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like to give the smallest positive amount to each worker consistent with the constraint that if a developer has written more lines of code than their neighbor, they should receive more money. Given an array representing a line of seats of employees at MegaCorp, determine how much each one should get paid. For example, ... | {
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the domino has just been pushed to the left, * `R`, meaning the domino has just been pushed to the right, or * `.`, meaning the domino is standing still. Determine the orientation of each tile when the dominoes stop falling. Note that if a domino receives a force from the left and right side simultaneously, it will rem... | {
"page_id": null,
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is possible to throw `N` dice with some number of faces each to get a specific total. For example, `throw_dice(3, 6, 7)` should equal `15`. Solution'`, you should return `4`. Solution` worst-case time complexity. If the pattern is found, return the start index of its location. | {
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If not, return `False`. [Solution]( * * * ### Problem 277 []( This problem was asked by Google. UTF-8 is a character encoding that maps each symbol to one, two, three, or four bytes. For example, the Euro sign, `€`, corresponds to the three bytes `11100010 10000010 10101100`. The rules for mapping characters are as fol... | {
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list such as the one above, determine the number of friend groups in the class. Solution` is defined by the equation `a^2 + b^2 = c^2`. [Solution]( * * * ### Problem 283 []( This problem was asked by Google. A regular number in mathematics is defined as one which evenly divides some power of `60`. Equivalently, we can ... | {
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whose only prime divisors are `2`, `3`, and `5`. These numbers have had many applications, from helping ancient Babylonians keep time to tuning instruments according to the diatonic scale. Given an integer `N`, write a program that returns, in order, the first `N` regular numbers. Solution` tuples, which tell us where ... | {
"page_id": null,
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it is. The skyline itself can be described by a list of `(x, height)` tuples, giving the locations at which the height visible to a distant observer changes, and each new height. Given an array of buildings as described above, create a function that returns the skyline. For example, suppose the input consists of the bu... | {
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The procedure is as follows: For a given input `x`, create two new numbers that consist of the digits in `x` in ascending and descending order. Subtract the smaller number from the larger number. For example, this algorithm terminates in three steps when starting from `1234`: ``` 4321 - 1234 = 3087 8730 - 0378 = 8352 8... | {
"page_id": null,
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come in three colors: red, green, and blue. One power of the Qux is that if two of them are standing next to each other, they can transform into a single creature of the third color. Given N Quxes standing in a line, determine the smallest number of them remaining after any possible sequence of such transformations. Fo... | {
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= { 0: , 1: , 2: [1, 4], 3: [0, 4, 5], 4: [2, 3], 5: } ``` On the other hand, given the input below, you should return `False`. ``` students = { 0: , 1: , 2: [1, 3, 4], 3: [0, 2, 4, 5], 4: [2, 3], 5: } ``` [Solution]( * * * ### Problem 293 []( This problem was asked by Uber. You have N stones in a row, and would like... | {
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4: 10} paths = { (0, 1): 10, (0, 2): 8, (0, 3): 15, (1, 3): 12, (2, 4): 10, (3, 4): 5, (3, 0): 17, (4, 0): 10 } ``` In this case, the shortest valid path would be `0 -> 2 -> 4 -> 0`, with a distance of `28`. Solution` space? [Solution]( * * * ### Problem 296 []( This problem was asked by Etsy. Given a sorted array, con... | {
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longest portion will involve types `1` and `3`, with a length of four. Solution` to a text file. Write a program that reads this file as a stream and returns the top 3 candidates at any given time. If you find a voter voting more than once, report this as fraud. Solution`: Add a value to the set of values. * `check(val... | {
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may return occasional false positives (in other words, incorrectly identifying an element as part of the set), but should always correctly identify a true element. [Solution]( * * * ### Problem 302 []( This problem was asked by Uber. You are given a 2-d matrix where each cell consists of either `/`, `\`, or an empty sp... | {
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element at index `4` might end up at indices `3`, `4`, or `5`. Come up with an algorithm that sorts this list in `O(N log k)` time. Solution & T` and `F | (T & T)`. [Solution]( * * * ### Problem 309 []( This problem was asked by Walmart Labs. There are `M` people sitting in a row of `N` seats, where `M < N`. Your task ... | {
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seat. We can consider the cost of a solution to be the sum of the absolute distance each person must move, so that the cost here would be `5`. Given an input such as the one above, return the lowest possible cost of moving people to remove all gaps. Solution` time. An element is considered a peak if it is greater than ... | {
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lock becomes stuck in that state and cannot be opened. Let us consider a "move" to be a rotation of a single wheel by one digit, in either direction. Given a lock initially set to `000`, a target combination, and a list of dead ends, write a function that returns the minimum number of moves required to reach the target... | {
"page_id": null,
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number of ways we can produce `i` units of change. For example, `[1, 0, 1, 1, 2]` would indicate that there is only one way to make `0`, `2`, or `3` units, and two ways of making `4` units. Given such an array, determine the denominations that must be in use. In the case above, for example, there must be coins with val... | {
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a positive integer `N`, find the smallest number of steps it will take to reach `1`. There are two kinds of permitted steps: * You may decrement `N` to `N - 1`. * If `a * b = N`, you may decrement `N` to the larger of `a` and `b`. For example, given `100`, you can reach `1` in five steps with the following route: `100 ... | {
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to the correct amount of any other unit. You should also allow for additional units to be added to the system. [Solution]( * * * ### Problem 326 []( This problem was asked by Netflix. A Cartesian tree with sequence `S` is a binary tree defined by the following two properties: It is heap-ordered, so that each parent val... | {
"page_id": null,
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DOWN DUE TO AMAZON'S COPYRIGHTS INFRINGEMENT** * * * ### Problem 330 []( This problem was asked by Dropbox. A Boolean formula can be said to be satisfiable if there is a way to assign truth values to each variable such that the entire formula evaluates to true. For example, suppose we have the following formula, where ... | {
"page_id": null,
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does not know anyone in return (the "celebrity"). To help figure out who this is, you have access to an `O(1)` method called `knows(a, b)`, which returns `True` if person `a` knows person `b`, else `False`. Given a list of `N` people and the above operation, find a way to identify the celebrity in `O(N)` time. Solution... | {
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a user will stop searching. Given a directed graph of links between various websites, write a program that calculates each site's page rank. Solution, return `9` (`1001`). Solution` on a 2D cartesian plane, find the two closest points. For example, given the points `[(1, 1), (-1, -1), (3, 4), (6, 1), (-1, -6), (-4, -3)... | {
"page_id": null,
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matrix of random letters and a dictionary of words. Find the maximum number of words that can be packed on the board from the given dictionary. A word is considered to be able to be packed on the board if: * It can be found in the dictionary * It can be constructed from untaken letters by other words found so far on th... | {
"page_id": null,
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a range `[a, b]` (inclusive), return the sum of the elements of the binary search tree within the range. For example, given the following tree: ``` 5 / \ 3 8 / \ / \ 2 4 6 10 ``` and the range `[4, 9]`, return `23 (5 + 4 + 6 + 8)`. Solution` satisfies our requirement. Write a function that returns the maximum number of... | {
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different cities around the world on a given day. These are all direct flights. Each element in the list has the format `(source_city, destination, price)`. Consider a user who is willing to take up to `k` connections from their origin city `A` to their destination `B`. Find the cheapest fare possible for this journey ... | {
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* left child nodes link to words lexicographically earlier than the parent prefix * right child nodes link to words lexicographically later than the parent prefix * middle child nodes continue the current word For instance, since code is the first word inserted in the tree, and `cob` lexicographically precedes `cod`, `... | {
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Solution. Write a program to determine whether a given matrix qualifies as a crossword grid. [Solution]( * * * ### Problem 353 []( This problem was asked by Square. You are given a histogram consisting of rectangles of different heights. These heights are represented in an input list, such that `[1, 3, 2, 5]` correspon... | {
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only from the bars of the histogram. For the diagram above, for example, this would be six, representing the `2 x 3` area at the bottom right. [Solution]( * * * ### Problem 354 []( This problem was asked by Google. Design a system to crawl and copy all of Wikipedia using a distributed network of machines. More specific... | {
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This problem was asked by Netflix. Implement a queue using a set of fixed-length arrays. The queue should support `enqueue`, `dequeue`, and `get_size` operations. Solution`, where `l` corresponds to the left child and `r` corresponds to the right child. If either `l` or `r` is null, it will be represented as a zero. Ot... | {
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was asked by Spotify. You have access to ranked lists of songs for various users. Each song is represented as an integer, and more preferred songs appear earlier in each list. For example, the list `[4, 1, 7]` indicates that a user likes song `4` the best, followed by songs `1` and `7`. Given a set of these ranked list... | {
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same after being rotated `180` degrees. For example, `16891` is strobogrammatic. Create a program that finds all strobogrammatic numbers with N digits. Solution -> 7 add_subtract(1)(2)(3) -> 1 + 2 - 3 -> 0 add_subtract(-5)(10)(3)(9) -> -5 + 10 - 3 + 9 -> 11 ``` Solution` time. Solution`: add a new item `x` to the left ... | {
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Title: A Map-like Micro-Organization of Grid Cells in the Medial Entorhinal Cortex URL Source: Markdown Content: A Map-like Micro-Organization of Grid Cells in the Medial Entorhinal Cortex - ScienceDirect =============== Typesetting math: 100% Skip to main content []( "My account") []( "Sign In") * View**PDF** 2. Summ... | {
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license]( Open archive Highlights ---------- * •Grid cells form clusters and are mostly stellate cells between pyramidal patches * •Grid modules cluster, with intermingling of adjacent modules at the borders * •Co-modular grid cells form a noisy two-dimensional lattice according to grid phases * •The layout of grid pha... | {
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-------- medial entorhinal cortex grid cell grid module grid phase pyramidal cell stellate cell calcium imaging microprism virtual reality continuous attractor network models Introduction ------------ Topographical maps have been observed in many sensory and motor systems. For example, neurons in primary visual cortex ... | {
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but not others indicates that topography is not required for the function of neural networks, as some networks can operate by enforcing a certain connectivity diagram on randomly arranged neurons. However, in the presence of topography, the anatomical arrangement of neurons mirrors the pattern of projections they recei... | {
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(Kitamura et al., 2014 are organized. In one class of continuous attractor networks (CAN) that model grid firing, neuronal activity across the population is manifest as multiple bumps of activity in a two-dimensional (2D) sheet of phase-arranged grid cells (Burak and Fiete, 2009 uses the efficiently implemented synapti... | {
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al., 2012]( Yoon et al., 2013. Such topographical randomness increases the difficulty of establishing the precise synaptic connectivity matrix required for CAN models. In general, a better understanding of the micro-organization of grid phases will help to elucidate the potential biological implementation of CAN models... | {
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a triangular lattice. Bottom: relative anatomical arrangement of cells in local brain neighborhoods corresponds to their phase offsets (phase overlay in (B)) and repeats on the cell sheet. (ii) Grid cell somas and activity bumps are randomly arranged. The anatomical arrangement of cells with identical phases (middle) a... | {
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AI-generated Topic Pages") (wolframin ER transmembrane glycoprotein 1) and REELIN antibodies. Region between the two dashed yellow curves is layer 2, in which GCaMP6f was highly expressed in stellate (REELIN+) and pyramidal cells (WFS1+). D: dorsal; V: ventral; P:posterior; A: anterior. Same in all figures. Scale bar: ... | {
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of GCaMP6f in layer 2 neurons of the MEC; WFS1 staining reveals pyramidal cells; REELIN staining reveals stellate cells. Middle panels: overlay of GCaMP6f with WFS1 (left) or REELIN (right). Right panel: diameters of cell bodies. Each dot represents the COM of one cell with a color representing the diameter of its cell... | {
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COMs of stellate and pyramidal cells, respectively. Scaler bar: 100μm. D: dorsal. V: ventral. M: medial. L: lateral. Same in all following figures. (O) Schematic diagram of experimental apparatus, consisting of an air-supported spherical treadmill, axle positioned to constrain treadmill rotation to the forward/backward... | {
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its correlation to the cue template. Top: cross-correlation between the cue cell response and cue template under spatial shifts (lags) up to 300 cm in both directions. Middle: cue template. Bottom: 1D response of the cue cell was shifted by the amount of the lag, at which the correlation was maximal. (T) Cue score was ... | {
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set of sequential traversals. Middle: mean ΔF/F versus linear track position. Bottom: overlay of cue template (C.T., in red) and shifted mean ΔF/F (M. ΔF/F, in gray) according to the lag. Error bars: mean ± SEM. A, B and O were modified from Low et al. (2014) (Dana et al., 2014 (Figures S1 diameters: stellate cells gen... | {
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classified as grid cells), which represents environmental features (Diehl et al., 2017 than among pyramidal cells (18.4% ± 2.9%) (Figures 2, and most grid cells were stellate (75.6% ± 3.2%). Relatedly, significant calcium transients in stellate cells generally showed higher frequencies and larger amplitudes than in pyr... | {
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stellate and 408 pyramidal cells in 18 FOVs of six mice). p= 2.5× 10−4. (D) Pairwise distances between grid cells (G/G) and grid and non-grid cells (G/NG) (294 grid and 631 non-grid cells in 18 FOVs of six mice). p=5.2× 10−29. (E) Percentage of pyramidal grid cells at different distances from centers of pyramidal patch... | {
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of six mice). p= 2.7× 10−9 and 1.1× 10−9 for amplitudes and frequencies, respectively. (E) Amplitudes (left) and frequencies (right) of significant transients of stellate grid cells (G-S) and pyramidal grid cells (G-P) (75 pyramidal grid cells and 219 stellate grid cells in 18 FOVs of six mice). (F) Example showing fre... | {
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vivo_ two-photon image of GCaMP6f-labeled cell bodies in layer 2 of the MEC in Ai mouse. Scale bar: 50μm. Note that the labeled cell bodies cluster in a patch, consistent with the immunohistochemistry results that most labeled cells were pyramidal cells. (L) Spatial dependence of calcium transients of an imaged grid ce... | {
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dot represents the percentile of the fitting score of cells in one module compared to those of 100 shuffled datasets. Red dashed line marks the 75 th percentile of the shuffled fitting scores. (V) Ratios of 2D grid scales of successive modules, which were the 2D spacings of their fitted 2D triangular lattices. Each dot... | {
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biased by the lower percentage of GCaMP6f labeling of pyramidal cells than stellate cells in the GP 5.3 mice. In summary, grid cells in layer 2 form clusters that are comprised of mostly stellate cells and some pyramidal cells at patch edges (Figure 2 scales of neurons in 2D environments (Stensola et al., 2012]( "Downl... | {
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cells in two modules. Scale bar, 50 μm. (E) Pairwise distances of cells in (D). 1-1, 2-2, and 1-2 are distances of cells in module 1, in module 2, and between modules 1 and 2, respectively. p= 4.9× 10−9 for 1-1 and 1-2, and 2.6× 10−14 for 2-2 and 1-2. (F) Intra- and inter-module pairwise distances of multiple modules (... | {
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2D real environments (1.42) (Stensola et al., 2012, we identified the anatomical locations of grid cells and calculated their pairwise distances (Figure 3 were greater than those between cells in the same module (intra-module distances) (Figure 3 of the environment in the unit-rhombus, which is a repeating unit of the ... | {
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locations]( "Learn more about point locations from ScienceDirect's AI-generated Topic Pages") throughout the rhombus, and the phase distance between a pair of grid cells is the distance between their point locations within the rhombus (Figure 4 distances between grid cells (linear correlation of 2D and 1D phase distanc... | {
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fitted slices (red and black dots) in the same unit-rhombus (white). (E) Pairwise phase versus physical distances (bin width, 30 μm) of the nine cells in (C). (F) Phase plot showing relative anatomical locations of cells in (C) with small (80 th percentile), axes as in (C). (G) Pairwise phase versus physical distances ... | {
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test. p values in (E) and (G) were calculated as the percentage of shuffled data points that are below (if mean of real data ≤ mean of shuffled data) or above real data (if mean of real data ≥ mean of shuffled data). ∗p ≤ 0.05, ∗∗p ≤ 0.01, ∗∗∗p ≤ 0.001. Error bars: mean ± SEM. See also Figure S3]( "Download high-res im... | {
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a ground truth dataset, testing the accuracy of identifying grid phase distances based on slice fit of 1D grid responses. Four grid cells were simultaneously recorded with tetrodes in 2D real and 1D VR environments. Their 1D responses were fitted as parallel slices in the same triangular lattice. For each cell: left to... | {
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Each cell was colored according to its phase distance to the reference cell. Here we show examples for two different reference cells, but plots for all nine reference cells were similarly generated. (2) The nine plots described in (1) were overlaid, with colors from those plots (indicating phase distances between pairs... | {
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datasets of five mice). Blue rectangle indicates the portion of the plot corresponding to physical distances shorter than 120μm. (K) Relationship of pairwise physical distances and percentage of module 2 cell pairs with small (black: 80 th percentile, right y axis). Only cell pairs physically closer than 120μm are show... | {
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(when the mean of real data ≤ the mean of shuffled data) or above real data (when the mean of real data ≥ the mean of shuffled data). ∗p ≤ 0.05. ∗∗p ≤ 0.01. ∗∗∗p ≤ 0.001. Error bars: mean ± SEM. Using this method, we examined the relationship between grid phase and physical distance. In a cell group with one reference ... | {
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connected using non-overlapping triangles (“brain triangles”), and the spatial tuning phases of the same cells were connected using the same triangles (“phase triangles”). If the layouts of their anatomical and spatial tuning phases match, the phase triangles should show a low degree of overlap (high “folding score”). ... | {
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module with larger spacing (Figures S4 than pyramidal patches (Figures S4. !Image 19]( "Download high-res image (3MB)") 2. Download: Download full-size image Figure 5. Global Arrangement of Grid Phases (A) Phase clusters of a group of module 1 grid cells. Cells with similar phase (phase distances <10 th percentile of a... | {
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were normalized so that shuffled scores of each module had mean 0 and SD 1. Probabilities were normalized so that the maximal probabilities of real and shuffled data were 1. p= 1.8× 10−11. (F) Two models for global arrangement of grid phases. Left: spatial tuning phases of three different phase cluster sets (red, blue ... | {
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very similar; and (3) the cell migration distances in (I) are longer than that in (H). (J) Comparison of fit scores of cells in (G) with real (red) and shuffled phases (gray). The score was the mean migration distance of all cells in the best fit lattice. (K) Comparison of normalized fit scores of cells with real (red)... | {
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2. Download: Download full-size image Figure S4. Additional Methods and Results for Global Phase Arrangement, Related to Figure 5 Transformation of a lattice to a regular triangular lattice and calculation of grid score. Left: the original autocorrelogram of the distribution of phase clusters, shown in Figure 5. Step 2... | {
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of phase clusters. (F) Comparison of grid scores of phase clusters in 29 sets of co-modular cells with those of shuffles. The red dashed line indicates 60 th percentile of shuffles. Each dot represents one set of co-modular cells. Note that all the grid scores are above the 60 th percentile of shuffles. (G–I) Shapes of... | {
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spacings of grid modules determined from their spatial tuning responses. Each dot represents one module (n= 29). Red dashed line is the best fit line to the data. p value of the correlation between the two sets of spacings is 3.4× 10−5. (K) Four examples of the relative distribution of phase clusters and pyramidal clus... | {
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examples of 40 total choices. Each pair of these 40 pair choices will serve as generating vectors of an anatomical lattice, as described in (O) below. (O) Calculation of fit score. (1) Cell locations were first mapped in an anatomical lattice by sending the vectors v 1,v 2 to the generating vectors in the parallelogram... | {
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with similar spatial tuning phases form a phase cluster lattice, how are different phase cluster lattices relatively arranged in the brain? Our previous results showed that the local arrangements of anatomical and spatial tuning phases were well-matched. This local match and the existence of the phase cluster lattice t... | {
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as reflected by their similar autocorrelograms to real data, and allowed us to understand the organization of phases beyond clustering. We observed that for the best fit lattice, the total migration distance of real cells was shorter than that of the “locality preserving” phase shuffles (Figures 5, suggesting that grid... | {
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the Anatomical Phase Map, Related to Figure 5 Modeling of anatomical phase maps with noise. (1) To represent different spatial tuning phases, the spatial tuning phase unit-rhombus was divided into nine color zones. The anatomical phase unit-rhombus was divided accordingly. (2) In the anatomical phase unit-rhombus, the ... | {
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anatomical lattice (limited choices of lattice sizes and offsets in the brain, etc.), small migrations were still necessary. However, the fit score for the perfect case, which was equal to the average migration distance of all cells in the fitted lattice, was very low. In contrast, in the noisy case, larger migrations ... | {
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dot on the x axis). (C) Noise levels of anatomical phase maps of all 29 sets of co-modular cells. The dashed line indicates the mean noise level (0.22). (D) Comparison of the mean noise level of real data (0.22, black line) to that of 50 randomized datasets (gray histogram). Each randomized dataset was developed from t... | {
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map in the brain. However, this map is noisy. Note that the noise observed here is the new reduced noise in the fitted lattice. In (G), we provided modeled phase maps to reveal the original noise (for example, 0.22 on average, as shown in (C)) of the phase map before the global lattice fit. (G) The modeled anatomical p... | {
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"title": "from dpo"
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patterns to those in E, and the maximal-noise lattice (random) maps show random color-patterns, the “Original” maps with mean data noise (0.22) and matched noise to each FOV show comparable color patterns. The color patterns of their “Fit” anatomical phase unit-rhombuses are similar to those of real data shown in (F). ... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
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high-res image (2MB)]( "Download high-res image (2MB)") 2. Download: Download full-size image Figure S6. Global Lattice Fit and Anatomical Phase Map of Individual Mice; Co-active Cells Form a Lattice Similar to that Formed by Phase Clusters, Related to Figures 5 Global lattice fit results, anatomical phase maps, and no... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
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spatial fields are highlighted in pink and the peak mean ΔF/F of each field is indicated by a green dot. These peak locations represent field locations. Note that all the seven cells showed fields within the range of bin n (dotted rectangular area), so they were determined as co-active cells. Top right: an image frame ... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
permuted among the cells (50 shuffles). The real correlation coefficient was higher than 98% of shuffled coefficients. (F) Comparisons of the autocorrelograms of co-active cells and phase clusters of three more groups of co-modular cells ((1)-(3)). Scale bars: 100μm. (G) Comparison of correlation coefficients of the au... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
downstream cell), regardless of their anatomical distances (“short and long vectors”), may be oriented differently, such that the resultant vector has reduced amplitude (Figure 6. To test these hypotheses, we studied the directionality of vectors connecting sequentially active cells, whose spatial fields sequentially o... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
boxes). Bottom: overlay of mean ΔF/F of the two cells. Note that for each pair of sequential fields, the field of cell 1 always occurred before that of cell 2, so they are a sequential cell pair and cell 1 was the upstream cell. (D) Short vectors between a group of co-modular grid cells (gray dots). Gray: fitted anatom... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
similar phases would be co-active and generate activity bumps forming the same lattice. We tested this hypothesis by identifying the anatomical distribution of co-active cells, which represent the pattern of activity bumps during navigation (Figure S6, it is possible that cells in different units exhibit some functiona... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
functional independence of phase clusters further supports the lattice map of grid phases. !Image 24]( "Download high-res image (1MB)") 2. Download: Download full-size image Figure 7. Phase Clusters Are Independent Functional Units (A) Phase clusters of a set of co-modular grid cells, color-coded based on their phase d... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
Note that the phase map is distorted in at least two ways: (1) the global distortion of a rigid lattice to match the geometry of the module; (2) the local distortion of grid phases within each unit of the lattice: while most cells are located in color zones matching their spatial tuning phases, some cells are located i... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
or not (missed-field, black). Right: the missed-field patterns were converted to binary vectors (show-field= 1, missed-field= 0) and then averaged across all fields to obtain the missed-field pattern for the cell, which was a vector with one entry between 0 and 1 for every run. This missed-field pattern was then used t... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
a particular location of the environment during animal’s locomotion. Left:grid cells are locally generated within stellate cells in layer 2, which are recurrently connected (red arrows). During locomotion, activity bumps are made to move via the communication between layer 2 grid cells and cells in deep layers of the M... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
pre- and parasubiculum, which do not contain stellate cells (Boccara et al., 2010 The connectivity pattern of stellate cells is favorable for the formation of grid cells (illustrated in (D)) Although it is still unclear how grid cell activity emerges, models propose that it can arise through local lateral (recurrent) c... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
strong lateral inhibitory input, b) receive direct recurrent excitation, c) communicate with grid-head direction conjunctive cells to receive velocity signals and drive path-integration based updates of the location code in grid cells. Based on current experimental findings summarized below, stellate cells better meet ... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
3 pyramidal cells only overlap with stellate area and avoid pyramidal patches (Tang et al., 2015 Grid cell activity patterning is locally generated among layer 2 stellate cells ((E), left panel), and updated in accordance with animal movements based on interactions with the deeper layers: The grid-like activity bumps c... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
excitatory inputs from the deep layers. Discussion ---------- Our results revealed a close correspondence between the functional and anatomical organization of the grid cell network at multiple levels ([Figure 7]( First, grid cells were mainly stellate and clustered. Second, co-modular grid cells formed clusters. Third... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
al., 2013]( Schmidt et al., 2017 connectivity within a network (Burak and Fiete, 2009 of grid cell phases directly correlates with the local anatomical organization of cells with different phases, and therefore, anatomically nearby grid cells share more similar phases than distal cells. According to different implement... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
and implications of these distortions remain unclear. Last, the micro-organization of grid phases within a short physical distance is consistent with the recently identified short-range synapses in layer 2 of the MEC, which are mostly from excitatory cells to other cells within 100 μm (Schmidt et al., 2017 likely occur... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
2015]( | N/A | | Mouse: wild type C57BL/6J mice | The Jackson Laboratory | Stock No: 000664 | Black 6 | | **Software and Algorithms** | | MATLAB | MathWorks | | | ImageJ | National Institutes of Health | [ | | ScanImage 5 | Vidrio Technologies | [ | | ViRMEn (Virtual Reality Mouse Engine) | [Aronov and Tank, 2014 | Gi... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
about pathogens from ScienceDirect's AI-generated Topic Pages") (Surveillance PRIA®, Charles River, Wilmington, MA), were not involved in previous procedures, and were drug and test naive. ### Method Details #### Implantation of microprism for MEC imaging The microprism implant assembly and surgical procedures were sim... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
Topic Pages"), centered 3.4mm lateral to the midline and 0.75mm posterior to the center of the transverse sinus (at 3.4mm lateral). The dura over the cerebellum was removed. Mannitol (3g/kg) was administered by IP injection 30-60 min before the durotomy. The microprism assembly was manually implanted, with the prism in... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
Topic Pages") (Vibratome Model 1500). All slices were stored in 0.1M phosphate buffer (PB, 0.019M NaH 2 PO 4, 0.081M NaH 2 PO 4, pH 7.4) with 0.1% NaN 3. ##### Immunohistochemistry To examine the expression of GCaMP6f in layer 2 of the MEC, we performed immunohistochemistry on the sagittal slices generated above with d... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
about Alexa fluor from ScienceDirect's AI-generated Topic Pages") dye 568 or 647 so that their emission spectra were largely separated from that of GCaMP6f. We observed that GCaMP6f was expressed in three major cell types (interneurons, pyramidal and stellate cells), which were characterized using specific antibodies a... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
of REELIN, the signal of WFS1 could contaminate the signal of REELIN. We therefore performed a spectrum excitation over the range of 547-733 nm and isolated the emission signals from two major peaks, which corresponded to REELIN and WFS1, using the “blind unmixing” function in the NIS elements confocal software (Nikon)... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
function “regionprops”). For cells in an _in vivo_ field-of-view (FOV), we took a two-photon z stack containing the focal plane of the FOV to identify their maximal cell bodies. We found that the cells with clear boundaries and nuclearly excluded GCaMP6f expression in the FOV were mostly “in-focus” cells and their maxi... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
##### Identification of pyramidal cells in the same patch In the same FOV, the pyramidal cells in different patches were identified based on their physical locations (in X and Y axes) in the FOV. The X and Y coordinates of all pyramidal cells were clustered by k-means and the different clusters correspond to individual... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
axle inserted into the equator on one side so that the sphere only rotated in the forward/backward direction. Forward and backward motions were measured using an optical motion sensor (ADNS3080; red LED illumination) controlled with an Arduino Due. The VR environment, which was projected onto a toroidal screen surround... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
mode-locked Ti:sapphire laser (Chameleon Ultra II, Coherent, 140fs pulses at 80MHz). The laser scanning was achieved by a resonant scanning mirror (Cambridge Tech.). Fluorescence of GCaMP6f was isolated using a bandpass emission filter (542/50nm, Semrock) and detected using GaAsP photomultiplier tubes (1077PA–40, Hamam... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
correction Two-photon image time series were analyzed using custom MATLAB code. Motion correction was performed using a whole-frame, cross-correlation-based method via MATLAB scripts and ImageJ (Schneider et al., 2012. In general, the imaging stacks were read, down-sampled in MATLAB and then imported to ImageJ to obtai... | {
"page_id": null,
"source": 7370,
"title": "from dpo"
} |
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