of cortical rhythms in cognition, Physiol Rev 2010 [Open] This review paper discusses a framework that goes beyond the conventional theory of coupled oscillators to explain field oscillations and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations.Why there are compliementary learning systems in the hippocampus and neocortex:Insights from the successes and failures of connectionist models of learning and memory,Pshcological review 1995 [Open]A Synaptically Controlled, Associative Signal for Hebbian Plasticity in Hippocampal Neurons, Science 1997Hippocampal-cortical interaction during periods of subcortical silence, Nature 2012Reliability of spike timing in neocortical neurons, Science 1995 [Open] This paper offers evidence for a possible role for spike timing in the processing of information. A constant stimulus to a neuron leads to spike trains which become imprecise over time, whereas stimuli with fluctuations resembling synaptic activity (constant input along with computer generated filtered Gaussian white noise) produces spike trains with timings reproducible to less than 1 millisecond. Even though this experiment has no physiological significance since it does not factor in actual delays present in real life scenario (such as synaptic transmission delays) it is consistent with theories of cortical information processing where spike timing is important.Oscillatory correlates of memory in non-human primates, NeuroImage 2014Theta oscillations orchestrate medial temporal lobe and neocortex in remembering autobiographical memories, NeuroImage 2014[ Open]Principles of rhythmic motor pattern generation Phys. Review 1996Central pattern generators for bipedal locomotion, J. Math. Biol 2006[Open]The spike timing dependence of plasticity, Neuron 2012[Open] This paper reviews the cellular mechanisms for spike time dependent plasticity. When neuron A spikes ~0 to 20 msecs before neuron B, which it connects to fires, long term potentiation (connection strengthening) occurs. If neuron B precedes the spiking of neuron A by ~0 to 20-100 msecs, long term depression (connection weakening) occurs.Phase locking control in the Circle Map, Nonlinear dynamics 2007 This paper discusses how phase-locking between two oscillators happens when the ratio of their frequencies become locked in a ratio of p/q of integer numbers over some finite domain of parameter values.Brain oscillations and memory, Current opinion in neurobiology 2010 [Open]Working memory and neural oscillations: alpha-gamma versus theta-gamma codes for distinct working memory information? Cell 2014[Open]Detection of n:m phase locking from noisy data: application to magnetoencephalography, Physical review letters, 1998 [Open]Assessment of cross-frequency coupling with confidence using generalized linear models, NeuroImage 2013 [Open]Role of experience and oscillations in transforming a rate code into a temporal code, Nature 2002[Open]A Method for Event-related Phase/Amplitude Coupling, NeuroImage 2013[Open] The first author of this paper, Bradley Voytek is here on Quora.A θ-γ Oscillation Code for Neuronal Coordination during Motor Behavior, Journal of Neuroscience 2013Phase-amplitude cross-frequency coupling in the human nucleus accumbens tracks action monitoring during cognitive control, Frontiers in human neuroscience, 2013[Open]Cross-Frequency Phase-Phase Coupling between Theta and Gamma Oscillations in the Hippocampus, Journal of Neuroscience, 2013[Open]Neural syntax: cell assemblies, synapsembles and readers, Neuron 2010[Open]High-order synchronization, transitions, and competition among Arnold tongues in a rotor using harmonic forcing, Physical Review 2008 [Open] Discusses the possibility of two or more coupled oscillators becoming synchronized when their autonomous frequencies are different but close, where the synchronization occurs as adjustment of those frequencies due to coupling. This form of coupling is in contrast to weak coupling where the frequencies of the individual oscillators do not change but oscillations still emerge due to coupling.Memories-getting wired during sleep, Science 6, June 2014Sleep promotes branch-specific formation of dendritic spines after learning Science, 6 June 2014Updated additional referencesA recent video lecture (Feb 2017) on the neuroscience of consciousness. Has references embedded in video related to oscillations. One particular mention of a paper (after 30 mins) examines how the brain perhaps reduces it prediction errors by adjusting its prediction in concert with sensory input - all within a single oscillatory cycle. The paper mentioned in video Journal of Cognitive Neuroscience - 28(9):1318 - Full Text (not open access)30 Sept 2019An informative talk on how the brain computes. It offers an explanation of how different sensory inputs (vision, auditory) that occur simultaneously can form associations when the inputs are projected randomly to a downstream region. This can happen not just across inputs but within a sensory stream. For instance, an experiment of former President Obama’s face shown along with an Eiffel tower makes a neuron that only fired for Eiffel tower later fires when shown just the face of the former President. Even if only a model, it is biologically grounded (for the most part) and the primitives for computation are fairly simple. The paper https://ccneuro.org/2019/proceedings/0000998.pdf

Earlier this month, a 64-year-old, white man opened fire on a crowd of thousands gathered for a music festival in Las Vegas. He left 58 people dead and 527 wounded.It’s tragic, the highest tally for a mass shooting in our lifetime. In the aftermath, we struggle to find an adequate response. There are abundant opportunities to give in support of the tragedy. And that provides help for survivors and an outlet for those of us who want to contribute. But we want something more, don’t we, or something different?We want to stop the violence.So, we turn to law enforcement and legislators. Yet, as we’ve experienced before, that route quickly turns into a tangle. There seems to be no gun-buying program, no gun feature, no gun, that we can agree to legislate. Quickly, almost reflexively, arguments give way to deadlock, and then to despair.But what if there were another way toward safety, an entirely different approach to peace? Maybe there is. The idea comes from an unexpected corner—the economist and author, Steven Levitt.Levitt took up the question of gun violence on a podcast based on his popular Freakonomics books, the books that explain baffling social behavior through the application of economic research. He gave the interview, not in response to the Las Vegas shooting, but rather five years ago, in response to the gun violence at Sandy Hook Elementary School. A shooting that took 27 lives.In the interview, Levitt proposed an unexpected answer to mass shootings. In a word: empathy.“…fundamentally that’s where the answer lies. Right? If you don’t have people who have the desire to go kill large numbers of other people then you don’t have a problem with gun violence.”We might be tempted to dismiss his prescription as merely hopeful and naïve. After all, Levitt isn’t a member of law enforcement. He’s not a legislator, not an attorney, or a mental health specialist. He’s a behavioral economist. Not the kind of profession we’d normally turn to in order to understand and reduce mass shootings.But maybe we should.Because Steven Levitt is not only coauthor, with Steven Dubner, of the highly acclaimed Freakonomics series. He’s also Dr. Steven Levitt, winner of the 2003 John Bates Clark medal, the most prestigious award in economics after the Nobel Memorial Prize. He’s the guy a survey of economics professors named as the fourth favorite living economist under the age of 60.And his specialty is crime.His proposal, then, isn’t rooted in wishful thinking or “can’t we all just get along” sentimentality, but rigorous research and a dispassionate drive to understand human motivations and predict actions.So, when Levitt recommends empathy, he isn’t asking if you’ve hugged a mass murderer today. He’s making a deliberate calculation – drawing a line between an act of horror and the deep-seated needs that drive human behavior – needs like connection, acceptance, or significance.Levitt thinks of mass shootings as having three foundational components: an available gun, someone with the will to use the gun to kill, and a way to put the two together.It’s not coincidental, in Levitt’s analysis, that guns feature so prominently in modern mass murders. Guns are destructive, but not just destructive. They’re disruptive.Here, Levitt draws from Fist Stick Knife Gun: A Personal History of Violence in America, the landmark memoir from activist Geoffrey Canada. Throughout most of history, even on the streets of the U.S. through the 50’s and 60’s, personal confrontations were settled hand to hand or hand to knife. And because those were the only available options, many fights that could have been fought, weren’t.That’s because, as punishing as rocks or even knives can be, they don’t offset the natural advantages that big, strong, men have in fights. And because they don’t change the fundamental balance of power, the outcome of many fights were foregone conclusions. They didn’t need to be fought.In Canada’s words:“As we got older and more sensible, we recognized that there was a system of checks and balances on violence, we learned to weigh acting violently with the consequences.”Until you introduce guns.Guns are so destructive they change the calculus of fighting. They make the outcome of a confrontation uncertain, more than offsetting any advantage that accrues to size and strength. “Kids with guns often see no limits on their power,” says Canada.As a point of comparison, can you even imagine a man with a rock or a knife killing 58 people and wounding 527. It staggers the mind. But give a man an arsenal of guns that are powerful, long range, and capable of shooting many rounds in little time, and suddenly the unimaginable is entirely manageableSo, why isn’t regulation the go-to answer?A common impulse is to get rid of guns or to heavily regulate them. We’ve found it difficult, though, in the United States, even to limit types of guns or their features. Witness the surge in sales of bump stocks since legislators pointed out that they were an element of the Las Vegas shooting that was both destructive and possible to regulate or outlaw.Not only are guns disruptive, they’re abundant. No one knows how many guns are held in the U.S. but the most reliable surveys put the number anywhere from 270 million to 310 million, or nearly a gun for every man, woman, and child in the country. And guns aren’t only plentiful, they’re durable as well. A gun, reasonably well taken care of, will last 50 to 100 years. The implication Levitt draws is that even our best attempts to regulate the flow of new guns impacts only a small portion of the total stock.The inevitable outcome of looking to regulation to stop mass gun violence in the current political climate, in Levitt’s analysis, is frustration.“…anyone with any sense looks at the current political climate, thinks about the kinds of proposals that are being made and accepts the fact that none of these proposals are going to have any real impact at all.”So, we’ve saddled ourselves with a ready supply of guns for people who want to use them. Our only option may be to lessen the likelihood that people will want to pick up a gun to hurt others.But can we?Levitt thinks we can.“…if we’re not going to get rid of guns, but you want to get rid of gun violence, you got to get rid of the people who are doing violence with guns.”That’s a provocative answer. And it’s frankly drawn a lot of ire and skepticism from people who question the kind of policy Levitt might be advocating. Some have suggested his position seems to verge on pro-abortion.To be clear, Levitt has said he believes his work has little to no implication for abortion policy. Rather, he’s suggesting we find ways to raise children so they are less inclined to violence.“By get rid of I don’t mean, you know…There are a lot of ways to get rid of them. I mean, one is to parent better, to have society indoctrinate people into more empathy…I think those are the ultimate solutions.”But – and it’s a big but – is there any reason to believe that empathy can work to stem mass shootings? It turns out, there are at least two.First, mass shootings tend to be committed by people who might respond to empathy.There’s a popular trope in the media of the mentally ill picking up a gun. That happens, but only in a small minority of cases. The Stanford Geospatial Center has compiled a database of so-called indiscriminate murders. They, and others, have documented mental illness as a primary factor behind 15% to 23% of mass murders.The great majority of mass murders, on the other hand, stem from people with a grudge. Or rather, not just a grudge, but people who see themselves as victims in life. After studying mass shooters for decades, Northeastern University criminologist, James Alan Fox, concluded that mass killers are often driven by a constellation of motivations, but above all else, revenge.“They seek payback for what they perceive to be unfair treatment by targeting those they hold responsible for their misfortunes.”Empathy addresses the pain and experience of victimhood. Recognize a person’s fundamental needs, and they have less reason to be bitter. There’s a surfeit of research showing the positive effects of receiving empathy, including fortifying kindness and cooperativeness, trust, support, and effectiveness in negotiations.In fact, new research shows that the ability for empathy to inhibit violence may be more than a mere social dynamic, it may be a biological one. Aggression and empathy share similar neuronal circuitry in the brain and “stimulation of these neuronal circuits in one direction reduces their activity in the other.” In other words, if you’re processing empathy, your brain may not have the bandwidth to practice aggression at the same time. Evidence indicates those effects can start in childhood giving credence to Levitt’s call for empathetic parenting.That’s certainly heartening and reason to hope for a more peaceful future. But what about today? Must we wait decades for the kids of enlightened parents to come of age?Maybe not.The second reason to believe that empathy could be a potent answer to mass murder and violence is an emerging body of anecdotal evidence.For a clear example of how empathy can stop gun violence, we can turn to Denmark in 2012. ISIS recruitment had begun to gain traction in earnest.Aarhus, a city about half the size of Seattle, was hit particularly hard. In the space of a few months, the town lost 34 recruits to Syria. Two cops on the missing persons beat—Allan Aarslev and Thorleif Link—put together that the missing Moslem kids had gone to Syria.That put Allan and Thorleif on the horns of a dilemma.They could see how authorities in Europe and the U.S. were responding to the recruitment of Moslem youth into ISIS. France was raiding mosques while countries like the U.S. and U.K. were tracking down suspected recruits, taking away passports, and mounting prosecutions.Given their experience, Allan and Thorleif could see two likely outcomes of such heavy-handed policies. Either the kids would stay in Syria and become hardened terrorists, or they would return home and bring their bitterness—and possibly their guns—with them.So, Allan and Thorleif took a different approach.They looked with an empathetic eye, asked themselves what the kids might need. Then, they found a city official who could hook the kids up with Denmark's extensive network of social services – help the youth get jobs, health care, an apartment, and even reenroll in school.The offerings met not only practical needs, but deeply emotional ones as well. The kids were able to find a sense of belonging, efficacy, and empowerment in their own communities, without resorting to flying across Europe in search of a new one.And the result?In the first year, 34 young men were recruited from Aarhus to Syria. Six were killed, and ten stayed in Syria. Eighteen came home; all of them showing up first in Allan and Thorleif's office. In the past four years, they've worked with 330 potential radicals in Aarhus. As the recruiting escalated across the rest of Europe, in 2015, only one boy left Aarhus for Syria.So, the question is, was the Aarhus approach an outlier? Were they lucky? Allan and Thorleif don't think so.Rather, it was an example of empathy—recognizing and feeding fundamental human needs—wielded powerfully. After working with 330 kids, Allan and Thorleif can readily identify common needs among these kids, “they want identity, recognition, mostly to belong. They are literally dying to belong.”But if we’re going to put our weight behind a program of empathy we want to know if this kind of approach is generalizable, and scalable. Can it stop the escalation of mass murder in the U.S.?For the answer to that question, one of our best sources perhaps is Andre Simons. Simons is in charge of Behavioral Analysis Unit 2 of the FBI’s Critical Incident Response Group. Yes, it’s one of those units made famous by TV shows that feature psychological profilers. But no, they don’t profile. At least not proactively.Instead, they do two things.They respond to tips about a person of concern, literally a person whose grandmother would agree is “behaving in any way that worries you.” And, when they find a person of concern, they intervene.In their world, intervening means plugging resources into the person’s life. Simons considers his colleagues consultants. He literally refers to persons of concern as “under the care of a threat assessment team.”Does that approach work, can it possibly, should you trust your life to it?At the end of 2016, then-Attorney General Eric Holder credited Simons and BAU2 with preventing no less than 148 mass shootings and violent attacks.Simons would qualify that number. He’d tell you that he and his team have participated in interventions with people on the “pathway to violence.” Five hundred since the unit was formed in 2010. And none have ever committed mass violence while under their care.So, what should be our take away, what does all that tell us?It tells us that it’s time. It’s time we change our minds about empathy and compassion. Whatever story we’ve told ourselves in the past about empathy, about it being for the weak, or for a fairer gentler world, about it calling us to be nice, or take on the emotions of others, it’s time to let that story go and to see it for what it is.Empathy is a powerful tool. A tool that can work when other can’t, maybe one of the few tools powerful enough to head off a future scarred by heavily armed men bent on revenge.And maybe, it’s a program or a policy we can all rally behind.———-To see more examples of using empathy skills powerfully, see my TEDx talk.This post originally appeared on TimothyDawes.com.

I tend to agree with Solomon Feferman on this subject. From the description on his book’s Amazon page:“[…] In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. […]”I agree with Feferman in that arithmetic, and the concept of number in particular, is a much better understood concept than set theory, or set in particular. And this is supported to a large degree by Kevin Knuth’s foundational work in physics. In his paper, The Deeper Roles of Mathematics in Physical Laws, Knuth shows that one can derive additivity, or additive measures in general, from the more fundamental notions (concepts) of order and symmetry; in set-theoretic measure theory, additivity is assumed! Us humans impose order on our environment and we often wish to quantify that order in a manner which respects the symmetries (commutativity and associativity) which we observe in that environment. This leads, in a very straightforward and natural ay, to arithmetical principles - and this is prevalent in human epistemology - that part which is quantified anyway:“There are some important symmetries at play when I combine sets of pencils or pennies or monkeys or stars. If I combine set [math]A[/math] with set [math]B[/math] to form the joint set [math]A U B[/math] , the result will be the same as if I combine set [math]B[/math] with set [math]A[/math]. This symmetry is called commutativity.[…]Now there is another important symmetry called associativity where the order in which one unites sets of objects also does not affect the final results. That is, in combining three sets [math]A[/math], [math]B[/math], and [math]C[/math], I could first combine [math]A[/math] with [math]B[/math] and then combine the result with [math]C[/math], or I could combine [math]A[/math] with the result of the combination of [math]B[/math] with [math]C[/math], and so on.[…]I feel relatively confident that these conceptual symmetries are, and need to be, experimentally observed when combining many things such as pencils and monkeys and so on. This is mainly because there are some examples where these symmetries are not experimentally observed.[…]Order theory focuses on the ways sets of objects, called elements, can be ordered (Birkhoff, 1967; Davey & Priestley, 2002). The useful concept is that of a partially ordered set of elements. A partially ordered set (or poset for short) is defined as a set of elements that can be compared with a binary ordering relation, generically denoted [math]≤[/math], that exhibits the properties of reflexivity, antisymmetry and transitivity (see Technical Endnotes). The sets [math]A[/math], [math]B[/math], and [math]C[/math] above along with the binary ordering relation of subset inclusion [math]⊆[/math] form a poset. However, this poset has additional properties that give it the special name of a lattice. Specifically, each pair of elements [math]x[/math] and [math]y[/math] has a unique least upper bound, [math]x ∨ y[/math] , called the join, and a unique greatest lower bound, [math]x ∧ y[/math], called the meet, such that the join and the meet are associative. So that in the case of our sets ordered by subset inclusion, we have that the lattice join is the set union, and the lattice meet is the set intersection.[…]Now, what is important in all of this is that the simple act of ordering objects and the properties of commutativity and associativity allows one to view things in two different ways. On one hand we have a sort of hierarchy of elements determined by the binary ordering relation. And on the other hand, we can consider the join and meet to be algebraic functions that take two elements to a third. The result is that a lattice is an algebra, and the ordering relation is related to the algebraic relation by what is called the consistency relation:[math]a ≤ b ⟺ a ∧ b = a[/math] and [math]a ∨ b = b[/math].[…]One can now see that ordering, commutativity and associativity underlie a class of universal phenomena. I will next discuss how this leads to mathematics which gives rise to physical laws with a degree of universal applicability.[…]We begin with the concept of quantification. The idea here is very simple. To each element we will assign a numeric value [math]v(p)[/math]. Now, if we want our quantification scheme to maintain some representation of the ordering relation then for elements [math]p[/math] and [math]q[/math] where [math]p ≥ q[/math] we assign values such that [math]v(p) ≥ v(q)[/math]. Essentially, here we are mapping elements to a total order—thus ranking them. This puts a strong constraint on the values we can assign.[…]First, if we want the assigned quantification to encode the underlying relationship, then we must assume that the number [math]v(x ∨ y)[/math] we assign to the join of two disjoint elements, [math]x [/math]and [math]y[/math], is a function of the numbers [math]v(x)[/math] and [math]v(y)[/math]. That is, we should be able to write [math]v(x ∨ y) = v(x) ⊕ v(y)[/math] where [math]⊕[/math] is a real-valued binary function to be determined.[…]. . . the operator [math]⊕[/math] must be commutative . . . the operator [math]⊕[/math] must also be associative . . The equation above is a functional equation called the Associativity Equation where the aim is to determine the function [math]⊕[/math]. The solution to this functional equation is known to be such that the function [math]⊕[/math]must be an invertible transform of addition (Aczél, 1966; Craigen & Páles, 1989; Knuth & Skilling, 2012).[…]In terms of the values we assigned to the elements this can be re-written as[math]f(v(x) ⊕ v(y)) = f(v(x)) + f(v(y))[/math].This is significant because we can simply perform a regraduation on the valuations [math]v[/math] by instead assigning different values [math]u(x)[/math] defined by [math]u(x) = f(v(x))[/math] so that[math]u(x) ⊕ u(y) = u(x) + u(y)[/math][math]⊕[/math] is additive. The fact that we can always do this means that order, commutativity and associativity results in additive measures. We have, in fact, derived the countable additivity axiom of measure theory from a deeper symmetry principle![…]We now can understand why we add quantities when we combine things. It doesn’t always work. The properties of order, commutativity and associativity must apply to the selected description. So now when I take a pair of pencils and combine them with another pencil, I can quantify the union of these sets of pencils by simple addition. This works because sets of pencils are closed and can be ordered, and combining pencils is commutative and associative.[…]The additive rule above was derived for disjoint elements. One can show that in general (see Technical Endnotes) the additive rule is[math]u(x ∨ y) = u(x) + u(y) - u(x ∧ y)[/math],where we have to subtract off the value assigned to the meet of the two elements to avoid double-counting (Knuth, 2003; Knuth, 2010). In order theory, this is known as the inclusion-exclusion principle (Klain & Rota, 1997; Knuth, 2003). Others simply call it the Sum Rule. What is remarkable is that the Sum Rule appears over and over again, and now we can understand why. This is a consequence of closure, ordering, commutativity and associativity.”So this, to me, is the foundations of mathematics: closure; ordering; commutativity; and associativity.