Equitable voting rules

May's Theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a weakening of May's symmetry assumption allows for a far richer set of rules that still treat voters equally. We show that such rules can have minimal winning coalitions comprising a vanishing fraction of the population, but not less than the square root of the population size. Methodologically, we introduce techniques from group theory and illustrate their usefulness for the analysis of social choice questions.Comment: 43 pages, 5 figure

Equitable Voting Rules

A celebrated result in social choice is May's Theorem (1952), providing the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a modification of May's symmetry assumption allows for a far richer set of rules that still treat voters equally, but have minimal winning coalitions comprising a vanishing fraction of the population. We conclude that procedural fairness can coexist with the empowerment of a small minority of individuals. Methodologically, we introduce techniques from discrete mathematics and illustrate their usefulness for the analysis of social choice questions

Evaporation kinetics of pure water drops: Thermal patterns, Marangoni flow, and interfacial temperature difference

We report a systematic study on the role of Marangoni convection on the evaporation kinetics of pure water drops, considering the influence of heating regime and surface wettability. The Marangoni flows were induced via heating under constant wall temperature (uniform heating) and constant heat flux (local heating) regimes below the drops. To visualize the thermal patterns/flows emerging within the water drops we employed infrared (IR) thermography and we captured the evolution of the drop profile with a CCD camera to follow the evaporation kinetics of each drop. We observed a strong correlation between the temperature difference within the drop and the evolution of drop shape during different modes of evaporation ({i.e.} constant radius, angle or stick-slip) resulting in different Marangoni flow patterns. Under uniform heating, stable recirculatory vortices due to Marangoni convection emerged at high temperature which faded at later stages of the evaporation process. On the other hand, in the localized heating case, the constant heat flux resulted in a rapid increase of the temperature difference within the drop capable of sustaining Marangoni flows throughout the evaporation. Surface wettability was found to also play a role in both the emergence of the Marangoni flows and the evaporation kinetics. In particular, recirculatory flows on hydrophobic surfaces were stronger when compared to hydrophilic for both uniform and local heating. To quantify the effect of heating mode and the importance of Marangoni flows, we calculated the evaporative flux for each case and found to it to be much higher in the localized heating case. Evaporative flux depends on both diffusion and natural convection of the vapor phase to the ambient. Hence, we estimated the Grashof number for each case and found a strong relation between natural convection in the vapor phase and heating regime or Marangoni convection in the liquid phase. Subsequently, we demonstrate the limitation of previously reported diffusion-only} model in describing the evaporation of heated drops

Structural Studies of Yeast Mitochondrial Peripheral Membrane Protein Tim44

Tim44 is a peripheral membrane protein and a component of the TIM23 translocon on the matrix side. It is well established that Tim44 tethers the presequence associated motor (PAM) complex to the Inner Mitochondrial Membrane (IMM), through its C-Terminal Domain (CTD). This study focuses on understanding the high resolution structure of Tim44 CTD and the molecular basis for its membrane anchoring mechanism. The crystal structure of Tim44 CTD revealed that it exists as a single domain. The N-terminal amphipathic helices A1 and A2 protrude away from the main body of Tim44 CTD. These two flexible helices have been tested for their putative role in membrane anchoring by functional analyses. Biochemical studies were conducted using mutant forms of Tim44 CTD. Deletion and site directed mutants of Tim44 in the A1 and A2 helical region were used to study if the membrane binding ability is hindered. The deletion mutants included two constructs in which either a part of the A1-A2 helical region or the entire A1-A2 helical region was removed. The results showed that the A1 and A2 helices are required for Tim44 CTD to bind membranes. The point mutants included three constructs in which three conserved residues within A1 and A2 helices were mutated. Hydrophobic point mutations compromised the membrane binding ability. These investigations along with other structural data suggested that the A1-A2 helical region undergoes a conformational change along a hinge during ii membrane binding. This hinge is present in the loop that follows the A2 helix and is composed of two conserved glycine residues. This conformational change exposes the hydrophobic residues of the A1 and A2 helices to the IMM. In a soluble form these helices conceals the hydrophobic residues towards the protein core but during membrane binding, these residues seem to get exposed and interact with the membrane. We propose a mechanism by which the A1 and A2 helices turn along the glycine hinge either to conceal or to expose their hydrophobic side-chains based on the nature of the surrounding environment. The studies enumerated in this dissertation reveal the structure of Tim44 CTD at an atomic resolution. The membrane anchoring region of Tim44 CTD has been revealed using functional studies. Utilizing the structural and the functional data, a plausible mechanism for Tim44 CTD membrane binding has been proposed and tested

Concert/C: A language for distributed programming

Concert/C is a new language for distributed C programming that extends ANSI C to support distribution and process dynamics. Concert/C provides the ability to create and terminate processes, connect them together, and communicate among them. It supports transparent remote function calls (RPC) and asynchronous messages. Interprocess communications interfaces are typed in Concert/C, and type correctness is checked at compile time wherever possible, otherwise at runtime. All C data types, including complex data structures containing pointers and aliases, can be transmitted in RPCs. Concert/C programs run on a heterogeneous set of machine architectures and operating systems and communicate over multiple RPC and messaging protocols. The current Concert/C implementation runs on AIX 3.2 1, SunOS 4.1, Solaris 2.2 and OS/2 2.1, and communicates over Sun RPC, OSF/DCE and UDP multicast. Several groups inside and outside IBM are actively using Concert/C, and it is available via anonymous ftp from software.watson.ibm.com:/pub/concert.

Statistical modelling of critical cut-in trajectories based on naturalistic driving data

Cut-in maneuvers are events when a vehicle changes lane and moves close to another vehicle in the adjacent lane. This phenomenon is quite common on highways and has adverse impact on traffic safety. Statistics from the Fatality Analysis Reporting System (FARS) by National Highway Traffic Safety Administration (NHTSA) show that there have been more than 290,000 traffic crash injuries associated with cut-in maneuvers (including rear-end, angle or sideswipe collision) between years 2015 and 2019. Active safety systems and autonomous vehicles are being developed to achieve safe driving and should be able to detect potentially dangerous scenarios like critical cut-ins, and act to avoid them. Statistical models of cut-in scenario trajectories are useful for developing and evaluating both active safety systems and autonomous vehicles. This thesis aims to increase our understand of and model cut-in trajectories of vehicles performing cut-in maneuvers, using SHRP2 (The Second Strategic Highway Research Program) naturalistic driving data. To conduct the study, the SHRP2 event data has been manually categorized. Thereafter, a dataset of kinematic variables, which were extracted using a video annotation tool, has been prepared to enable studying the trajectories in detail. Specifically, this study uses a quintic polynomial of time to model lateral and longitudinal trajectories of the vehicle that cuts in (or principle another vehicle; POV). One of the required inputs is the event duration which is calculated by identifying maneuver start and end times . The event durations follow a normal distribution and range from 2.1 to 6.4 seconds. Then, two linear models of event duration are built to calculate the remaining two variables required for a polynomial trajectory model, which are initial POV lateral acceleration and final POV longitudinal position. Using these three variables a range of trajectories have been generated, representing SHRP2 naturalistic driving for right to left single lane change cut-ins. This thesis also uses a probabilistic regression model to calculate the distribution of parameters of quintic polynomial of lateral position of POV. Using this model, new (other than training data) trajectories have been generated. Both these generative models of trajectories can be used as one of the inputs to simulations used in the design and evaluation of active safety systems and automated driving systems

Numerical investigation of fracture behaviour of polyurethane adhesives under the influence of moisture

Polyurethane adhesives are extensively used in manufacturing of the lightweight components. These adhesives are hygroscopic in nature causing the material to degrade their mechanical properties due to ageing under environmental conditions. Polyurethane adhesive shows non-linear rate-dependent behaviour due to viscoelastic properties and assumes nearly incompressible deformation. Finite-strain viscoelastic model is formulated based on the continuum rheological model by combining spring and Maxwell elements in parallel. Nearly incompressible property is considered by decomposing the mechanical free energy into volumetric and isochoric parts. This work focuses on the investigation of the influence of moisture on the fracture behaviour. Phase-field damage model proved to be an efficient method to investigate the fracture behaviour. Therefore, the finite-strain viscoelastic material model is coupled with the phase-field model to investigate fracture behaviour. Material is assumed to be isotropic, therefore the total mechanical energy is considered for bulk degradation. Experiments are conducted on the samples aged for different humid conditions to understand tear strength. These test results are used to identify the phase-field damage material parameters from numerical investigation