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# Deep Residual Network Predicts Cortical Representation and Organization of Visual Features for Rapid Categorization

## Abstract

The brain represents visual objects with topographic cortical patterns. To address how distributed visual representations enable object categorization, we established predictive encoding models based on a deep residual network, and trained them to predict cortical responses to natural movies. Using this predictive model, we mapped human cortical representations to 64,000 visual objects from 80 categories with high throughput and accuracy. Such representations covered both the ventral and dorsal pathways, reflected multiple levels of object features, and preserved semantic relationships between categories. In the entire visual cortex, object representations were organized into three clusters of categories: biological objects, non-biological objects, and background scenes. In a finer scale specific to each cluster, object representations revealed sub-clusters for further categorization. Such hierarchical clustering of category representations was mostly contributed by cortical representations of object features from middle to high levels. In summary, this study demonstrates a useful computational strategy to characterize the cortical organization and representations of visual features for rapid categorization.

## Introduction

The visual cortex is capable of rapid categorization of visual objects1,2. This ability is attributable to cortical representation and organization of object information3,4. In the ventral temporal cortex, object representations are topologically organized5, spanning a high-dimensional space6 and being largely invariant against low-level appearance1,7. Knowledge about object categories is also represented in dorsal visual areas8,9,10 or even beyond the visual cortex11 where non-visual attributes of objects are coded12,13. In addition to their distributed representations14,15, object attributes are hierarchically organized and progressively emerge from visual input4. It is thus hypothesized that the brain categorizes visual objects based on their attributes represented in multiple stages of visual processing5,13.

To understand the basis of object categorization, it is desirable to map cortical representations of as many objects from as many categories as possible. The resulting maps provide the stimulus-response samples to address the representational structure that enables the brain to categorize or differentiate visual objects. Many studies have used functional magnetic resonance imaging (fMRI) to map brain activations with category-specific images12,15,16,17,18,19. Although such approaches are valuable for studying object categorization, it is expensive to cover many objects or categories in experiments, and it is arguably difficult to extrapolate experimental findings to new objects or categories. Moreover, object representations in the voxel space do not directly reveal the neural computation that give rise to such representations. It is also desirable to develop a model of hierarchical visual processing20 to be able to explain (or predict) cortical representations of visual objects with (or without) experimental data.

Advances in deep learning21 have established a range of deep neural networks (DNN) inspired by the brain itself4,22. Such models have been shown to be able to achieve human-level performance in object classification, segmentation, and tracking21. On the basis of DNNs, encoding models could be built to predict cortical responses to natural images23,24,25,26,27 or videos28,29. As the accuracies of predicted responses were high and robust in the entire visual cortex29, DNN-based encoding models are arguably advantageous than other models that only account for either the lowest30,31 or highest32 level of visual processing.

Recent studies also suggest that DNN-based encoding models may be generalized to new images or videos24,25,27,29. In this sense, the models provide a platform to simulate cortical representations of in principle infinite exemplars of a large number of object categories27,29, beyond what is experimentally attainable17,33,34,35,36. In addition, DNN views an image as a set of hierarchically organized features, rather than as a pixel array. The features are learned from millions of images to model image statistics in different levels of abstraction21. The learned features are much richer and more fine-grained than what may be intuitively defined (by humans) as the mid-level features. Through DNN-based encoding models, it is plausible to map object representations of specific features from each layer in DNN, allowing object categorization to be addressed at each level of visual processing.

Extending from recent studies23,24,25,26,27,29, we used a deep residual network (ResNet)37 to define, train, and test a generalizable, predictive, and hierarchical model of natural vision by using extensive fMRI data from humans watching >10 hours of natural videos. Taking this predictive model as a “virtual” fMRI scanner, we synthesized the cortical response patterns with 64,000 natural pictures including objects from 80 categories, and mapped cortical representations of these categories with high-throughput. We evaluated the category selectivity at every voxel in the visual cortex, compared cortical representational similarity with their semantic relationships, and evaluated the contributions from different levels of visual features to the cortical organization of categories. Consistent but complementary to prior experimental studies12,15,16,32,38,39,40,41,42,43, this study used a model-based computational strategy to study how cortical representations of various levels of object knowledge sub-serve categorization.

## Results

### ResNet predicted widespread cortical responses to natural visual stimuli

In line with recent studies23,24,25,26,27,29, we used a deep convolutional neural network to establish predictive models of cortical fMRI representations of natural visual stimuli. Specifically, we used ResNet – a deep residual network for computer vision37. With a much deeper architecture, ResNet offers more fine-grained layers of visual features, and it performs better in image recognition than similar but shallower networks, e.g. AlexNet44 as explored in prior studies23,24,25,26,27,29,45. In this study, we used ResNet to extract visual features from video stimuli, and used the extracted features to jointly predict the evoked fMRI response through a voxel-wise linear regression model. This encoding model was trained with a large amount of fMRI data during a training movie (12.8 hours for Subject 1, and 2.4 hours for Subject 2, 3), and tested with an independent testing movie (40 minutes).

The encoding accuracy (i.e. the correlation between the predicted and measured fMRI signals during the testing movie) was overall high (r = 0.43 ± 0.14, 0.36 ± 0.12, and 0.37 ± 0.11 for Subject 1, 2 and 3, respectively) and statistically significant (permutation test, corrected at FDR q < 0.01) throughout the visual cortex in every subject (Fig. 1a). The encoding accuracy was comparable among the higher-order ventral-stream areas, e.g. fusiform face area (FFA) and parahippocampal place area (PPA), as well as early visual areas, e.g. V1, V2, and V3 (Fig. 1c). The accuracy was relatively lower at dorsal-stream areas such as lateral intraparietal area (LIP), frontal eye fields (FEF), parietal eye fields (PEF), but not the middle temporal area (MT) (Fig. 1c). Different cortical regions were preferentially correlated with distinct layers in ResNet. The lower to higher level visual features encoded in ResNet were gradually mapped onto areas from the striate to extrastriate cortex along both ventral and dorsal streams (Fig. 1b), in agreement with previous studies25,26,27,28,29,45,46. The prediction accuracy was consistently higher with (the deeper) ResNet than with (the shallower) AlexNet (Fig. 1c). These results suggest that the ResNet-based voxel-wise encoding models offer generalizable computational accounts for the complex and nonlinear relationships between natural visual stimuli and cortical responses at widespread areas involved in various levels of visual processing.

### Encoding models predicted cortical representations of various object categories

As explored before27,29, the voxel-wise encoding models constituted a high-throughput platform to synthesize cortical activations with an infinitely large number of natural pictures that are unrealistic or expensive to acquire with most experimental approaches. Here, we used this strategy to predict the pattern of cortical activation with each of the 64,000 natural pictures from 80 categories with on average 800 exemplars per category. By averaging the predicted activation maps across all exemplars of each category, the common cortical activation within this category was obtained to report its cortical representation.

For example, averaging the predicted responses to various human faces revealed the cortical representation of the category “face” regardless of the position, size, color, angle, perspective of various faces (Fig. 2a). Such a model-simulated “face” representation was consistent with the fMRI-mapping result obtained with a block-design functional localizer that contrasted face vs. non-face pictures (Fig. 2b). In a similar manner, cortical representations of all 80 categories were individually mapped (Fig. 3). The resulting category representations were found not only along the ventral stream, but also along the dorsal stream albeit with relatively lower amplitudes and a smaller extent.

For each voxel, the model-predicted response as a function of category was regarded as the voxel-wise profile of categorical representation. The category selectivity – a measure of how a voxel was selectively responsive to one category relative to others47, varied considerably across cortical locations (Fig. 4a). Voxels with higher category selectivity were clustered into discrete regions including the bilateral PPA, FFA, lateral occipital (LO) area, the temporo-parietal junction (TPJ), as well as the right superior temporal sulcus (STS) (Fig. 4a). The profile of categorical representation listed in a descending order (Fig. 4b), showed that FFA, OFA, and pSTS were selective to humans or animals (e.g. man, woman, monkey, cat, lion); PPA was highly selective to places (e.g. kitchen, office, living room, corridor); and the ventral visual complex (VVC) was selective to man-made objects (e.g. cellphone, tool, bowl, car). In general, the ventral stream tended to be more category-selective than early visual areas (e.g. V1, V2, V3) and dorsal-stream areas (e.g. MT, LIP) (Fig. 4c).

### Distributed, overlapping, and clustered representations of categories

Although some ventral-stream areas (e.g. PPA and FFA) were highly (but not exclusively) selective to a certain category, no category was represented by any single region alone (Fig. 3). As suggested previously15, object categories were represented distinctly by distributed but partially overlapping networks (see examples in Supplementary Fig. S1). In the scale of nearly the entire visual cortex that was predictable by the encoding models (Fig. 1a), the spatial correlations in cortical representation between different categories were shown as a representational similarity matrix (Fig. 5a). This matrix revealed a clustered organization: categories were clustered into three groups such that cortical representations were more correlated among categories within the same group than across different groups (Fig. 5a, left), and the degree of clustering (quantified as the modularity index, Q) was high (Q = 0.35). Interestingly, categories clustered together on the basis of their cortical representations tended to have higher conceptual similarities, or closer relationships between the corresponding category labels as measured by their Leacock-Chodorow (LCH) similarity in WordNet48 (Fig. 5a, middle), or by the cosine distance between their vector representations after word2vec49 or GloVe50 transformation (Supplementary Fig. S5). Regardless of the distinct methods for measuring the semantic similarity, there was a significant correlation between the similarity in cortical representation and the similarity in semantics across all pairs of categories (Fig. 5a, right). Moreover, we examined the category representations in a finer scale confined to individual visual areas (V1, V2, V3, LO, FFA, PPA). For each of these areas, we evaluated the correlation between representational similarity and semantic similarity across all pairs of categories. The correlation tended to increase from lower (e.g. V1) to higher (e.g. FFA/PPA) areas in the ventral stream (Supplementary Fig. S3). However, the correlation was significant (p < 0.0001, permutation test) not only in higher ventral-stream areas, but also in mid-level areas (e.g. LO) or even lower areas (V2, V3). In sum, categories with closer cortical representations tend to bear similar semantic meanings, in the spatial scale of the whole visual cortex as well as visual areas at different stages of visual processing.

The representational clusters in the entire visual cortex grouped basic-level categories into super-ordinate-level categories. The first cluster included non-biological objects, e.g. airplane, bottle and chair; the second cluster included biological objects, e.g. humans, animals, and plants; the third cluster included places and scenes (e.g. beach, bedroom) (Fig. 5b). The cortical representation averaged within each cluster revealed the general cortical representations of superordinate categories. As shown in Fig. 5b, non-biological objects were represented by activations in bilateral sub-regions of the ventral temporo-occipital cortex (e.g. VVC); biological objects were represented by activations in the lateral occipital cortex and part of the inferior temporal cortex (e.g. FFA) but deactivations in parahippocampal cortex (e.g. PPA); background scenes were represented by activations in PPA but deactivations in the lateral occipital complex, partly anti-correlated with the activations with biological objects. The spatial correlations between the cortical representations of biological objects and background scenes were on average –0.17 ± 0.29, which should be cautiously taken as a tendency of anti-correlation instead of strong evidence for precisely opposite patterns of representations of these two kinds of categories.

### Mid-level visual features primarily accounted for superordinate categorization

Which levels of visual features accounted for such a clustered organization of cortical category representation? To address this question, we simulated the cortical representation of single-layer features of every image exemplar in each category, by setting to zero all other layers in ResNet except one before inputting the feature representations into voxel-wise linear encoding models. Then we evaluated the similarity in cortical representation between categories at an increasing level of visual processing, progressively defined by the first through last layer in ResNet. Figure 6a (left) shows the representational similarity matrix attributed to features in each layer, thus decomposing the clustered organization in Fig. 5a by layers. In the earliest level of visual processing as specified by V1-like neurons in the first layer of ResNet, the similarity (or dissimilarity) among different categories was not apparent within (or across) the three superordinate categories (non-biological objects, biological objects, and background scenes). At layer 4, non-biological objects differed themselves from biological objects or background scenes, as the representational similarity appeared to reveal two clusters, rather than three clusters. Starting from layer 10 through 19, the three clusters emerged in the corresponding representational similarity matrices. Starting from layer 25, anti-correlations became clearly notable between the cluster of biological objects and the cluster of background scenes.

In a more quantitative way, we evaluated the modularity index of the three-cluster organization due to layer-wise features. Figure 6a (right) shows the modularity index as a function of the layer in ResNet. It suggests that the clustering of basic-level categories into superordinate categories emerged progressively and occurred in many levels of visual processing, while the clustering was the most apparent in the middle level (i.e. layer 31 in ResNet). To gain intuition about the types of visual information from the 31st layer, the features encoded by individual units in this layer were visualized. Figure 6b illustrates the visualizations of some example features, showing shapes or patterns (both 2-D and 3-D), animal or facial parts (e.g. head and eye), scenic parts (e.g. house and mountain). Beyond these examples, other features were of similar types.

In addition, we evaluated the correlation between the inter-category semantic similarity and the corresponding similarity in cortical representation of the features in each layer. It turned out that the layer-wise correlations were significant (p < 0.001) for middle and high-level features, and the greatest correlation was not necessarily in the highest layer, but in the middle layer (around layer 31) (Fig. 6c). It suggests that semantic relationships emerge from object attributes in different levels of visual processing, and that the mid-level attributes (e.g. object shapes or parts) contribute the most to superordinate-level categorization.

### Clustered organization of cortical representation within superordinate categories

We further asked whether the similarly clustered organization could be extended to a lower level of categorization. That is, whether object representations were organized into sub-clusters within each superordinate-level cluster. For this purpose, we confined the scope of analysis from the whole visual cortex to finer spatial scales highlighted by the co-activation patterns within biological objects, non-biological objects, or background scenes (Fig. 7a). For example, within the regions where biological objects were represented (Fig. 7a, top), the representational patterns were further clustered into four sub-clusters: terrestrial animals, aquatic animals, plants, and humans (Fig. 7b, top). Similarly, the fine-scale representational patterns of background scenes were clustered into two sub-clusters corresponding to artificial (e.g. bedroom, bridge, restaurant) and natural scenes (e.g. falls, forest, beach) (Fig. 7, middle). However, the two clusters of non-biological objects did not bear any reasonable conceptual distinction (Fig. 7, bottom).

We also evaluated the contribution of layer-wise visual features to the fine-scale representational similarity and clustering. For biological objects, the modularity index generally increased from the lower to higher layer, reaching the maximum at the highest layer (Fig. 8a). Note that the highest layer encoded the most abstract and semantically relevant features, whose visualizations revealed the entire objects or scenes (see Supplementary Fig. S4) rather than object or scenic parts (Fig. 6b). In contrast, the modularity index reached the maximum at the 28th layer for background scenes (Fig. 8b), but was relatively weak and less layer-dependent for non-biological objects (Fig. 8c).

## Discussion

This study demonstrates a high-throughput computational strategy to characterize hierarchical, distributed, and overlapping cortical representations of visual objects and categories. Results suggest that information about visual-object category entails multiple levels and domains of features represented by distributed cortical patterns in both ventral and dorsal pathways. Categories with similar cortical representations are more semantically related to one another. In a large scale of the entire visual cortex, cortical representations of objects are clustered into three superordinate categories (biological objects, non-biological objects, and background scenes). In a finer spatial scale that is specific to each cluster, cortical representations are organized into sub-clusters for finer categorization, e.g. biological objects are categorized into terrestrial animals, aquatic animals, plants, and humans. The clustered organization of cortical representation is more observable for object features in middle and high levels of complexity compared to low-level features. Therefore, the brain categorizes visual objects through the hierarchically clustered organization of object attributes emerging from various levels of visual processing, rather than any operation that only occurs at the highest level of the ventral-stream hierarchy.

Central to this study is the use of the categorization-driven deep ResNet for synthesizing the cortical representations of thousands of natural visual objects from many categories. This strategy has a much higher throughput in sampling a virtually infinite number of exemplars of visual objects27,29, compared to prior studies that are limited to fewer categories with much fewer exemplars per category17,33,34,35,36. The sample size could be further extendable, since the ResNet-based encoding models presumably account for the relationships between cortical responses and visual features that are generalizable to different and new natural images, objects, and categories beyond which the models have been explicitly trained with. The model predictions are highly accurate and consistent with experimentally observed cortical responses to video stimuli and cortical representations to specific objects (e.g. human faces). The encoding accuracy may be further improved given an even larger and more diverse video-fMRI dataset to train the model, and a more biologically relevant deep neural net that better matches the brain and better performs in computer-vision tasks24. In this sense, the encoding models in this study are based on so far the largest video-fMRI training data from single subjects; and ResNet also outperforms AlexNet in categorizing images37,44 and predicting the brain (Fig. 1c). The encoding models reported here are thus arguably more powerful for predicting and mapping hierarchical cortical representations in the entire visual cortex, compared to other conceptually similar models in prior studies23,24,25,26,27,29.

What is also advantageous is that ResNet decomposes category information into multiple layers of features progressively emerging from low to middle to high levels. As such, ResNet offers a computational account of hierarchical cortical processing for categorization, yielding quantitative description of every object or category in terms of different layers of visual features. Mapping the layer-wise features from the ResNet onto the brain helps to address what drives the cortical organization of object knowledge and supports various levels of categorization.

The ResNet is trained with large-scale image set (~1.3 million natural images) for recognizing 1,000 visual object categories37. Though specific categories are used in training the ResNet, the trained model is generalizable enough to represent the semantics in our training and testing stimuli, and is transferrable for recognizing new categories based on the generic representations in the learned feature space for transfer learning51,52. The generalizability of the feature space enables prediction of the cortical representations of a wide range of categories far beyond what the network has been explicitly trained with. For example, the model is able to predict the face representation even though the ResNet is not trained for recognizing faces (Fig. 2).

Our results support the notion that visual-object categories are represented by distributed and overlapping cortical patterns15 rather than clustered regions16,38,39. Given this notion, the brain represents a category not as a single entity but a set of defining attributes that span multiple domains and levels of object knowledge. Different objects bear overlapping representational patterns that are both separable and associable, allowing them to be recognized as one category in a particular level, but as different categories in another level. For example, a lion and a shark are both animals but can be more specifically categorized as terrestrial and aquatic animals, respectively. The distributed and overlapping object representations, as weighted spatial patterns of attribute-based representations12, constitute an essential principle underlying the brain’s capacity for multi-level categorization.

Category representations may become highly selective at spatially clustered regions16,38,39. The category-selective regions are mostly in the ventral temporal cortex (Fig. 4), e.g. the FFA, PPA, and LO. The existence of category-selective regions does not contradict with distributed category representation. Instead, a region specific to a given category is thought to emerge from its connectivity with other locations that represent the defining attributes of that category53, or subserve the category-specific action and cognition54.

The cortical representational similarity between different categories is highly correlated with their semantic relationship (Fig. 5). In other words, the semantic relationship is preserved by cortical representation. This finding lends support for the notion of a continuous semantic space underlying the brain’s category representation32, which is a parsimonious hypothesis to bridge neural representation and linguistic taxonomy55. However, category information is not limited to semantic features, but includes hierarchically organized attributes, all of which define categories and their conceptual relationships. For example, “face” is not an isolated concept; it entails facial features (“eyes”, “nose”, “mouth”), each also having its own defining features. The similarity and distinction between categories may be attributable to one or multiple levels of features. In prior studies32, the hierarchical nature of category information is not considered as every exemplar of each category is annotated by a pre-defined label. This causes an incomplete account of category representation, leaving it difficult to disentangle the various levels of category information that may be used to associate or distinguish categories.

We have overcome this limit by disentangling multiple layers of features from visual objects and evaluating their respective cortical representations. Our results show that different levels of features make distinctive contributions to the clustering of category representation in the visual cortex. Coarse categories (i.e. biological objects, non-biological objects, and background scenes) are most attributable to mid-level features, e.g. shapes, textures, and object parts (Fig. 6). In a finer level of categorization, terrestrial animals, aquatic animals, plants, and humans are most distinguishable in the semantic space; categorization of man-made and natural scenes is most supported by mid-level features (Fig. 8). In addition, the semantic similarity between categories is correlated with the spatial similarity in cortical representation of their middle to high-level visual features (Fig. 6), not necessarily confined to one level or domain of features or a single cortical region, e.g. ITC41. Recent studies have also shown that the cortical organization of visual objects may be explained in part by similarity in low-level visual features56,57,58, shape57,59,60,61,62,63,64, and the real-word or conceptual size of objects65,66. This study further expands the dimension of visual or conceptual features beyond what can be intuitively defined67, by using data-driven features extracted from ResNet37,

This study is focused on the use of CNN-based encoding models to study the brain’s mechanism for categorization, rather than only on the validation of a CNN against neuroscience data. Arguably, if a model is able to predict cortical responses to natural visual stimuli, it is reasonable to use the model as a computational tool to characterize the brain itself. Similar ideas have been utilized to map the brain’s semantic representation by using semantics-based encoding models32, yielding insightful findings about how the brain represents natural language. However, it should be noted that although it is successful explaining significant variance of cortical responses to video stimuli, ResNet is not a perfect model of the visual cortex, and does not reach the noise ceiling. ResNet, or other types of feed-forward-only CNN, ignores the temporal relationships between video frames. Thus, the ResNet-based encoding models are more suitable to be trained with well-separated static image stimuli, which would take much longer time to acquire an equivalent amount of training data (as with video stimuli) for training the encoding models with millions of parameters. In addition, ResNet does not include any feedback connections or account for active attention, and fails to mimic the brain’s ability of unsupervised learning68. For these reasons, ResNet is by no means an ultimate model of the visual cortex. Nevertheless, a feed-forward CNN is appropriate for modeling the brain’s mechanism for rapid visual categorization, which is arguably mostly feed-forward1,69. Our results suggest that CNN can be used to reproduce the cortical organization of category representations, selectivity, and clustering, which often require extensive experimental efforts to reveal17,33,34,35,36. The CNN-based encoding models may allow researchers (or students) to run “virtual-fMRI” experiments with arbitrary visual stimuli, simulate cortical activations, and accordingly raise hypotheses for testing with real experiments. In the meantime, it awaits future studies to validate this strategy with more experimental data and a rich stimulus set with different configurations, and to develop more biologically plausible models to replace CNN in this computational strategy.

## Materials and Methods

### Experimental data

We used and extended the human experimental data from our previous study29, according to experimental protocols approved by the Institutional Review Board at Purdue University with informed consent from all human subjects prior to their participation. All methods were performed in accordance with the relevant guidelines and regulations. Briefly, the data included the fMRI scans from three healthy subjects (Subject 1, 2, 3, all female) when watching natural videos. For each subject, the video-fMRI data were split into two independent datasets: one for training the encoding model and the other for testing it. For Subject 2 & 3, the training movie included 2.4 hours of videos; the testing movie included 40 minutes of videos; the training movie was repeated twice, and the testing movie was repeated ten times. For Subject 1, the training movie included not only those videos presented to Subject 2 and 3, but also 10.4 hours of new videos. The new training movie was presented only once. The movie stimuli included a total of ~9,300 video clips manually selected from YouTube, covering a variety of real-life visual experiences. All video clips were concatenated in a random sequence and separated into 8-min sessions. Every subject watched each session of videos (field of view: 20.3° × 20.3°) through a binocular goggle with the eyes fixating at a central cross (0.8° × 0.8°). During each session, whole-brain fMRI scans were acquired with 3.5 mm isotropic resolution and 2 s repetition time in a 3-T MRI system by using a single-shot, gradient-recalled echo-planar imaging sequence (38 interleaved axial slices with 3.5 mm thickness and 3.5 × 3.5 mm2 in-plane resolution, TR = 2000 ms, TE = 35 ms, flip angle = 78°, field of view = 22 × 22 cm2). Structural MRI data with T1 and T2 weighted contrast were also acquired with 1 mm isotropic resolution for every subject. The volumetric fMRI data were preprocessed and co-registered onto a standard cortical surface template70. For each cortical location, the 4th-order polynomial trend was removed from the fMRI signal. For training and testing encoding models (as described latter), the fMRI signals were averaged over repetitions if there were multiple repeats and then standardized (i.e. remove the mean and normalize the variance). More details about the movie stimuli, data preprocessing and acquisition are described elsewhere29.

### Deep residual network

In line with previous studies23,24,25,26,27,29,45, a feedforward deep neural network (DNN) was used to model the cortical representations of natural visual stimuli. Here, we used a specific version of the DNN known as the deep residual network (ResNet), which had been pre-trained to categorize natural pictures with the state-of-the-art performance37. In the ResNet, 50 hidden layers of neuron-like computational units were stacked into a bottom-up hierarchy. The first layer encoded location and orientation-selective visual features, whereas the last layer encoded semantic features that supported categorization. The layers in between encoded increasingly complex features through 16 residual blocks; each block included three successive layers and a shortcut directly connecting the input of the block to the output of the block37. Compared to the DNNs in prior studies24,25,26,29,45,71, the ResNet was much deeper and defined more fine-grained hierarchical visual features. The ResNet could be used to extract feature representations from any input image or video frame by frame. Passing an image into the ResNet yielded an activation value at each unit. Passing a video yielded an activation time series at each unit as the fluctuating representation of a given visual feature in the video.

### Encoding models

For each subject, we trained an encoding model to predict each voxel’s fMRI response to any natural visual stimuli72, using a similar strategy as previously explored25,27,29. The voxel-wise encoding model included two parts: the first part was nonlinear, converting the visual input from pixel arrays into representations of hierarchical features through the ResNet; the second part was linear, projecting them onto each voxel’s fMRI response. The encoding model used the features from 18 hidden layers in the ResNet, including the first layer, the last layer, and the output layer for each of the 16 residual blocks. For video stimuli, the time series extracted by each unit was convolved with a canonical hemodynamic response function (HRF) with the peak response at 4 s, and down-sampled to match the sampling rate of fMRI, and then standardized (i.e. remove the mean and normalize the variance).

The feature dimension was reduced by applying principle component analysis (PCA) first to each layer and then to all layers in ResNet. The principal components of each layer were a set of orthogonal vectors that explained > 99% variance of the layer’s feature representations given the training movie. The layer-wise dimension reduction was expressed as equation (1).

$${{\boldsymbol{f}}}_{l}({\bf{x}})=\,{{\boldsymbol{f}}}_{l}^{o}({\bf{x}}){{\bf{B}}}_{l}$$
(1)

where $${{\boldsymbol{f}}}_{l}^{o}({\bf{x}})$$ (1 × p l ) is the original feature representation from layer l given a visual input x, B l (p l  × q l ) consists of unitary columnar vectors that represented the principal components for layer l, $${{\boldsymbol{f}}}_{l}({\bf{x}})$$ (1 × q l ) is the feature representation after reducing the dimension from p l to q l .

Following the layer-wise dimension reduction, the feature representations from all layers were further reduced by using PCA to retain > 99% variance across layers. The final dimension reduction was implemented as equation (2).

$${\boldsymbol{f}}({\bf{x}})={{\boldsymbol{f}}}_{1:L}({\bf{x}}){{\bf{B}}}_{1:L}$$
(2)

where $${{\boldsymbol{f}}}_{1:L}({\bf{x}})=[\frac{{{\boldsymbol{f}}}_{1}({\bf{x}})}{\sqrt{{p}_{1}}},\,\ldots \,,\frac{{{\boldsymbol{f}}}_{L}({\bf{x}})}{\sqrt{{p}_{L}}}]$$ is the feature representation concatenated across L layers, $${{\bf{B}}}_{1:L}$$ consists of unitary principal components of the layer-concatenated feature representations of the training movie, and $${\boldsymbol{f}}({\bf{x}})$$ (1 × k) is the final dimension-reduced feature representation.

For the second part of the encoding model, a linear regression model was used to predict the fMRI response $${r}_{v}({\bf{x}})$$ at voxel $$v$$ evoked by the stimulus $${\bf{x}}$$ based on the dimension-reduced feature representation $${\boldsymbol{f}}({\bf{x}})$$ of the stimulus, as expressed by equation (3).

$${r}_{v}({\bf{x}})={\boldsymbol{f}}({\bf{x}})\,{{\bf{w}}}_{v}+{\varepsilon }_{v}$$
(3)

where $${{\bf{w}}}_{v}$$ is a columnar vector of regression coefficients specific to voxel $$v$$, and $${\varepsilon }_{v}$$ is the error term. As shown in equation (4), L2-regularized least-squares estimation was used to estimate $${{\bf{w}}}_{v}$$ given the data during the training movie (individual frames were indexed by i = , …, N), where the regularization parameter was determined based on nine-fold cross-validation.

$$\mathop{\,{\hat{{\bf{w}}}}_{v}={\rm{\arg }}\,{\rm{\min }}}\limits_{\,{{\bf{w}}}_{v}}\frac{1}{N}\sum _{i=1}^{N}{({r}_{v}({{\bf{x}}}_{i})-{\boldsymbol{f}}({{\bf{x}}}_{i}){{\bf{w}}}_{v})}^{2}+\lambda {\Vert {{\bf{w}}}_{v}\Vert }_{2}^{2}$$
(4)

After the above training, the voxel-wise encoding models were evaluated for their ability to predict the cortical responses to the novel testing movie (not used for training). The prediction accuracy was quantified as the temporal correlation (r) between the predicted and observed fMRI responses at each voxel given the testing movie. Since the testing movie included five distinct sessions, the prediction accuracy was evaluated separately for each session, and then averaged across sessions. The significance of the voxel-wise prediction accuracy was evaluated with a block-permutation test73 (corrected at false discovery rate (FDR) q < 0.01), as used in our prior study29.

We also evaluated the correspondence between the hierarchical layers in ResNet and the hierarchical cortical areas underlying different stages of visual processing, in line with previous studies23,24,25,26,27,28,29,45. For this purpose, we calculated the variance of the response at a voxel explained by the visual features in single layers. Specifically, the features extracted from the testing movie were kept only for one layer in the ResNet, while setting to zeros for all other layers. Through the voxel-wise encoding model, the variance (measured by R-squared) of the response explained by the single layer was calculated. For each voxel, we identified the best corresponding layer with the maximum explained variance and assigned its layer index to this voxel. The assigned layer index indicated the processing stage this voxel belonged to.

We also tested whether the deeper ResNet outperformed the shallower AlexNet44 in predicting cortical responses to natural movies, taking the latter as the benchmark given its state-of-the-art encoding performance in prior studies25,26,29. For this purpose, we trained and tested similar encoding models based on the AlexNet with the same analysis of the same dataset. We compared the prediction accuracy between ResNet and AlexNet for regions of interest (ROIs) defined in an existing cortical parcellation74, and further evaluated the statistical significance of their difference using a paired t-test (p < 0.001) across all voxels within each ROI. Considering the noise in the data, we also calculated the noise ceiling of the predictability at each voxel. The noise ceiling indicated the maximum accuracy that a model could be expected to achieve given the level of noise in the testing data75. The noise and signal in fMRI were assumed to follow Gaussian distribution and the mean of noise was zero. For each testing session, we estimated the noise level and the mean/SD of the signal for every voxel. We used Monte Carlo simulation to obtain the noise ceiling. For each simulation, we generated a signal from the signal distribution, and generated a noisy data by adding the signal and the noise drawn from the noise distribution, and calculated the correlation between the signal and the data. We performed 1,000 simulations for each testing session, and took the median correlation as the noise ceiling. The ceiling was then averaged across sessions.

### Human-face representations with encoding models and functional localizer

The ResNet-based encoding models were further used to simulate cortical representations of human faces, in comparison with the results obtained with a functional localizer applied to the same subjects. To simulate the cortical “face” representation, 2,000 human-face pictures were obtained by Google Image search. Each of these pictures was input to the voxel-wise encoding model, simulating a cortical response map as if it were generated when the subject was actually viewing the picture, as initially explored in previous studies27,29. The simulated response maps were averaged across all the face pictures, synthesizing the cortical representation of human face as an object category.

To validate the model-synthesized “face” representation, a functional localizer76 was used to experimentally map the cortical face areas on the same subjects. Each subject participated in three sessions of fMRI with a randomized block-design paradigm. The paradigm included alternating ON-OFF blocks with 12 s per block. During each ON block, 15 pictures (12 novel and 3 repeated) from one of the three categories (face, object, and place) were shown for 0.5 s per each picture with a 0.3 s interval. The ON blocks were randomized and counter-balanced across the three categories. Following the same preprocessing as for the video-fMRI data, the block-design fMRI data were analyzed with a general linear model (GLM) with three predictors, i.e. face, object, and place. Cortical “face” areas were localized by testing the significance of a contrast (face > object and face > place) with p < 0.05 and Bonferroni correction.

### Synthesizing cortical representations of different categories

Beyond the proof of concept with human faces, the similar strategy was also extended to simulate the cortical representations of 80 categories through the ResNet-based encoding models. The category labels were shown in Fig. 3. These categories were mostly covered by the video clips used for training the encoding models. For each category, around 800 pictures were obtained by Google Image search with the corresponding label, and were visually inspected to replace any exemplar that belonged to more than one category. There was a total of 64,000 objects from 80 categories. The cortical representation of each category was generated by averaging the model-simulated response map given every exemplar within the category.

We focused on cortical representations of basic-level object categories, as opposed to individual images. Although the models were able to simulate and characterize cortical activations with each of the images, as already done in our prior study29, herein the total number of images (64,000) was too large. This choice was also given our primary interest in representations of object knowledge, regardless of the luminance, position, and size of any object. However, the exclusive focus on category-average representations, may be biased by how categories were defined and how images were selected (by humans). More detailed analysis of responses to individual image exemplars is helpful to mitigate this bias or ambiguity17.

### Category selectivity

Following the above analysis, cortical representations were compared across categories to quantify the category selectivity of various locations and ROIs. For each voxel, its selectivity to category $$i$$ against other categories $${i}^{c}$$ was quantified with equation (5), as previously suggested47.

$${d}_{i}^{\text{'}}=\frac{{\bar{r}}_{i}-{\bar{r}}_{{i}^{c}}}{\sqrt{({\sigma }_{i}^{2}+{\sigma }_{{i}^{c}}^{2})/2}}$$
(5)

where $${\bar{r}}_{i}$$ and $${\sigma }_{i}^{2}$$ are the mean and variance of the responses to the exemplars in category $$i$$, and $${\bar{r}}_{{i}^{c}}$$ and $${\sigma }_{{i}^{c}}^{2}$$ were counterparts to all exemplars in other categories $${i}^{c}$$. Irrespective of any specific category, the general category-selectivity for each voxel was its maximal d′ index among all categories, i.e. $$d^{\prime} =\mathop{{\rm{\max }}}\limits_{i}\{{d}_{i}^{\text{'}}\}$$. A d′ index of zero suggests non-selectivity to any category, and a higher d′ index suggests higher category-selectivity. The category selectivity of any given voxel was also inspected by listing the categories in a descending order of their representations at the voxel. We also obtained the ROI-level category selectivity by averaging the voxel-wise selectivity across voxels and subjects. ROIs were defined in an existing cortical parcellation74.

### Categorical similarity and clustering in cortical representation

To reveal how the brain organizes categorical information, we assessed the similarity (i.e. the Pearson’s correlation of the spatial response patterns across the predictable voxels with q < 0.01 in permutation test and prediction accuracy r > 0.2) in cortical representations between categories. Based on such inter-category similarity, individual categories were grouped into clusters using k-means clustering77. The goodness of clustering was measured as the modularity index, which quantified the inter-category similarities within the clusters relative to those regardless of the clusters78. The number of clusters was determined by maximizing the modularity index. To quantify the modularity index, the categorical similarity was viewed as a signed, weighted, and undirected network78. Each node represented one category, and each weighted edge represented the similarity between two categories. The modularity was then measured as the probability of having edges falling within clusters in the network against a random network (null case) with the same number of nodes and edges placed at random preserving the degree of each node. Specifically, given a positive weighted matrix S (S ij denotes the weight between categories i and j, and $$S=2\sum _{i}\sum _{j}{S}_{ij}$$ denotes the double total weight), the modularity index Q was defined as $$Q=\sum _{i}\sum _{j}({p}_{ij}-{q}_{ij}){\rm{\delta }}({C}_{i},{C}_{j})$$, where p ij  = S ij /S is the probability of connecting category i and j in the network with edge weight S ij , $${q}_{ij}=(\sum _{j}{S}_{ij}/S)(\sum _{i}{S}_{ij}/S)$$ denotes the expected probability of having edge between i and j in random networks, and $${\rm{\delta }}({C}_{i},{C}_{j})$$ is the Kronecker delta function with value 1 if i and j are in the same cluster and 0 otherwise. Since the correlation coefficients ranged from −1 to 1, we separated the positive and negative weights by $${S}_{ij}={S}_{ij}^{+}-{S}_{ij}^{-}$$ where $${S}_{ij}^{+}=\,{\rm{\max }}\{0,{S}_{ij}\}$$ and $${S}_{ij}^{-}=\,{\rm{\max }}\{0,-{S}_{ij}\}$$, and calculated their corresponding modularity Q+ and Q. Then the total modularity was quantified as $$Q=\frac{{S}^{+}}{{S}^{+}+{S}^{-}}{Q}^{+}-\frac{{S}^{-}}{{S}^{+}+{S}^{-}}{Q}^{-}$$. The significance of the modularity index was assessed by permutation test against the null distribution obtained from shuffling the pair-wise similarities randomly for 100,000 times. The larger modularity means the larger deviation from the null case and the better differentiation between clusters. Noted that higher similarity within clusters and less similarity across clusters gives larger modularity.

The similarity in cortical representation between different categories was compared with their similarity in semantic meaning. Here, we explored three different models to measure the semantic similarity between categories. For the first model, the semantic similarity between categories was evaluated as the Leacock-Chodorow similarity (LCH)48 between the corresponding labels based on their relationships defined in the WordNet79 – a directed graph of words (as the nodes) and their is-a relationships (as the edges). Briefly, LCH computes the similarity (s) between two labels based on the shortest path (p) that connects the labels in the taxonomy and the maximum depth (d) of the taxonomy in which the labels occur through $$s=-\mathrm{log}(p/2d)$$. The second model was the word2vec model that represented text words in a continuous vector space that captured a large number of precise syntactic and semantic word relationship49. We used the published model that was pretrained by Google on 100 billion words from Google News. The model was trained to accurately predict surrounding words given the current word. We used it to transform the category labels to vectors, and then calculated the semantic similarity between labels as the cosine distance of their corresponding vectors. The third model was the GloVe model that also represented words in vectors and captured fine-grained semantic and syntactic regularities using vector arithmetic50. GloVe was trained on global word-word co-occurrence statistics from a corpus of text. Similarly, we used the pretrained GloVe (trained on a large corpus including 840 billion tokens) to derive the vectors of category labels and calculate their semantic similarity as the cosine distance between the vectors. After obtaining the inter-category semantic similarity (LCH, word2vec, or GloVe), we evaluated the Pearson’s correlation between the cortical and semantic similarities. Before computing the correlation, the cortical similarity was transformed to z-score by using the Fisher’s z-transformation. Since the similarity was symmetric, the correlation was computed over the values in the upper (or equivalently the lower) triangular region of the similarity matrix80. The significance was assessed by random permutation of the category labels (i.e. reordering rows and columns of the cortical similarity matrix according to this permutation and computing the correlation). By repeating the permutation step 10,000 times, we obtained a distribution of correlations simulating the null hypothesis that the two similarity matrices are unrelated80.

### Layer-wise contribution to cortical categorical representation

We also asked which levels of visual information contributed to the clustered organization of categorical representations in the brain. To answer this question, the cortical representation of each category was dissected into multiple levels of representations, each of which was attributed to one single layer of features. For a given category, the features extracted from every exemplar of this category were kept only for one layer in the ResNet, while setting to zeros for all other layers. Through the above trained encoding models (see Encoding models in Materials and Methods), the single-layer visual features were projected onto a cortical map that only represented a certain level of visual information shared in the given category. The similarity and modularity in cortical representations of individual categories were then re-evaluated as a function of the layer in the ResNet. The layer with the highest modularity index contributed the most to the clustered organization in cortical categorical representation. The features encoded by this layer were visualized for more intuitive understanding of the types of visual information underlying the clustered organization. The feature visualization was based on an optimization-based technique81. Briefly, to visualize the feature encoded by a single unit in the ResNet, the input to the ResNet was optimized to iteratively maximize the output from this unit, starting from a Gaussian random pattern. Four optimized visualizations were obtained given different random initialization.

After obtained the layer-wise similarities in cortical representations of object categories, we further evaluated the correlation between the cortical similarity and the semantic similarity for each layer, and assessed its significance by using the aforementioned permutation test (p = 0.0001).

### Finer clustering of categorical representation

Considering object categories were defined hierarchically in semantics79, we asked how hierarchy of categorization5. More specifically, we tested whether the representational similarity and distinction in a larger spatial scale gave rise to a coarser level of categorization, whereas the representation in a smaller spatial scale gave rise to a finer level of categorization. To do so, we first examined the category representation in the scale of the entire visual cortex predictable by the encoding models, and clustered the categories into multiple clusters by using the clustering analysis of the representational similarity in this large scale. The resulting clusters of categories were compared with the superordinate-level semantic categories. Then, we focused on a finer spatial scale specific to the regions where category representations overlapped within each cluster. The cluster-specific region included the cortical locations whose activation was significantly higher for objects in the cluster compared to 50,000 random and non-selective objects (p < 0.01, two-sample t-test, Bonferroni correction). Given the spatial similarity of category representation in this finer scale, we defined sub-clusters within each cluster using the same clustering analysis as for the large-scale representation. The sub-clusters of categories were compared and interpreted against semantic categories in a finer level.

### Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

The authors are thankful to Dr. Xiaohong Zhu and Dr. Byeong-Yeul Lee for constructive discussion, and Kuan Han for his assistance in collecting natural images, and Yizhen Zhang for her help in acquiring fMRI. The research was supported by NIH R01MH104402, MH111413, and Purdue University.

## Author information

### Affiliations

1. #### Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA

• Zhongming Liu
2. #### School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA

• Haiguang Wen
• , Junxing Shi
•  & Zhongming Liu
3. #### Purdue Institute for Integrative Neuroscience, Purdue University, West Lafayette, IN, USA

• Haiguang Wen
• , Junxing Shi
•  & Zhongming Liu

• Wei Chen

### Contributions

H. Wen, J. Shi, W. Chen and Z. Liu designed the study. H. Wen and J. Shi collected the data. H. Wen analyzed the data. H. Wen collected the natural images. H. Wen, Z. Liu and W. Chen wrote the paper. All authors contributed to data interpretation.

### Competing Interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Zhongming Liu.


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# Finding the information sets of a linear code.

I'm trying to get a better understanding of linear codes, so I decided to work on problems from various textbooks. I'm having trouble understanding how to do this problem, and I was wondering if anyone can lead me in the right direction.

Problem The matrix $G = [I_{4} | A]$, where $$G = \left[ \begin{array}{cccc|ccc} 1 & 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 1\end{array} \right]$$

is a genrator matrix in standard form for a $[7,4]$ binary code, denoted by $\mathcal{H}_3$. The parity check matrix for $\mathcal{H}_3$ is $$H = [A^{T} | I_{3}] = \left[ \begin{array}{cccc|ccc} 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 \end{array} \right].$$

Find at least four information sets in $\mathcal{H}_3$. Find at least one set of four coordinates that do not form an information set. $\blacksquare$

The book defines an information set as follows: Given a $[n,k]$ linear code $\mathcal{C}$, a generator matrix for $\mathcal{C}$ is any $k \times n$ matrix $G$ whose rows form a basis for $\mathcal{C}$. For any set of $k$ independent columns of $G$, the corresponding set of coordinates forms an information set for $\mathcal{C}$.

Any help would be greatly appreciated since I've been staring at this for quite some time. Thanks!

-

Are you having trouble finding sets of 4 independent/dependent columns in $G$? or are you having trouble finding the corresponding set of coordinates, given the set of 4 independent columns?

If your problem is the first of the above, then the question is, do you know what it means for a set of vectors to be (linearly) independent, and how to test a set of vectors for this property? Can you see, for example, that the first 4 columns of $G$ are independent, while columns 2, 3, 4, 5 are not? There is a non-trivial linear combination of columns 2 through 5 giving the zero vector, namely, the 5th minus the sum of the other three; but there is no linear combination of the first 4 columns giving zero, other than the combination with all four coefficients being zero.

-
Gerry, this has been helpful. I was unsure as to how to find the information sets, but after reading your answer, it makes more sense. From linear algebra, I remember how to test for independence by using row operations. From what you said, I understand that $(1, 2, 3, 4)$ would form an information set. From the book's definition, would I have to find another set of 4 columns that are independent, or would I have to find any number of columns that are independent? For instance, can I say $(1, 2, 3)$ is an iformation set? –  josh Aug 30 '12 at 12:19
You quoted the book as saying "any set of $k$ independent columns," and it's evident in your example that $k=4$, so, no, it would appear that $(1,2,3)$ is not an information set. –  Gerry Myerson Aug 30 '12 at 13:10
Ok, that's what I figured, but I wanted to make sure it was correct. After some calculations, I was able to find 4 more information sets, namely: $(1, 5, 6, 7)$, $(2, 5, 6, 7)$, $(3, 5, 6, 7)$, $(4, 5, 6, 7)$. Thanks again for your help! –  josh Aug 30 '12 at 13:59
There is also a code in the text called the $[n, 1]$ repitition code, which has a generator matrix of $G = [1 | 1 \cdots 1]$. Would this code have $n$ information sets since there are $n$ sets of 1 independent columns? –  josh Aug 30 '12 at 14:20
Yes.${}{}{}{}{}$ –  Gerry Myerson Aug 30 '12 at 23:22

As I interpret your book's definition of an "information set", the "set of coordinates" that corresponds to a set of columns is literally the index of those columns in the matrix $G$. So if $$G=\left[\begin{array}{cccc|ccc} 1 & 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 1 \end{array}\right],$$ the "set of coordinates" corresponding to "the first, second, fourth, and seventh columns" is literally just (1,2,4,7). Since these columns are not linearly independent, this would be an example of a set of four coordinates which do not form an information set.

That $G$ has four independent columns is what allows it to uniquely encode a message of length four. If you take any four-digit message $m$ and multiply $mG$ then the resulting 7-digit codeword can be translated uniquely back to the original message; if $G$ had fewer than $4$ independent columns, this multiplication would yield the same result for more than one 4-digit message, and in a sense you would lose information. You could never be sure you decoded certain messages correctly.

Another way to think of the situation is that because $G$ has four independent columns, it has rank 4 and thus when you put it in row-reduced echelon form, it will be a standard generator matrix (the $G$ in this example already is a standard generator matrix). If it wasn't, though, and yet it still had four independent columns, you could convert it easily. Now, if you look at what happens when you multiply $mG$, the result is the message $m$ itself with three additional digits tacked onto the end. If the columns of the identity matrix were at other coordinates, the codeword would have the message $m$ rearranged as those columns are rearranged, with additional digits inserted where the other columns are.

I hope this rambling was useful rather than even-more confusing. This document has a pretty good explanation of information sets as well (see p. 39). (I'm not sure who to credit, but the document originally came from Jonathan Hall's MSU webpage)

-
Thank you Kirk! From what you said, I understand that $(1,2,4,7)$ is a set of 4 coordinates that does not form an information set. Would $(1, 2, ,3, 4)$ be an information set since these columns are Linearly Independent? To find another one, would I have to find another set of 4 columns that are Linearly Independent? –  josh Aug 30 '12 at 12:04
Yup, that's exactly right. The list of indices of the columns is the same as the "corresponding coordinates" of the columns, and ANY $k$ linearly independent ones are what make up an information set, so long as there are enough of them. It doesn't matter which set of them you find :) –  Kirk Boyer Aug 30 '12 at 15:29
Thank you Kirk! I have another observation for you. In the commments above, I mentioned a generating code of the form $G = [1 | 1 , \cdots , 1]$ for the $[n,1]$ binary repetition code of length $n$. Would this code have $n$ information sets since there are $n$ columns of legnth 1 that are independent? –  josh Aug 30 '12 at 15:56

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# How do I install and configure OBSIDIAN with the relevant plug-ins?

The Post Created(Updated) On 05/6/2022，Please note the timeliness of the article!

I’ve tried logseq before, but it’s hard to sync across devices, and then I was planted on Obsidian, and I feel it works much better than logseq these days. I’ve been thinking about how to reasonably plan the migration of tag and wiznote notes, though I don’t think it can completely replace wiznote. this is still more suitable for plain text records, and less friendly to files and other synchronization.

# Sync

## Plugin sync: Self-hosted LiveSync

Here I choose the better cross-device synchronization Self-hosted LiveSync

### Server setup couchdb

• Install the base environment docker

• Generate configuration file local.ini

vim local.ini
### The contents are as follows

[couchdb]
single_node=true

[chttpd]
require_valid_user = true

[chttpd_auth]
require_valid_user = true
authentication_redirect = /_utils/session.html

[httpd]
WWW-Authenticate = Basic realm="couchdb"
enable_cors = true

[cors]
origins = app://obsidian.md,capacitor://localhost,http://localhost
credentials = true
headers = accept, authorization, content-type, origin, referer
methods = GET, PUT, POST, HEAD, DELETE
max_age = 3600

• Start
docker run -d --name obsidian --restart always -e COUCHDB_USER=admin -e COUCHDB_PASSWORD=passwd -v /home/obsidian/local.ini:/opt/couchdb/etc/ local.ini -p 5984:5984 couchdb

• Connection configuration

Remember to click Test to test after the configuration is done, the pit I stepped in here is that I didn’t fill in the DataBase name, which led to an error all the time. Each device keeps the information on the line.

I’ve stepped in a hole here because I didn’t fill in the DataBase name.

• Synchronization settings reference, I did not choose LiveSync here, feel a little problem in the conflict

# Other plug-ins recommended

## MindMap

• Brain map generation, the only thing that is a bit of a gripe here is the need to set shortcuts to use, did not find other methods. At the same time the text file format requirements are very high, a slight error will not be generated.

• The software actually has a sidebar by default, and I personally feel that his preview is still pretty cool.
    toc

## Calendar

• A calendar table, it depends on personal preference. I have a daily diary here to get a TODO, not finished in the calendar table can be seen (the hollow point below), although it is not too big.

https://blog.emperinter.info/2022/05/06/how-do-i-install-and-configure-obsidian-with-the-relevant-plug-ins


text:
# Shadow Extra Dimension & Fuzzy Branes via Exorcized Infinite Derivative Field Theory

Authors
Publication Date
Jan 18, 2022
Source
HAL
Keywords
Language
English
Particle physics models with extra dimensions of space (EDS's) and branes are very interesting extensions beyond the standard model (BSM), allowing to shed new light on electroweak and flavor naturalness. Usually, such models are formulated in the framework of \emph{local} effective field theories (EFT's). The scope of this article is to propose new model building issues in BSM constructions with EDS and branes, arising in the framework of \emph{exorcized} (ghost-free) \emph{infinite derivative field theories} (IDFT's), which are intrinsically \emph{nonlocal} above some ultraviolet (UV) scale $\Lambda_{NL}$. First, with a warped EDS, the warp transmutation of the mass term of a brane-localized scalar field is revisited, where it is shown that $\Lambda_{NL}$ is also redshifted. This may provide a new way to solve the little hierarchy problem related to the Higgs boson mass. Moreover, if the (redshifted) $\Lambda_{NL}$ is around the mass scale of the first Kaluza-Klein (KK) excitations of the bulk fields, it is argued that it would be much more difficult to probe the KK tower in an experiment, which is reminiscent to the UV opaqueness of IDFT's: such EDS is then dubbed \emph{shadow}. After that, it is shown that a 4D field localized on a $\delta$-like 3-brane is still delocalized in the bulk on a distance $\mathcal{O}(1/\Lambda_{NL})$ of the brane position, such as 2 fields localized on 2 different $\delta$-like branes are allowed to interact with suppressed couplings, which is impossible in a local EFT. By using this new possibility of \emph{fuzzy} branes, a new realization of the split fermion idea is presented, allowing to build new BSM models of flavor.


text:
# How to clip cut-off text in a textbox?

I'm writing a textbox class for my XNA game and I'm using SpriteFont to draw the text. It's only a single line textbox so when the text width exceeds the size of the rectangle box, it currently just keeps going.

In Windows textboxes extra text is cut off so that you may only see half a letter. I'd like to emulate this with my custom control. However, I see no overload with SpriteBatch.DrawString that would allow for anything that could cut off text that didn't fit within certain bounds.

Does anyone know of a method that would allow for this? I'm still quite new to the XNA API so I'm not sure what out there exists for this sort of thing.. Thanks

The way I handled this in my simple textbox UI element was to use a scissor rectangle (as Nicolas Bolas said while I was writing this :P).

Here's the basic idea:

1. First off, create a RasterizerState field in whatever class does the drawing of the text like so:

RasterizerState _rasterizerState = new RasterizerState() { ScissorTestEnable = true };

You'll pass this to the spritebatch to tell it to use the GraphicsDevice.ScissorRectangle.

2. Then, your Draw method would go something like this:

public void Draw(GameTime gameTime) {
spriteBatch.Begin();
//Draw other stuff
spriteBatch.End();

//Set up the spritebatch to draw using scissoring (for text cropping)
spriteBatch.Begin(SpriteSortMode.Immediate, BlendState.AlphaBlend,
null, null, _rasterizerState);

//Optional: Draw the border using a 1x1 white square texture that is
//          stretched to fill a slightly larger rectangle behind the
//          background (below).
spriteBatch.Draw(_boxTexture, _borderRectangle, _borderColor);

//Optional: Draw the background
spriteBatch.Draw(_boxTexture, _textboxRectangle, _backColor);

//Copy the current scissor rect so we can restore it after
Rectangle currentRect = spriteBatch.GraphicsDevice.ScissorRectangle;

//Set the current scissor rectangle
spriteBatch.GraphicsDevice.ScissorRectangle = _textboxRectangle;

//Draw the text at the top left of the scissor rectangle
spriteBatch.DrawString(_font, _text, Vector2.Zero, _fontColor);

//Reset scissor rectangle to the saved value
spriteBatch.GraphicsDevice.ScissorRectangle = currentRect;

//Draw more textboxes or whatever else using the scissor rectangles here

//End the spritebatch
spriteBatch.End();
}

You can probably get away with not resetting the scissor rectangle for this basic situation, but you need to reset it if you want to draw other things (like those backgrounds). This example also assumed a lot of variables which you can infer (I hope :-) ) from their names.

A few other notes on the variables:

1. _textboxRectangle is the clipping rectangle to use. I pulled this from my textbox UI class which is where that and basically all other variables comes from.
2. _borderRectangle is just a rectangle that is a few pixels larger than _textboxRectangle so that when the background is drawn over top of it, it will appear as the border for the box. Pretty simple.

Hope this helps!

If you want to clip things to a certain region, you use the scissor box. It's a property of the GraphicsDevice: GraphicsDevice.ScissorTestEnable and either RenderState.ScissorRectangle pre-XNA 4.0 or RasterizerState.ScissorTestEnable in XNA 4.0.

You don't need to measure text for it; just set the scissor box to the area you want to clip to. You can draw all the text you want after that. Indeed, scissoring is useful in all kinds of places for GUIs.

Just don't forget to turn off scissoring when you're done.

• This actually looks like a great solution, I didn't know about this – John McDonald Feb 29 '12 at 4:03
• This looks promising! However, I'm not sure exactly where ScissorTestEnable is.. I'm using XNA 4.0. Do I need to create a RenderState? – John Price Feb 29 '12 at 4:04
• @JohnPrice: Sorry, I had some of the names and links wrong. They're corrected now. – Nicol Bolas Feb 29 '12 at 4:17
• Thanks, I got it working now. I'm a bit unsure on how to turn off scissoring though. Whenever I call rs.ScissorTestEnable = false; after my drawing I get an exception: Cannot change read-only RasterizerState State objects become read-only the first time they are bound to a GraphicsDevice. – John Price Feb 29 '12 at 4:29
• Then you'll need to keep two of them around. One with scissor test enable and one with it disabled. Switch the state bindings when you need to change them. – Nicol Bolas Feb 29 '12 at 4:30

What you need to do is use SpriteFont.MeasureString()

Loop through your string and check MeasureString(substring) to see when it exceeds your maximum width. Then use that substring to render.

Edit: Sorry didn't realize you wanted that precision.

What you want to use is a ScissorRectangle.

• Set GraphicsDevice.ScissorRectangle to the rect of your textbox.
• Set ScissorTestEnable to true in the RasterizerState
• Pass that RasterizerState to your SpriteBatch.Begin()
• Yes that is what I am currently doing but the problem is it doesn't cut off text like the regular Windows textbox does. It gives no option towards rendering half a letter, for example, if the textbox size allows for it. – John Price Feb 29 '12 at 3:37

You need to use multiple render targets. You need to create an off-screen texture where you will draw the text-box area, then draw that to the main render target. Here's a post on the MSDN forum about this: http://social.msdn.microsoft.com/forums/en-US/xnaframework/thread/71263016-b26a-44bd-80f3-8cd620b119ff


text:
MathSciNet bibliographic data MR188093 (32 #5534) 05.25 Yang, C. H. Some designs for maximal $(+1,\,-1)$$(+1,\,-1)$-determinant of order $n\equiv 2\,({\rm mod}\,4)$$n\equiv 2\,({\rm mod}\,4)$. Math. Comp. 20 1966 147–148. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.


text:
# $sin (n+1) A sin (n-1) A+cos (n+1) A cos (n-1) A=cos 2 A$

###### Question:

$sin (n+1) A sin (n-1) A+cos (n+1) A cos (n-1) A=cos 2 A$

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