Let θ₁, θ₂…θN ∈ [0, 2π) the preferred orientations of a network of N neurons with circular Normal tuning curves and Poisson firing rates. Model input is a target orientation (θt, ct) superimposed on a mask orientation (θm, cm), where a pair (θ, c) represents an orientation θ at contrast c. Tuning response of ith neuron to a set of orientations (θj, cj): $$\lambda_i := \sum_j g \cdot c_j e^{2\kappa \cos(\theta_j)},$$ where g is the gain of the network. The Poisson response is a random sample from the Poisson distribution with λ as the mean firing rate: $$r_i \sim (\lambda_i)$$ The Poisson response acts as the input drive to divisive normalization, so we can normalized response: $$R_i^{(t)} = {\sigma^2 + \rfloor^2}}$$ Then the weights are updated based on the Hebbian learning rule: $$^{(t)} = ^{(t-1)} + \alpha (^T - )$$ where α is the Hebbian learning rate, C is the Hebbian learning homeostatis target. This feedforward network runs until tsat such that network responses are stable. We initialize the network with initial weights W(0) and a homeostatis target C. The initial weights W(0) is a uniform matrix scaled by the network’s mean tuning response to gratings that are at full contrast and each neuron’s preferred orientation. That is equivalent to the tuning response of a single neuron to a full-contrast grating at this neuron’s preferred orientation. Thus: $$^{(0)} := _{NN}}{\lambda_i(\theta = \theta_i, c=1)}$$ The homeostatis target is set to the network’s mean response product over some period t₀ to tmax to a set of orientations θ₁, θ₂…θk equally spaced within [0, 2π), normalized by the size of the network: $$ := }(\theta_1, \theta_2 \ldots \theta_k) }(\theta_1, \theta_2 \ldots \theta_k)^T / N,$$ $$} := (\theta_j) = ^{t_{max}} R_i(\theta_j)}{t_{max}},$$ where Ri(θj) is the normalized (but not Hebbian weight learned) response of ith neuron to the orientation θj from the set of equally spaced orientations. Furthermore, since the input to the time average of the normalized responses is Poisson process, the time average asymptotes to the Poisson rate λ. Thus, we could replace the time average by the asymptote for better precision and computational efficiency. That is: $$R_{ij} := \to +\infty}} = \to +\infty}(\theta_j) = \to +\infty} ^{t_{max}} R_i(\theta_j)}{t_{max}} = \to +\infty} ^{t_{max}} {\sigma^2 + )} \rfloor^2}}}{t_{max}} = {\sigma^2 + )} \rfloor^2}}$$ Here is a simple model readout that takes the normalized response of the neuron whose preferred orientation θi (pre-learning) matches target orientation θt: $$d := R_i, \theta_i = \theta_t$$ Alternatively, we could normalize that w.r.t. the total network response: $$d := {\sum }, \theta_i = \theta_t$$ Or we can weight the network response with their pre-learning sensitivity to the target: $$d := w , $$ $$ w_i := \lambda_i(\theta_t, c = 1)$$

NYU CENTER FOR URBAN SCIENCE AND PROGRESS CAPSTONE PROJECT

Abstract / Executive SummaryUrban bicycle usage has gained in importance across many cities with progressive transportation policies. According to \cite{hu_more_2017}, as of this paper's publication,  "there are more than 450,000 daily bike trips in New York City, up from 170,000 in 2005, an increase that has outpaced population and employment growth".  About one in five bike trips is by a commuter. Biking serves as an important transportation option to many around the world and we argue that the need for effective bicycle lane maintenance should be a top concern for municipalities.Conventionally, street maintenance is an expensive, often inaccurate, and time intensive process that either uses subjective data prone to error or uses very precise data that is very expensive to collect citywide. There exists a clear need for cities to adopt a cost-effective and data intensive maintenance practice that can scale to the entire city and be performed frequently. These needs have been explored through the Street Quality Identification also known as the SQUID project \cite{adibhatla_digitizing_2016} to develop standardized methods for digital street inspection. This work extends the SQUID project and repurposes it for citywide bike lane measurements.In this paper, we describe the development of a data and analytics framework to measure bicycle lane quality using street imagery and accelerometer data obtained from an open source smartphone application, OpenStreetCam (OSC)  \cite{telenav_openstreetmap_nodate} . This framework can be used in crowdsourced or situated settings with the overall purpose being the standardized measurement of citywide bike lane quality.IntroductionIn recent years, bike based mobility in cities around the world has been growing rapidly. Compared to cars, bikes are cheaper, safer, more sustainable, allow for higher traffic flows, and require far less space for parking. Many city governments have invested in a permanent bike-sharing infrastructure and programs in an effort to improve transit conditions within the urban core.

ABSTRACT The District Attorney’s office of Santa Clara County, California has observed long durations for their prosecution processes. It is interested in assessing the drivers of prosecutorial delays and determining whether there is evidence of disparate treatment of accused individuals in pre-trial detention and criminal charging practices. A recent report from the county's civil grand jury found that only 47% of cases from 2013 were resolved in less than year, far less than the statwide average of 88%. We describe a visualization tool and analytical models to identify factors affecting delays in the prosecutorial process and any characteristics that are associated with disparate treatment of defendants. Using prosecutorial data from January through June of 2014, we find that the time to close the initial phase of prosecution (the entering of a plea), the initial plea entered, the type of court in which a defendant is tried and the main charged offense are important predictors of whether a case will extend beyond one year. Durations for prosecution are found not significantly different for different racial and ethnic population, and do not appear as important features in our modeling to predict case durations longer than one year. Further, we find that, in this data, 81% of felony cases were resolved in less than one year, far greater than the value reported by the civil grand jury.

EXECUTIVE SUMMARY

ContextMotivationThe motivation of this report is to explore the team contribution to the Dr. Bianco's "Hypertemporal Imaging of NYC Grid Dynamics" proof of concept project, an alternative technology to monitor grid dynamics and energy consumption patterns, in contrast to a traditional approach which is based on in-situ monitoring of energy grids and buildings. This approach can, by analysing the lights of a city landscape, infer similar results obtained by sensors through images taken by a single camera.On the traditional approach, in order to provide reliable and affordable energy distribution, cities have to monitor the health of electric grid and energy consumption patterns. Those measurements are fundamental to provide good service during peak hours, to guarantee that the electrical grid is working in its healthy condition and to support future plans for increasing demand as cities grow and citizens use more electrical equipment.Measurements about electric grid are collected by a Phase Monitor Unit (PMU), a synchrophasor measurement device that captures information about the voltage and phase angle of the system which allows identifying possible shifts on phase and measure grid stability. Also, to access individualized energy consumption information, it is necessary the deployment of smart meters, devices that have to be installed on buildings to report real-time energy consumption information.The deployment of sensors and equipments is expensive and not possible to all cities worldwide. The PMU unitary overall cost is at a range from $40,000.00 - $180,000.00 (U.S. Department of Energy, 2009) and it is estimated that to monitor building energy consumption NYC will spend $1.5B for 1 million buildings during the next five years, values that can be impeditive for many cities in the world.The Hyperthemporal Imaging technology comes as an indirect, real-time, and affordable way to get electric grid health information and a non-intrusive and indirect way to achieve energy disaggregation and observe energy consumption patterns. In this context, this study will explore the expected improvement by using a new camera to capture images of city landscape and a study about cost and area covered by a single camera, estimating the ideal number of cameras needed to cover NYC. Previous Research\citet{bianco_hypertemporal_2016} showed a proof of concept that hypertemporal visible imaging can be used to monitor grid dynamics and identify phase changes in individual light sources from the city landscape. This technique relies on the fact that the United States grid provides electricity as an alternate current (AC) with a frequency of 60 Hz (some countries use 50 Hz standard instead). The alternate current at 60 Hz induces a flickering twice as fast, at 120 Hz, in most of the lights in the city, including incandescent, halogen, and some fluorescent lights. LED and  more modern fluorescent lights have a different behavior.Analyzing a signal with a frequency of 120 Hz would require at the very least a four times faster sampling rate, at 480 Hz, ideally eight times faster, which would require specialized and more expensive equipment. Since one of the main goals of developing this alternative technology is to provide an affordable way for cities in developing nations to monitor the dynamics of their electric grid, the equipment costs had to be kept low and, therefore, the solution was to use a liquid crystal shutter mounted at the lens aperture of the camera. The shutter is then set to oscillate between the states 'open' and 'closed' at a frequency (119.75 Hz) close to the one corresponding to the flickering of the lights (120 Hz), which, in turn, down-converts the flicker to 0.25 Hz, the beat frequency given by Equation 1.

Ozgur L. Akkas

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  PUI2015 Extra Credit Project2016 U.S. Election Exit Poll Results Modeling  <Xianbo Gao, gaogxb, xg656>Abstract: Using PCA and Lasso regression to build a regression model for 2016 U.S. Election Exit Poll Results to find which factors and to what extent contribute to the result.Introduction: In this project, I aim to discover the main factors influence the percentage of people voting for Trump and Clinton in state level in the 2016 U.S. Election Exit Poll Result, how much each factor contributes to the percentage and build a model to fit the percentage of the voting result in state level. Then I can explain the reason which Trump won the election by the election exit poll result.Data: County level election results and information of people provided by United States Department of AgricultureEconomic Research ServiceElection results and information of people in excel format provided by uselectionatlas.orgThe data only have population in 2014. Besides, there are only information of 37 states, not all the states.There are 51 columns which are factors or variables. The names of these columns are codes which should be replaced by description, so I rename these columns. I try to convert all the data into percentage format. 30 factors are or can be converted into percentage (such as percentage of age under 18). 21 factors which are not able to be converted into percentage level are normalized (such as mean time to work). After that, the data are summed into state level by weighted average which is based on population in each County. The format of data is shown below.

Time Series Analysis of Beijing Air Pollution<Chunqing Xu, cx495, cx495>

Abstract: The project is focused on exploring fatalities occurred in New York City (NYC) among 3 major groups involved in traffic accidents between 2009 and 2016: pedestrians, bicyclists, and motor vehicle occupants (MVO). The project’s results show that overall trend in fatalities is declining, while trend analysis for each group shows that fatalities among bicyclists is increasing. Also, further analysis revealed that the highest number of fatalities that occurred: for pedestrians in lower east side downtown Manhattan, zip code 10002; for bicyclists in east Harlem uptown Manhattan zip code 10029; for MVO in East Flatbush, Brooklyn, zip code 11203. Original GitHub link for code:https://github.com/ak6129/PUI2016_ak6129/blob/master/ExtraCreditProject_ak6129/ExtraCreditsProject_ak6129.ipynb

Student Name: Xinge Zhong(viola), Github account: xingezhong, NetID: xz1809

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Note: Throughout this paper, ‘taxis’ include green and yellow taxis and ‘other FHVs’ include all the for hire vehicles other than Uber vehicles and taxis.Abstract: For Hire Vehicles have played an important role in New York City’s transportation. With the increasing number of platforms providing these services, the number of actors in the city’s transportation network have increased, raising a wide range of concerns, including their role played in the city’s traffic congestion.   This project was chosen in light of the debate between Uber and Mayor de Blasio. For my analysis, I used the ‘Aggregate FHV Data’ which was available on FiveThirtyEight’s Github account who have been analyzing the data for the same purposes. This data contains information in the number of pick ups per day by yellow and green taxis, Uber, Lyft and the other ‘For Hire Vehicles’ in Midtown Manhattan. For my analysis of the research question – Does Uber have an impact on the Traffic congestion of the city, I performed a test of means – Z test to compare the mean of daily pick ups made by Uber vehicles to the mean of daily pick ups made by the other FHVs in Midtown Manhattan. With the calculated Z statistic, I rejected the Null Hypothesis, which proved that Uber vehicles did not lead to traffic congestion in the city (at a significance level of 0.05).  Introduction: According to an article published in the blog ‘Hot Air’ in August 2016, when Uber was launched in New York City in the year 2011, the taxi business in the city was booming, increasing the number of medallion licenses being issued. This led to an increase in the number of vehicles on the streets, resulting in traffic congestion.  In Summer 2015, New York City Mayor Bill de Blasio raised his concerns about the increase in traffic congestion due to the increasing number of ride hailing apps, most popular of them being Uber. Mayor de Blasio decided to cap the number of Uber vehicles on the streets in the city implying that the uncapped number of vehicles along with the number of taxis on the streets of the city may lead to ‘urban gridlock’ (FiveThirtyEight, October 2015).  As a result, to study this further, in January 2016, de Blasio administration released the ‘For-Hire Vehicle Transportation Study’ which highlighted that even though the number of Uber vehicles have increased in the city, they are not responsible for the increasing traffic congestion because they are replacing the yellow cabs. Similarly, a study done by FiveThirtyEight (a website involved in a number of poll analysis in the fields of politics, economics, sports etc.) performed a similar statistical test and came up with the same conclusion as the report by the Mayor’s administration.  Based on the above mentioned studies, I have attempted to answer the following research question:Does Uber have an impact on the traffic patterns in New York City? Null Hypothesis:The average number of Uber pick ups in a day on the streets in Midtown Manhattan is more than the average number of ‘For Hire Vehicles’ and taxi pick ups in a day on the streets in Midtown Manhattan.Alternate Hypothesis: The average number of Uber pick ups in a day on the streets in Midtown Manhattan is less than or equal to the average number of ‘For Hire Vehicles’ and taxi trips in a day on the streets in Midtown Manhattan. The significance level for this analysis is 0.05. To answer this question, I first specified my null and alternate hypothesis, followed by specifying the significance level. I decided to perform a Z test to answer this research question. The Z test compares the standard deviation of the expected distribution and the observed result. It tells us how many standard deviations from the mean an observation is, under the assumption of normality. The logic behind using this test will be detailed out further in the next section.  Data: To answer my research question, I needed the following information:1.     Number of Uber pick ups2.     Number of Taxi pick ups 3.     Number of other For Hire Vehicles pick upsSince Midtown Manhattan is one of the Central Business Districts of New York City, I realized that it would be a good area to analyze traffic in. I received data for the months of July, August and September 2014. I got all this information from FiveThirtyEight’s github account which had this information apart from other numbers such as:·      Average trips per Hour and day of week (Uber, Lyft and the other FHVs)·      Uber, Lyft pick ups per day within Manhattan core, LaGuardia airport and JFK (2014)·      Taxi pick ups per day within Manhattan core, LaGuardia airport and JFK (2013 and 2014)·      Change in daily Uber and Lyft trips in Manhattan Core (Sept 2014)·      Change in daily yellow taxi trips in Manhattan Core (September 2013 compared with September 2014)However, I did not need this information to answer my research question, so I dropped these columns while data wrangling. Since the document had a lot of unfilled columns and rows, I dropped them all so that I could get a clean dataframe which was good for processing the data quickly.  Methodology: To make the dataframe easy to understand, I made a new column in the dataframe which added the total number of FHVs (excluding Uber vehicles, yellow and green taxis) on the streets. Similarly, I combined both the green and yellow taxis. I also grouped the information given in groups of three (using groupby) – for the months of July, August and September – this gave me a clear look at the traffic patterns through the three months in summer 2014.I also plotted the total daily trips made by Uber, Taxis and other For Hire Vehicles everyday from July 1, 2014 to September 30, 2014 to look at the trends. 

Ekaterina Levitskaya, github: el2666, NYU ID: el2666  

INTRODUCTION Our project is aimed at children growing up in NYC, by investigating the information of recreation facilities like playgrounds around zip codes zones and residential neighborhoods. Through this project we want to supply information of the playgrounds within walking distance in neighborhood units, the amounts for average children living in communities, the crime rates around the playgrounds, the transportation situation, the restaurants and schools around the playgrounds for parents to consider that when they plan to take children out.

Several researches have been done since The NYC Taxi & Limousine Commission has released the detailed historical dataset covering over 1.1 billion individual taxi trips, from January 2009 through June 2016. Many Data scientists have examined this dataset passionately, in order to discover this great city’s neighborhoods, nightlife, airport traffic, and more. In this contribution, the likelihood of occurrence of long taxi trips during the day and night has been studied, as well as the relationship of weather and taxi demands. The present study has investigated NYC yellow taxi trips by looking at the two months period of 2016(January and June) based on the temporal factors and weather condition. The results show it was more likely long trip would occur during the nighttime compares to daytime, and the snow depth does greatly affect the demand of taxi trips, but precipitation does not display evident correlation with demand of taxi rides. Keywords: NYC, yellow taxi, data, demand

The notion of a digital divide has been increasingly addressed by policy makers for the last two decades. In the year 2013 the Census Bureau included questions regarding internet access for the first time in the federal agency’s history. The results of the survey highlighted the situation of hundreds of thousands of low-income Americans with no computer ownership and deficient access broadband. For New York City, the American Community Survey (ACS) stressed estimates for its most vulnerable segments of the population located in all five boroughs. According to the Comptroller’s Office’ analysis of ACS results, 20% of the city’s youth and 45% of its senior population lacked broadband at home. The deficient access was concentrated in the Bronx and Brooklyn with 34% and 30% of residents lacking internet access, respectively. Aiming to address this increasing divide, Mayor Bill de Blasio announced LinkNYC program, a municipal Wi-Fi network that will eventually replace more than 7,000 phone booths with as many as 10,000 interactive kiosks with the capacity to provide New Yorkers with free high-speed internet within a 150-foot radius from each device. This project evaluates the spatial relationship between the current disposition of the self-funded LinkNYC kiosks (Links) and the areas of New York City hosting population living below poverty. Specifically, this study was designed to examine whether or not, low-income members of the community were more likely to be located in long-proximity to Links, compared to high-income segments of the population. The study was done by utilizing American Community Survey population and internet use estimates for 2015 and 2014, respectively and the LinkNYC locator provided by New York City’s open data portal. Among the findings of this project, a strong presence of Links was identified in the borough of Manhattan, with 90% of total free Wi-Fi devices installed within community districts of higher median household income and the greatest number internet subscriptions. Conversely, Brooklyn was the borough with lower median income households, the least number of internet subscriptions and had, at the time of the analysis, only two installed LinkNYC kiosks (representing less than 1% of the total installed Links). Findings indicated that population below poverty was more likely to be located at longer-distance from their nearest LinkNYC kios than their higher-income neighbors. The limitations of the linear nature measurements and results’ implications within New York City’s digital divide, however, will be explored in depth throughout the sections below.