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Pages
- Title
- Aerial view of the Illinois Institute of Technology campus, Chicago, Illinois, 1955
- Date
- 1955
- Description
-
Aerial photograph of the northwest section of the Illinois Institute of Technology campus, looking northeast. Photographer unknown.
- Collection
- IIT Campus Aerial photographs, 1940-2002
- Title
- Aerial view of the Illinois Institute of Technology campus, Chicago, Illinois, 1957
- Date
- 1957
- Description
-
Aerial photograph of the south portion of the Illinois Institute of Technology campus, looking north. Photographer unknown.
- Collection
- IIT Campus Aerial photographs, 1940-2002
- Title
- Aerial view of the Illinois Institute of Technology campus, Chicago, Illinois, 1955
- Date
- 1955
- Description
-
Aerial photograph of the Illinois Institute of Technology campus, looking northwest. Photographer unknown.
- Collection
- IIT Campus Aerial photographs, 1940-2002
- Title
- View of the Illinois Institute of Technology campus, looking north, Chicago, Illinois, 1953
- Date
- 1953
- Description
-
Photograph of the Illinois Institute of Technology campus, looking north. Photographer unknown.
- Collection
- IIT Campus Aerial photographs, 1940-2002
- Title
- Aerial view of the Illinois Institute of Technology campus, Chicago, Illinois, 1953
- Date
- 1953
- Description
-
Aerial photograph of the Illinois Institute of Technology campus, looking northwest. Photographer unknown.
- Collection
- IIT Campus Aerial photographs, 1940-2002
- Title
- Aerial view of the Illinois Institute of Technology campus, Chicago, Illinois, 1953
- Date
- 1953
- Description
-
Aerial photograph of the Illinois Institute of Technology campus, looking southwest. Photographer unknown.
- Collection
- IIT Campus Aerial photographs, 1940-2002
- Title
- Mentions of Ethics Codes in Social Media: A Twitter Analysis
- Creator
- Laas, Kelly, Hildt, Elisabeth, Wu, Ying
- Date
- 2022, 2022-01-03
- Publisher
- Springer, Cham
- Collection
- Codes of Ethics and Ethical Guidelines: Emerging Technologies and Changing Fields
- Title
- An Introduction to the Societal Roles of Ethics Codes
- Creator
- Laas, Kelly, Davis, Michael, Hildt, Elisabeth
- Date
- 2022, 2022-01-03
- Publisher
- Springer, Cham
- Description
-
In this collected volume, we are interested in the roles of ethics codes and ethical guidelines in professions in which research and...
Show moreIn this collected volume, we are interested in the roles of ethics codes and ethical guidelines in professions in which research and innovation play an important role and where emerging technologies bring about considerable, sometimes fast-paced change.
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- Codes of Ethics and Ethical Guidelines: Emerging Technologies and Changing Fields
- Title
- Informed Consent in Digital Data Management
- Creator
- Hildt, Elisabeth, Laas, Kelly
- Date
- 2022, 2022-01-03
- Publisher
- Springer, Cham
- Description
-
This article discusses the role of informed consent, a well-known concept and standard established in the field of medicine, in ethics codes...
Show moreThis article discusses the role of informed consent, a well-known concept and standard established in the field of medicine, in ethics codes relating to digital data management. It analyzes the significance allotted to informed consent and informed consent-related principles in ethics codes, policies, and guidelines by presenting the results of a study focused on 31 ethics codes, policies, and guidelines held as part of the Ethics Codes Collection. The analysis reveals that up to now, there is a limited number of codes of ethics, policies, and guidelines on digital data management. Informed consent often is a central component in these codes and guidelines. While there undoubtedly are significant similarities between informed consent in medicine and digital data management, in ethics codes and guidelines, informed consent-related standards in some fields such as marketing are weaker and less strict. The article concludes that informed consent is an essential standard in digital data management that can help effectively shape future practices in the field. However, a more detailed reflection on the specific content and role of informed consent and informed consent-related standards in the various areas of digital data management is needed to avoid the weakening and dilution of standards in contexts where there are no clear legal regulations.
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- Codes of Ethics and Ethical Guidelines: Emerging Technologies and Changing Fields
- Title
- Letter from Frank T. Walsh to Mary Henry, May 27, 1966
- Creator
- Walsh, Frank T.
- Date
- 1966-05-27
- Description
-
Typescript letter with signature from Frank T. Walsh, Director of Corporate Industrial Design at the Ampex Corporation, to Mary Henry. The...
Show moreTypescript letter with signature from Frank T. Walsh, Director of Corporate Industrial Design at the Ampex Corporation, to Mary Henry. The letter was composed in response to the promotional material Henry provided Ampex in advance of her first solo exhibition, which opened in 1967 at the Ampex Corporation in Redwood City, California.
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- Mary Dill Henry Papers, 1913-2021
- Title
- Simulation and Experimental Testing of High-Gradient Dielectric Disk Accelerating Cavities
- Creator
- Weatherly, Sarah K.
- Date
- 2022
- Description
-
Structure-based wakefield acceleration can be accomplished using either Collinear Wakefield Acceleration (CWA) where the drive beam and the...
Show moreStructure-based wakefield acceleration can be accomplished using either Collinear Wakefield Acceleration (CWA) where the drive beam and the witness beam are located on the same beamline or Two Beam Acceleration (TBA) where the RF power generated by the drive beam is extracted and transferred to the witness beam line. A Dielectric Disk Accelerator (DDA) is an accelerating structure that is utilized by TBA that uses dielectric disks to improve the structure's shunt impedance and accelerate the witness beam. Dielectric based accelerators studied in this thesis are X-Band structures (have a working frequency between 8 and 12 GHz) that can use any pulse length but in this study utilize short (<20 ns) traveling wave pulses. Short pulse lengths are used to decrease breakdown probability and allow for a large gradient. DDAs have a higher group velocity and a larger shunt impedance compared to traditional metallic accelerating structures while maintaining a large accelerating gradient. DDAs are a strong candidate for use in the Argonne Wakefield Accelerator’s 500 MeV Demonstrator. Recent experimental results of a clamped single cell structure demonstrated a >100 MV/m accelerating gradient with no evidence of breakdown in the RF volume. Additional structures, including a brazed single cell model and a multicell structure, have been designed and are now being fabricated for high power testing.
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- Title
- A SCALABLE AND CUSTOMIZABLE SIMULATION PLATFORM FOR ACCURATE QUANTUM NETWORK DESIGN AND EVALUATION
- Creator
- Wu, Xiaoliang
- Date
- 2021
- Description
-
Recent advances in quantum information science enabled the development of quantum communication network prototypes and created an opportunity...
Show moreRecent advances in quantum information science enabled the development of quantum communication network prototypes and created an opportunity to study full-stack quantum network architectures. The scale and complexity of quantum networks require cost-efficient means for testing and evaluation. Simulators allow for testing hardware, protocols, and applications cost-effectively before constructing experimental networks. This work develops SeQUeNCe, a comprehensive, customizable quantum network simulator. We have explored SeQUeNCe for quantum communication network evaluation. We use SeQUeNCe to study the performance of the quantum network with different hardware and applications. Additionally, we extend SeQUeNCe to a parallel discrete-event simulator by using the message passing interface (MPI). We comprehensively analyze the benefit and overhead of parallelization. The parallelization technique significantly increases the scalability of SeQUeNCe. In the future, we would like to improve SeQUeNCe in three aspects. First, we plan to continue reducing overhead from parallelization and increasing the scalability of SeQUeNCe. Second, we plan to investigate means to model quantum memory, entanglement protocols, and control protocols to enrich simulation models in the SeQUeNCe library. Third, we plan to integrate hardware with SeQUeNCe to enable high-fidelity analysis.
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- Title
- Development of MIITRA T1w, DTI and FOD templates of the older adult brain in a common space
- Creator
- Wu, Yingjuan
- Date
- 2022
- Description
-
Human brain atlases play an important role in neuroimaging studies and are commonly used as references for spatial normalization, tissue...
Show moreHuman brain atlases play an important role in neuroimaging studies and are commonly used as references for spatial normalization, tissue segmentation, automated brain parcellation, seed selection for functional connectivity analyses and fiber-tracking, or standards for algorithm evaluation. A brain atlas typically consists of brain templates of different imaging modalities in a common space and semantic labels that delineate brain regions according to the characteristics of the underlying tissue.High-quality T1-weighted (T1w) and diffusion tensor imaging (DTI) brain templates that are representative of the individuals under study enhance the accuracy of template-based neuroimaging investigations, and when they are also located in a common space they facilitate optimal integration of information on brain morphometry and diffusion characteristics. However, such multimodal templates have not been constructed for the brain of older adults. This thesis introduced an iterative method for construction of multimodal T1w and DTI templates that aims at maximizing the quality of each template separately as well as the spatial matching between templates. The performance of the proposed method was evaluated across iterations and was compared to the performance of state-of-the-art multimodal template construction approaches based on multichannel registration. Using the proposed method, along with other recently developed techniques, high-quality T1w and DTI templates of the older adult brain were developed in a common space at 0.5mm resolution for the MIITRA atlas. In this thesis, the new templates were compared to other available templates in terms of the image quality, inter-subject and inter-modality spatial normalization accuracy achieved when used as a reference, and the representativeness of the older adult brain. Furthermore, as fiber orientation distribution (FOD) model is capable of resolving intravoxel heterogeneity, which overcomes the limitations of the DTI model especially in regions with complex neuronal microarchitecture, FOD template is in high demand to facilitate FOD-based, fixel-based analyses, white matter connectivity studies and white matter parcellations. In this thesis, several FOD template construction methods were compared and a FOD template was developed at 0.5mm resolution for the MIITRA atlas. Overall, the present work brought new insights into multimodal template construction, conducted a thorough, quantitative evaluation of available multimodal template construction methods, and generated much-needed high quality T1w, DTI and FOD templates of the older adult brain in a common space with 0.5mm resolution.
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- Title
- AN EXPLORATION INTO THE EFFECTS OF CHROMATIN STRUCTURAL PROTEINS ON THE DYNAMICS AND ENERGETIC LANDSCAPE OF NUCLEOSOME ARCHITECTURES
- Creator
- Woods, Dustin C
- Date
- 2022
- Description
-
Comprised of eight core histones wrapped around at least 147 base pairs of DNA, nucleosomes are the fundamental unit the chromatin fiber from...
Show moreComprised of eight core histones wrapped around at least 147 base pairs of DNA, nucleosomes are the fundamental unit the chromatin fiber from which long arrays are built to compact genetic information into the cell nucleus. Structural proteins, such as linker histones (LH) and centromere proteins (CENP), interact with the DNA to dictate the exact architecture of the fiber which can directly influence the regulation of epigentic processes. However, the mechanisms by which structural proteins affect these processes are poorly understood. In this thesis, I will explore the various way in which LHs and CENP-N affect nucleosome and, by extension, chromatin fiber dynamics. First, I present a series of simulations of nucleosomes bound to LHs, otherwise known as chromatosomes, with the globular domain of two LH variants, generic H1 (genGH1) and H1.0 (GH1.0), to determine how their differences influence chromatosome structures, energetics and dynamics. These simulations highlight the thermodynamic basis for different LH binding motifs, and details their physical and chemical effects on chromatosomes. Second, I examine how well the findings above translate from mono-nucleosomes to poly-nucleosome arrays. I present a series of molecular dynamics simulations of octa-nucleosome arrays, based on a cryo-EMstructure of the 30-nm chromatin fiber, with and without the globular domains of the H1 LH to determine how they influence fiber structures and dynamics. These simulations highlight the effects of LH binding on the internal dynamics and global structure of poly- nucleosome arrays, while providing physical insight into a mechanism of chromatin compaction. Third, I took a brief departure from LHs to study the effects that the centromere protein N (CENP-N) has on the poly-nucleosome systems. I present a series of molecular dynamics simulations of CENP-N and di-nucleosome complexes based on cryo- EM and crystal structures provided by Keda Zhou and Karolin Luger. Simulations were conducted with nucleosomes in complex with one, two, and no CENP-Ns. This work, in collaboration with the Karolin Luger Group (University of Colorado – Boulder) and the Aaron Straight Group (Stanford University), represents the first atomistic simulations of this novel complex, providing the foundation for a plethora of future research opportunities exploring centromeric chromatin the effect that its structure and dynamics have on epigenetics. Lastly, I return to the chromatosome to study how DNA sequence affects the free energy surface and detailed mechanism of LH transitions between binding modes. I used umbrella sampling simulations to produce PMFs of chromatosomes wrapped in three different DNA sequences: Widom 601, poly-AT, and poly-CG. This work, my final in the series, represents a culmination of my studies furthering the understanding of biophysical phenomena surrounding LHs and how they can be extrapolated towards epigentic mechanisms. I was able to report on the first PMFs illustrating a previously unknown transition and describe the transition mechanism as it depends on DNA sequence.
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- Title
- The Studio Practice for Sustainable (Craft) Production
- Creator
- Werdhaningsih, Hendriana
- Date
- 2022
- Description
-
Craft market demand globally is rising. On the other hand, the domination of economic goals in craft production is threading the social system...
Show moreCraft market demand globally is rising. On the other hand, the domination of economic goals in craft production is threading the social system and the environment. Craft production facts do not represent the sustainable development principles that should be a central concept for this age. Design as practice and method had not yet correctly facilitated craft production to embrace the harmony of the social, environmental, and economic systems. Believing that studio is a core design practice, this research investigated studio practice through interviews, field research, and action research conducted in Indonesia and the US. It developed a model called Studio Practice for Sustainable (Craft) Production, the SP2 Model. The Model helps designers, the crafts community, and stakeholders ensure their role in the studio practice and determine their goals for sustainable development. The SP2 Model offers alternative practical solutions in craft production, contributes to polycentric discourse, and designs interventions in sustainable development models.
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- Title
- ESTIMATING PM2.5 INFILTRATION FACTORS FROM REAL-TIME OPTICAL PARTICLE COUNTERS DEPLOYED IN CHICAGO HOMES BEFORE AND AFTER MECHANICAL VENTILATION RETROFITS
- Creator
- Wang, Mingyu
- Date
- 2021
- Description
-
PM2.5 are fine inhalable particles that are 2.5 micrometers or smaller in size. Indoor PM2.5 consists of outdoor PM2.5 (ambient PM2.5) that is...
Show morePM2.5 are fine inhalable particles that are 2.5 micrometers or smaller in size. Indoor PM2.5 consists of outdoor PM2.5 (ambient PM2.5) that is infiltrated into the indoor environment and indoor generated PM2.5 (non-ambient PM2.5). As people spend nearly 90% of their lifetimes indoors, with most of that time in their homes, PM2.5 exposure in homes results in severe health effects such as asthma. One strategy increasingly being used to dilute air pollutants generated indoors and improve indoor air quality (IAQ) in homes is the introduction of mechanical ventilation systems. However, mechanical ventilation systems also have the potential to introduce more ambient PM2.5 than relying on infiltration alone, although limited data exist to demonstrate the magnitude of impacts in occupied homes. The objective of this paper is to estimate the infiltration factor (Finf) of PM2.5 before and after installing mechanical ventilation systems in a subset of occupied homes. The data source utilized comes from the Breathe Easy Project, a more than 2-year-long study conducted in 40 existing homes in Chicago, IL aiming to explore the effects of three different types of mechanical ventilation system retrofits on IAQ and asthma. An automated algorithm was developed to remove indoor PM2.5 peaks in time-series data collected from optical particle counters deployed inside and outside of each home. The Finf was estimated using the resulting indoor/outdoor ratio with indoor peaks removed. Before mechanical ventilation retrofits, the weekly median Finf was 0.29 (summer median = 0.41, fall median = 0.26, winter median = 0.29, spring median = 0.30); after mechanical ventilation retrofits, the median Finf was 0.34 (winter median= 0.28, spring median = 0.45, summer median = 0.54, fall median = 0.20). Differences in Finf between pre- and post-intervention periods were not statistically significant (p = 0.23 from Wilcoxon signed rank tests). The median PM2.5 infiltration factor increased ~22% (from 0.27 to 0.33) with the installation of balanced ventilation systems with energy recovery ventilators (ERV), although differences were not statistically significant (Wilcoxon signed rank p = 0.35). The median PM2.5 infiltration factor decreased ~4% (from 0.28 to 0.27) after installing intermittent CFIS systems, which intermittently supply ventilation air through the existing central air handling units and associated filters (which were upgraded to a minimum of MERV 10 in all CFIS homes), although differences were not statistically significant (Wilcoxon signed rank p = 0.24). The median PM2.5 infiltration factor increased ~26% (from 0.35 to 0.44) with the installation of continuous exhaust-only systems, and differences were significant (Wilcoxon signed rank p = 0.04). These results suggest that the filtration mechanisms used on the CFIS and balanced systems were adequate for maintaining similar distributions of Finf values pre- and post-interventions whereas the increased delivery of outdoor air via the building envelope by exhaust-only systems significantly increased Finf following retrofits.
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- Title
- Architecture as a Communicator of Values and Identity Spaces for Public Safety and Community Benefits
- Creator
- Waidele Arteaga, Nicolas
- Date
- 2022
- Description
-
Urban segregation, violence, and crimes are linked to drug trafficking. El Castillo Social Factory is an urban strategy that aims to recover...
Show moreUrban segregation, violence, and crimes are linked to drug trafficking. El Castillo Social Factory is an urban strategy that aims to recover the El Castillo neighborhood and prevent drug trafficking from advancing, understanding that police action is necessary but insufficient.This neighborhood is located on the southern periphery of Santiago in a commune called La Pintana and aspires to make its neighborhoods “more livable, healthy, and economically viable.” This proposal explores how investing in civic commons can make these goals a reality. First, it is essential to increase the presence of the State, strengthening existing services and adding new ones, with a focus on the care of children and young people. The second is to recover vacant lots and public spaces in poor condition or deteriorated through an “urban acupuncture” strategy based on the construction of many small or medium-sized projects. Art and sports are fundamental, allowing us to protect children and young people and offer them horizons of recreation and hope. The public buildings, institutions, land, water bodies, and infrastructure inherited from earlier generations are ready for us to see anew—as a robust network of civic assets ready to be activated for the current needs, desires, and dreams of all the people who share and shape them. El Castillo Social Factory offers a fresh look at our community anchors and the vibrant hubs our public spaces can become when we invest in collective urban life. Its vision focuses on positive transformation at the architectural scale—where personal experience and aspirations meet broad, long-range planning efforts—to spark the imagination and spur us to work together toward realizing the abundant potential of what we hold in common.
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- Title
- A New Control and Decision Support Framework To Avoid Fast-Evolving System Collapse and Cascading Failure
- Creator
- Guha, Bikiran
- Date
- 2022
- Description
-
The modern power system is a vast and incredibly complex network with a very large number of equipment operating round the clock to reliably...
Show moreThe modern power system is a vast and incredibly complex network with a very large number of equipment operating round the clock to reliably transport electricity from generators to consumers. However, factors such as aging and faulty equipment, extreme and unpredictable weather, cyber attacks and increasing amounts of unpredictable renewable generation have made it increasingly vulnerable to cascading failure and wide-area collapse. Therefore, a lot of work has been done over the years on cascading failure vulnerability analysis and mitigation. However, to the best of our knowledge, the existing literature on this topic focus on preventive analysis and mitigation, mostly from a planning perspective. There is a lack of decision support schemes which can take real-time preventive action when the system becomes vulnerable to cascading failure, while taking into account the various dynamics and uncertainties involved in these types of failures. The only defense under these situations are pre-designed emergency control schemes. However, they are only effective against known vulnerabilities and can make matters worse if not accurately designed and calibrated.This research work has proposed a novel wide-area monitoring protection and control (N-WAMPAC-20) framework designed to make decisions in real-time to assess the vulnerabilities of the system (when a disturbance happens) and to implement mitigation actions, if necessary. The main contributions of this dissertation focus on the disturbance monitoring, real-time control and decision making aspects of this framework. The proposed framework has been divided into two major parts: an offline part and an online part. The offline part continuously runs extreme contingency analysis in the background (using combined dynamics and protection simulators) to generate elements which can assess system vulnerabilities and suggest suitable mitigation actions, if necessary. In this regard, a novel load shedding adjustment scheme is also proposed, which has been shown to be effective against a variety of fast-evolving cascading failure scenarios. The online part consists of real-time disturbance monitoring and decision-making components. The disturbance monitoring component focuses on real-time fault detection and location. If a fault has been identified and located, the real-time decision making component determines the vulnerability of the system, by consulting with the elements designed offline. If vulnerabilities are identified, targeted mitigation actions are implemented. The design and applicability of a prototype of N-WAMPAC-20 has been presented using a case of voltage collapse and a case of wide-area loss of synchronization on a synthetic model of the Texas grid.
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- Title
- Distinctive Categorization Deficits in Repeated Sorting of Common Household Objects in Hoarding Disorder
- Creator
- Hamilton, Catharine Elizabeth
- Date
- 2022
- Description
-
The present study examines sorting techniques and deficits among individuals with hoarding disorder (n = 34) compared to age- and gender...
Show moreThe present study examines sorting techniques and deficits among individuals with hoarding disorder (n = 34) compared to age- and gender-matched adults (n = 35) in the general population. Performance was compared on the Booklet Category Test (BCT), selected other neuropsychological measures, and an ecologically valid sorting task designed for the study to model the Delis-Kaplan Executive Function System (D-KEFS) Sorting subtest but with common household objects as stimuli. Contrary to predictions, individuals with hoarding disorder did not perform significantly worse than controls on the BCT or the sorting task designed for the present study. Also contrary to predictions, the hoarding group performed significantly better when initiating their own sorts of the objects than when tasked with naming categories grouped by the researcher. These findings are discussed as well as exploratory analyses suggesting participants with hoarding put forth more mental effort sorting the household objects (shoes and mail). They provided significantly more individual responses on the task with significantly more description errors. IQ and performance on other selected neuropsychological measures were not significantly different between groups. These findings provide preliminary evidence there may be specific types of real-life sorting difficulties associated with hoarding disorder that are subtle and beyond what existing neuropsychological tests can measure. Given that current CBT treatments for hoarding presuppose a certain level of competency in sorting (e.g., recognizing and naming different categories of household items to complete a personal organizing plan), it is important to clarify potential sorting and categorization deficits in this group as one possible avenue to help improve treatment response among individuals struggling with hoarding disorder.
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- Title
- Machine Learning On Graphs
- Creator
- He, Jia
- Date
- 2022
- Description
-
Deep learning has revolutionized many machine learning tasks in recent years.Successful applications range from computer vision, natural...
Show moreDeep learning has revolutionized many machine learning tasks in recent years.Successful applications range from computer vision, natural language processing to speech recognition, etc. The success is partially due to the availability of large amounts of data and fast growing computing resources (i.e., GPU and TPU), and partially due to the recent advances in deep learning technology. Neural networks, in particular, have been successfully used to process regular data such as images and videos. However, for many applications with graph-structured data, due to the irregular structure of graphs, many powerful operations in deep learning can not be readily applied. In recent years, there is a growing interest in extending deep learning to graphs. We first propose graph convolutional networks (GCNs) for the task of classification or regression on time-varying graph signals, where the signal at each vertex is given as a time series. An important element of the GCN design is filter design. We consider filtering signals in either the vertex (spatial) domain, or the frequency (spectral) domain. Two basic architectures are proposed. In the spatial GCN architecture, the GCN uses a graph shift operator as the basic building block to incorporate the underlying graph structure into the convolution layer. The spatial filter directly utilizes the graph connectivity information. It defines the filter to be a polynomial in the graph shift operator to obtain the convolved features that aggregate neighborhood information of each node. In the spectral GCN architecture, a frequency filter is used instead. A graph Fourier transform operator or a graph wavelet transform operator first transforms the raw graph signal to the spectral domain, then the spectral GCN uses the coe"cients from the graph Fourier transform or graph wavelet transform to compute the convolved features. The spectral filter is defined using the graph’s spectral parameters. There are additional challenges to process time-varying graph signals as the signal value at each vertex changes over time. The GCNs are designed to recognize di↵erent spatiotemporal patterns from high-dimensional data defined on a graph. The proposed models have been tested on simulation data and real data for graph signal classification and regression. For the classification problem, we consider the power line outage identification problem using simulation data. The experiment results show that the proposed models can successfully classify abnormal signal patterns and identify the outage location. For the regression problem, we use the New York city bike-sharing demand dataset to predict the station-level hourly demand. The prediction accuracy is superior to other models. We next study graph neural network (GNN) models, which have been widely used for learning graph-structured data. Due to the permutation-invariant requirement of graph learning tasks, a basic element in graph neural networks is the invariant and equivariant linear layers. Previous work by Maron et al. (2019) provided a maximal collection of invariant and equivariant linear layers and a simple deep neural network model, called k-IGN, for graph data defined on k-tuples of nodes. It is shown that the expressive power of k-IGN is equivalent to k-Weisfeiler-Lehman (WL) algorithm in graph isomorphism tests. However, the dimension of the invariant layer and equivariant layer is the k-th and 2k-th bell numbers, respectively. Such high complexity makes it computationally infeasible for k-IGNs with k > 3. We show that a much smaller dimension for the linear layers is su"cient to achieve the same expressive power. We provide two sets of orthogonal bases for the linear layers, each with only 3(2k & 1) & k basis elements. Based on these linear layers, we develop neural network models GNN-a and GNN-b, and show that for the graph data defined on k-tuples of data, GNN-a and GNN-b achieve the expressive power of the k-WL algorithm and the (k + 1)-WL algorithm in graph isomorphism tests, respectively. In molecular prediction tasks on benchmark datasets, we demonstrate that low-order neural network models consisting of the proposed linear layers achieve better performance than other neural network models. In particular, order-2 GNN-b and order-3 GNN-a both have 3-WL expressive power, but use a much smaller basis and hence much less computation time than known neural network models. Finally, we study generative neural network models for graphs. Generative models are often used in semi-supervised learning or unsupervised learning. We address two types of generative tasks. In the first task, we try to generate a component of a large graph, such as predicting if a link exists between a pair of selected nodes, or predicting the label of a selected node/edge. The encoder embeds the input graph to a latent vector space via vertex embedding, and the decoder uses the vertex embedding to compute the probability of a link or node label. In the second task, we try to generate an entire graph. The encoder embeds each input graph to a point in the latent space. This is called graph embedding. The generative model then generates a graph from a sampled point in the latent space. Di↵erent from the previous work, we use the proposed equivariant and invariant layers in the inference model for all tasks. The inference model is used to learn vertex/graph embeddings and the generative model is used to learn the generative distributions. Experiments on benchmark datasets have been performed for a range of tasks, including link prediction, node classification, and molecule generation. Experiment results show that the high expressive power of the inference model directly improves latent space embedding, and hence the generated samples.
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