Motivating Example. Consider two autonomous vehicles at a T-junction where only one car can pass at a time. Each vehicle can either Pass or Wait. If both vehicles decide to pass through the T-junction at the same time, they will collide. On the other hand, if both decide to wait, they may enter a deadlock state in which they wait indefinitely. Ideally, we would like one vehicle to wait and the other to pass, so that they can traverse the T-junction one at a time. We model the preference between system behaviors by assigning a reward (or penalty) to each combination of actions of the two vehicles, (u1, u2), where u1 is the action of vehicle 1 (M1) and u2 is that of vehicle 2 (M2). The objectives of 246 TABLE I: M1 Rewards
2 1 Wait Pass Wait −1 −1 Pass 3 −10 TABLE II: M2 Rewards
2 1 Wait Pass Wait −1 4 Pass −1 −10 the empty set. The intent is that an implementation M can only be used under a compatible environment. C is consistent if there exists a feasible implementation M for it. For a saturated contract, this is equivalent to G = 0/ . To reason about different abstraction layers in a design, contracts can be ordered according to a refinement relation. A contract C = (V, A, G) refines Cj = (V, Aj, Gj), written C ≤ Cj, if and M1 and M2 are to maximize the rewards associated with their actions, shown in Tab. I and II, respectively. Rewards are as low as 10 to penalize collision and take on a maximum value when a vehicle manages to traverse the junction. From the perspective of M1, the behavior that results in the optimal reward is (u1, u2)= (Pass, Wait). However, if M1 is not aware of the next action or associated reward of M2, it will instead opt for Wait since it must act conservatively to guarantee safety (i.e., no collision) for all the possible actions of M2. If M2 selects its action in the same manner as M1 (i.e., maximizes its own reward), the two vehicles will enter the deadlock state. On the other hand, if the vehicles were able to communicate their actions and rewards to each other, they may be able to avoid deadlock by making decisions in a cooperative manner. We would like to formally reason about the overall behavior of this system using A/G contracts, where each vehicle is modeled as a component implementing a contract, and the composition of M1 and M2 represents the end-to-end system. To do so, we seek for a framework that (1) captures the behaviors of a component while optimizing its objective, and (2) supports a composition mechanism that takes into account the...
Motivating Example. We can write an optimizing contract for each vehicle in the example of Sec. II as follows: C1 = ({U2},{U1}, u2 ∈ {Wait, Pass}, (u1 ∈ {Wait, Pass}) ∧ ((u1, u2) = (Xxxx, Xxxx)), R1) C2 = ({U1},{U2}, u1 ∈ {Wait, Pass}, (u2 ∈ {Wait, Pass}) ∧ ((u1, u2) = (Xxxx, Xxxx)), R2) The cooperative and non-cooperative compositions can be computed as follows, where C1⊗ˇ C2 = (Cˇ1,Cˇ2): C1⊗ˆ C2 = (0/ ,{U1,U2}, T, ((u1, u2) ∈ {Wait, Pass}2)∧ ((u1, u2) = (Xxxx, Xxxx)), R1 + R2) Cˇ1 = ({U2},{U1}, T, ((u1, u2) ∈ {Wait, Pass}2)∧ ((u1, u2) ƒ= (Xxxx, Xxxx)), R1) path planning objective function Oi(xH ) increases as a vehicle 2 Cˇ = ({U },{U }, T, ((u , u ) ∈ {Wait, Pass}2)∧ approaches the destination and decreases if a vehicle travels off the designated course or collides to another vehicle. ((u1, u2) ƒ= (Xxxx, Xxxx)), R2) The optimal guarantees with cooperation are G1⊗ˆ 2,max = argmaxu ,u (R1 + R2) s.t. ((u1, u2) ∈ {Wait, Pass}2) ∧
Motivating Example distributed computa- tion of k weighted averages) Consider a scenario where each agent is interested in computing, using local communication only, an agent-dependent weighted mean (i.e., with agent- dependent weights) of a certain quantity x∗ = (x1∗, . . . , x∗n), where xi∗ R is known only by agent i. More formally, let wi Rn, with wT1 = 1, denote desired weighting coefficients for agent i, with k of these vectors being linearly independent;
Motivating Example. 2 1.3 Limitations of Existing Methodology . . . . . . . . . . . . . . . . . . 3 1.4 Outline and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Motivating Example. Many phenomena in the biological, social, and physical sciences cannot be plainly viewed. Rather, only symptoms or indicators of the phenomena can be observed. For example, consider mild cognitive impairment (MCI). MCI refers to the clinical state in which a subject is cognitively impaired, usually in the memory domain, but is not suffering from dementia [41]. Although neuropsychological testing is often used to dif- ferentiate elderly individuals with MCI from those who experience normal aging, MCI is not a neuropsychological diagnosis, and no specific test or battery of tests currently exist to confirm a diagnosis of MCI. Determining that a patient has MCI is further complicated because not all patients present with an identical set of symptoms. In- deed, research has suggested tremendous heterogeneity in the clinical presentation of MCI. As a result, MCI is frequently classified into four subtypes: Amnestic MCI, Multidomain MCI-Amnestic, Multidomain MCI-Non-Amnestic, or Single Nonmem- ory MCI [14]. These subtypes were determined based on clinical observation rather than on a rigorous clustering approach. Further, MCI patients are typically classified based on a single clinical assessment, which ignores potential variation in the progres- sion of symptoms over time. Thus, the motivation for this dissertation research is to empirically validate the presence of MCI subtypes, to incorporate longitudinal data into subtype classification, and to model the progression of MCI within each subtype over time. In order to conceptualize MCI subtypes, longitudinal data on a large sample of pa- tients with a consensus diagnosis of MCI at baseline was obtained from the National Alzheimer’s Coordinating Center (NACC). The data included cognitive, functional, and behavioral assessments from the NACC Uniform Data Set (UDS)[2, 25]. Func- tioning was assessed using the Functional Assessment Questionnaire (FAQ)[23] as reported by an informant. Behavioral disturbances were assessed using the Geriatric Depression Scale (GDS)[73] and select items from the Neuropsychiatric Questionnaire (NPI-Q)[15]. Cognitive performance was assessed using the following ten neuropsy- chological items: mini-mental state exam (MMSE)[32], Trail-Making Test[83], Boston Naming Test[40], Category Fluency[75], Digit Span subtest, Digit Symbol subtest[84], Logical Memory, and Story A[85]. In addition to these assessments, the Xxxxx Mod- ification of the Hachinski Ischemic Score (RMHIS) [27] was used as an indi...
Motivating Example. Consider the AF in Figure 4.6, where t is omitted but still defended by partition Pfor. Nodes are labelled v11, ..., v15 and v21, ..., v26. The entire AF forms one SCC K with gcd (K) = 2 (so Pfor = P1) whose row-normalised in-matrix using this order of nodes is 1 0 2 2 2 2 4 0 0 0 0 0 HTP = 1 1 1
Motivating Example. The following example of a tree-PIN source with linear
Motivating Example. Job A: Duration: 2hrs Deadline: 4hrs Priority: 200 Job B: Duration: 2hrs Deadline: 2hrs Priority: 100 fig.1 An Example of this type of scheduling the problem the scheduler cannot manage. Out of the three job attributes of durtion, deadlines and priority the scheduler only uses the priority in making decisions. In the example there are two jobs to be run. Both the jobs have same duration of 3 hrs. Job A has to be completed within 3hrs and Job B is worthwhile to the owner if and only if it is completed within 2hrs.Currently, job have no way to specify the temporal constraints. Instead the scheduler simply uses the priority value of jobs in determining which job is to run first. In this case, Job A would be run first because of its higher priority values, job B would miss it deadline. An SLA can be considered a legal binding contract that specifies the terms and levels of service. The parties of an SLA can be distinguished into providers and consumers of a service. The terms are agreed upon between service providers and consumers.
Motivating Example. This problem was originally motivated by analysis of data from the Xxxxxxxxx Stroke Reg- istry [Xxxxxx et al., 2007], which was used as the basis for initial simulations. Wave I data were used, which included four states (MI, MA, OH, and GA) treated as strata and multiple hospitals within each state treated as clusters. Although this complicated data structure does present additional analytical challenges, it also motivates the application of propensity score methods - the degrees of freedom for any analysis of complex survey data are deter- mined by the number of primary sampling units (in our case, clusters), not the total number of individuals in the dataset. Although we are fortunate that this specific dataset contains many clusters, the number of covariates that it is reasonable to include in any analysis of complex survey data can become limited rather quickly. The Xxxxxxxxx Stroke Registry includes four stroke types (Ischemic, Transient Ischemic Attack, Intra-cranial Hemorrhage, and Sub-arachnoid Hemorrhage). Approximately 63% of patients had an Ischemic stroke, and this subpopulation forms the basis of our analyses. The population is predominantly white (75%) and we are interested in the causal effect of race on length of hospital stay following a stroke. Some causal inference researchers object to the use of race, gender, and other non-manipulable attributes as factors of interest, based primarily on Xxxx Xxxxxxx’x argument that “each unit be potentially exposable to any one of the causes.” [Holland, 1986] We argue that as stud- ies are beginning to manipulate an individual’s perception of race [Grogger and Xxxxxxxx, 2006] and gender [Xxxxxx and Xxxxx, 2000] this provides a conceptual framework for the es- timation of the causal effect of these attributes. Another similar argument is that possible covariates for the propensity score model are typically limited to pre-treatment (or pre- exposure) variables, and technically there are no variables that were measured before race was determined. However, continuing with the idea of the perception of race, it is possible that other demographic and medical history variables could be noted on a medical chart while omitting race, therefore there is a pool of variables that could be known to a doctor prior to his/her perception of a patient’s race. In this way, we fit Xxxxx’x requirement of well-defined units, treatments, and outcomes (see section 1.2.1 - SUTVA). Throughout this chapter we hope the reader w...
Motivating Example. In the ProTECT study patients who had suffered a traumatic brain injury (TBI) were randomized to receive either progesterone or a placebo. This was a small pilot study de- signed primarily to determine the safety (rather than efficacy) of progesterone to treat acute TBI. Seventy seven patients received the treatment (progesterone) and 23 received placebo. Thirty days post-injury, two primary outcome measures were used to assess recovery - the Glasgow Outcome Score Extended (XXXX) and the Disability Rating Scale (DRS). Patients were followed for one year, and DRS was measured again at this later follow-up time. The one year data were used for this paper and DRS was our outcome of interest for this secondary analysis. One year post injury, seven of the control patients and fourteen of the treatment patients were known to be deceased. Five control patients and twenty five treatment patients were of unknown status.
