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In a parking function, a lucky car is a car that parks in its preferred parking spot and the parking outcome is the permutation encoding the order in which the cars park on the street. We give a characterization for the set of parking outcomes arising from parking functions with a fixed set of lucky cars. This characterization involves the descent bottom set of a permutation, and we use the characterization to we give a formula for the number of parking functions with a fixed set of lucky cars. Our work includes the cases where the number of cars is equal to the number of parking spots, and where there are more spots than cars. We also give product formulas for the number of weakly increasing parking functions having a fixed set of lucky cars, and when the number of cars equals the number of spots this is a product of Catalan numbers.

In a parking function, a car is considered lucky if it is able to park in its preferred spot. Extending work of Harris and Martinez, we enumerate outcomes of parking functions with a fixed set of lucky cars. We then consider a generalization of parking functions known as vector parking functions or $\boldsymbol{u}$-parking functions, in which a nonnegative integer capacity is given to each parking spot in the street. With certain restrictions on $\boldsymbol{u}$, we enumerate outcomes of $\boldsymbol{u}$-parking functions with a fixed set of lucky cars or with a fixed number of lucky cars. We also count outcomes according to which spots contain lucky cars, and give formulas for enumerating $\boldsymbol{u}$-parking functions themselves according to their set of lucky cars.

Energy crisis has forced many countries to think of a replacement for energy supply. Renewable energy sources as firendly environment sources play a pivotal role in producing clean energy for various sectors in industry. Gas emissions originating from the transportation industry is another contributing factor to air pollution. Hence, designing and utilizing vehicles that run on renewable energy is crucial, as it provides a dependable energy source that is naturally abundant, leaves nearly no carbon footprint, and is sustainable. Solar powered electric cars make a significant impact on global climate change. To better understand this impact and building upon the plenty of research done on this topic, this paper aims to provide a comprehensive review of the various factors related to solar cars. Specifically, this review will examine the following key factors: Types and sizing of solar cars, solar vehicle power source configurations, leading solar car nations, and solar car challenges.

This paper explores the concept of creating a "self" for self-driving cars through a homeostatic architecture designed to enhance their autonomy, safety, and efficiency. The proposed system integrates inward focused sensors to monitor the car's internal state, such as the condition of its metal bodywork, wheels, engine, and battery, establishing a baseline homeostatic state representing optimal functionality. Outward facing sensors, like cameras and LIDAR, are then interpreted via their impact on the car's homeostatic state by quantifying deviations from homeostasis. This contrasts with the approach of trying to make cars "see" reality in a similar way to humans and identify elements in their reality in the same way humans. Virtual environments would be leveraged to accelerate training. Additionally, cars are programmed to communicate and share experiences via blockchain technology, learning from each other's mistakes while maintaining individualized training models. A dedicated language for self-driving cars is proposed to enable nuanced interpretation and response to environmental data. This architecture allows self-driving cars to dynamically adjust their behavior based on inter

Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of different cars is modelled by a system of two types of cars differing in maximal velocity or efficiency of brakes. Starting from conditional probabilities and using principle of maximum entropy, probability densities of car velocities and headways are calculated. It is shown that the first-order phase transition between free flow and congested traffic may be driven by number of fast cars in a system of slow cars, and, as a rule, admixture of cars of superior qualities does not increase but decreases the total flow. In the system of cars with poor brakes platoons of cars of the same velocity are formed. They are dissolved by a small addition of cars with good brakes. Application of principle of maximum entropy was justified by comparing the results with steady state properties of an equivalent kinetic model.

We present super-resolved coherent anti-Stokes Raman scattering (CARS) microscopy by implementing phase-resolved image scanning microscopy (ISM), achieving up to two-fold resolution increase as compared with a conventional CARS microscope. Phase-sensitivity is required for the standard pixel-reassignment procedure since the scattered field is coherent, thus the point-spread function (PSF) is well-defined only for the field amplitude. We resolve the complex field by a simple add-on to the CARS setup enabling inline interferometry. Phase-sensitivity offers additional contrast which informs the spatial distribution of both resonant and nonresonant scatterers. As compared with alternative super-resolution schemes in coherent nonlinear microscopy, the proposed method is simple, requires only low-intensity excitation, and is compatible with any conventional forward-detected CARS imaging setup.

Parking functions correspond with preferences of $n$ cars which enter sequentially to park on a one-way street where (1) each car parks in the first available spot greater than or equal to its preference and (2) all cars successfully park. When a car parks in its preferred spot then the corresponding car and corresponding spot are deemed ``lucky.'' This paper looks briefly at lucky cars which have previously been studied and in simple cases can be understood by a generalization of a result due to Pollak. We also consider lucky spots where the situation is more complex and not previously studied. Probabilities and asymptotics for lucky spots are given for the first few spots on the one-way street. We close with an exploration of the special cases when cars enter the one-way street in either weakly-increasing or weakly-decreasing order of their preferences.

We develop a computational framework to examine the factors responsible for scattering-induced distortions of coherent anti-Stokes Raman scattering (CARS) signals in turbid samples. We apply the Huygens-Fresnel Wave-based Electric Field Superposition (HF-WEFS) method combined with the radiating dipole approximation to compute the effects of scattering-induced distortions of focal excitation fields on the far-field CARS signal. We analyze the effect of spherical scatterers, placed in the vicinity of the focal volume, on the CARS signal emitted by different objects (2μm diameter solid sphere, 2μm diameter myelin cylinder and 2μm diameter myelin tube). We find that distortions in the CARS signals arise not only from attenuation of the focal field but also from scattering-induced changes in the spatial phase that modifies the angular distribution of the CARS emission. Our simulations further show that CARS signal attenuation can be minimized by using a high numerical aperture condenser. Moreover, unlike the CARS intensity image, CARS images formed by taking the ratio of CARS signals obtained using x- and y-polarized input fields is relatively insensitive to the effects of spherical sca

As autonomous cars are becoming tangible technologies, road networks will soon be shared by human-driven and autonomous cars. However, humans normally act selfishly which may result in network inefficiencies. In this work, we study increasing the efficiency of mixed-autonomy traffic networks by routing autonomous cars altruistically. We consider a Stackelberg routing setting where a central planner can route autonomous cars in the favor of society such that when human-driven cars react and select their routes selfishly, the overall system efficiency is increased. We develop a Stackelberg routing strategy for autonomous cars in a mixed-autonomy traffic network with arbitrary geometry. We bound the price of anarchy that our Stackelberg strategy induces and prove that our proposed Stackelberg routing will reduce the price of anarchy, i.e. it increases the network efficiency. Specifically, we consider a non-atomic routing game in a mixed-autonomy setting with affine latency functions and develop an extension of the SCALE Stackelberg strategy for mixed-autonomy networks. We derive an upper bound on the price of anarchy that this Stackelberg routing induces and demonstrate that in the li

Quicksort is a classical divide-and-conquer sorting algorithm. It is a comparison sort that makes an average of $2(n+1)H_n - 4n$ comparisons on an array of size $n$ ordered uniformly at random, where $H_n = \sum_{i=1}^n\frac{1}{i}$ is the $n$th harmonic number. Therefore, it makes $n!\left[2(n+1)H_n - 4n\right]$ comparisons to sort all possible orderings of the array. In this article, we prove that this count also enumerates the parking preference lists of $n$ cars parking on a one-way street with $n$ parking spots resulting in exactly $n-1$ lucky cars (i.e., cars that park in their preferred spot). For $n\geq 2$, both counts satisfy the second order recurrence relation $ f_n=2nf_{n-1}-n(n-1)f_{n-2}+2(n-1)! $ with $f_0=f_1=0$.

Coherent anti-Stokes Raman scattering (CARS) microscope system was built and applied to a non-intrusive gas concentration measurement of a mixing flow in a millimeter-scale channel. Carbon dioxide and nitrogen were chosen as test fluids and CARS signals from the fluids were generated by adjusting the wavelengths of the Pump and the Stokes beams. The generated CARS signals, whose wavelengths are different from those of the Pump and the Stokes beams, were captured by an EM-CCD camera after filtering out the excitation beams. A calibration experiment was performed in order to confirm the applicability of the built-up CARS system by measuring the intensity of the CARS signal from known concentrations of the samples. After confirming that the measured CARS intensity was proportional to the second power of the concentrations as was theoretically predicted, the CARS intensities in the gas mixing flow channel were measured. Ten different measurement points were set and concentrations of both carbon dioxide and nitrogen at each point were obtained. Consequently, it was observed that the mixing of two fluids progressed as the measurement point moved downstream. The results show the applicabi

Traffic Congestions and accidents are major concerns in today's transportation systems. This thesis investigates how to optimize traffic flow on highways, in particular for merging situations such as intersections where a ramp leads onto the highway. In our work, cars are equipped with sensors that can detect distance to neighboring cars, and communicate their velocity and acceleration readings with one another. Sensor-enabled cars can locally exchange sensed information about the traffic and adapt their behavior much earlier than regular cars. We propose proactive algorithms for merging different streams of sensor-enabled cars into a single stream. A proactive merging algorithm decouples the decision point from the actual merging point. Sensor-enabled cars allow us to decide where and when a car merges before it arrives at the actual merging point. This leads to a significant improvement in traffic flow as velocities can be adjusted appropriately. We compare proactive merging algorithms against the conventional priority-based merging algorithm in a controlled simulation environment. Experiment results show that proactive merging algorithms outperform the priority-based merging alg

Coherent anti-Stokes Raman scattering (CARS) and, in particular, femtosecond adaptive spectroscopic techniques (FAST CARS) have been successfully used for molecular spectroscopy and microscopic imaging. Recent progress in ultrafast nanooptics provides flexibility in generation and control of optical near fields, and holds promise to extend CARS techniques to the nanoscale. In this theoretical study, we demonstrate ultrafast subwavelentgh control of coherent Raman spectra of molecules in the vicinity of a plasmonic nanostructure excited by ultrashort laser pulses. The simulated nanostructure design provides localized excitation sources for CARS by focusing incident laser pulses into subwavelength hot spots via two self-similar nanolens antennas connected by a waveguide. Hot-spot-selective dual-tip-enhanced CARS (2TECARS) nanospectra of DNA nucleobases are obtained by simulating optimized pump, Stokes and probe near fields using tips, laser polarization- and pulse-shaping. This technique may be used to explore ultrafast energy and electron transfer dynamics in real space with nanometre resolution and to develop novel approaches to DNA sequencing.

Idling vehicles waste energy and pollute the environment through exhaust emission. In some countries, idling a vehicle for more than a predefined duration is prohibited and automatic idling vehicle detection is desirable for law enforcement. We propose the first automatic system to detect idling cars, using infrared (IR) imaging and deep networks. We rely on the differences in spatio-temporal heat signatures of idling and stopped cars and monitor the car temperature with a long-wavelength IR camera. We formulate the idling car detection problem as spatio-temporal event detection in IR image sequences and employ deep networks for spatio-temporal modeling. We collected the first IR image sequence dataset for idling car detection. First, we detect the cars in each IR image using a convolutional neural network, which is pre-trained on regular RGB images and fine-tuned on IR images for higher accuracy. Then, we track the detected cars over time to identify the cars that are parked. Finally, we use the 3D spatio-temporal IR image volume of each parked car as input to convolutional and recurrent networks to classify them as idling or not. We carried out an extensive empirical evaluation o

Cars are being sold more than ever. Developing countries adopt the lease culture instead of buying a new car due to affordability. Therefore, the rise of used cars sales is exponentially increasing. Car sellers sometimes take advantage of this scenario by listing unrealistic prices owing to the demand. Therefore, arises a need for a model that can assign a price for a vehicle by evaluating its features taking the prices of other cars into consideration. In this paper, we use supervised learning method namely Random Forest to predict the prices of used cars. The model has been chosen after careful exploratory data analysis to determine the impact of each feature on price. A Random Forest with 500 Decision Trees were created to train the data. From experimental results, the training accuracy was found out to be 95.82%, and the testing accuracy was 83.63%. The the model can predict the price of cars accurately by choosing the most correlated features.

Parking lots (PLs) are usually full with cars. If these cars are formed into a self-organizing vehicular network, they can be new kind of road side units (RSUs) in urban area to provide communication data forwarding between mobile terminals nearby and a base station. However cars in PLs can leave at any time, which is neglected in the existing studies. In this paper, we investigate relay cooperative communication based on parked cars in PLs. Taking the impact of the car's leaving behavior into consideration, we derive the expressions of outage probability in a two-hop cooperative communication and its link capacity. Finally, the numerical results show that the impact of a car's arriving time is greater than the impact of the duration the car has parked on outage probability.

Cybersecurity has gained importance for cars that increasingly rely on software and networks. "Smartphone on wheels" is often used as an analogy to highlight the need for security. As a high-value target of cyberattacks, modern smartphones implement layers of protection. Automotive embedded systems share many similarities with smartphones. We compare the security architecture of an iPhone and a car to identify gaps and discuss the potentials for the cars of the future.

Recent years have witnessed much interest in expanding the use of networking signals beyond communication to sensing, localization, robotics, and autonomous systems. This paper explores how we can leverage recent advances in 5G millimeter wave (mmWave) technology for imaging in self-driving cars. Specifically, the use of mmWave in 5G has led to the creation of compact phased arrays with hundreds of antenna elements that can be electronically steered. Such phased arrays can expand the use of mmWave beyond vehicular communications and simple ranging sensors to a full-fledged imaging system that enables self-driving cars to see through fog, smog, snow, etc. Unfortunately, using mmWave signals for imaging in self-driving cars is challenging due to the very low resolution, the presence of fake artifacts resulting from multipath reflections and the absence of portions of the car due to specularity. This paper presents HawkEye, a system that can enable high resolution mmWave imaging in self driving cars. HawkEye addresses the above challenges by leveraging recent advances in deep learning known as Generative Adversarial Networks (GANs). HawkEye introduces a GAN architecture that is custom

We survey research on self-driving cars published in the literature focusing on autonomous cars developed since the DARPA challenges, which are equipped with an autonomy system that can be categorized as SAE level 3 or higher. The architecture of the autonomy system of self-driving cars is typically organized into the perception system and the decision-making system. The perception system is generally divided into many subsystems responsible for tasks such as self-driving-car localization, static obstacles mapping, moving obstacles detection and tracking, road mapping, traffic signalization detection and recognition, among others. The decision-making system is commonly partitioned as well into many subsystems responsible for tasks such as route planning, path planning, behavior selection, motion planning, and control. In this survey, we present the typical architecture of the autonomy system of self-driving cars. We also review research on relevant methods for perception and decision making. Furthermore, we present a detailed description of the architecture of the autonomy system of the self-driving car developed at the Universidade Federal do Espírito Santo (UFES), named Intellige