The succinctness of first-order logic on linear orders

Succinctness is a natural measure for comparing the strength of different logics. Intuitively, a logic L_1 is more succinct than another logic L_2 if all properties that can be expressed in L_2 can be expressed in L_1 by formulas of (approximately) the same size, but some properties can be expressed in L_1 by (significantly) smaller formulas. We study the succinctness of logics on linear orders. Our first theorem is concerned with the finite variable fragments of first-order logic. We prove that: (i) Up to a polynomial factor, the 2- and the 3-variable fragments of first-order logic on linear orders have the same succinctness. (ii) The 4-variable fragment is exponentially more succinct than the 3-variable fragment. Our second main result compares the succinctness of first-order logic on linear orders with that of monadic second-order logic. We prove that the fragment of monadic second-order logic that has the same expressiveness as first-order logic on linear orders is non-elementarily more succinct than first-order logic

Biases at the Ballot Box: How Multiple Forms of Voter Discrimination Impede the Descriptive and Substantive Representation of Ethnic Minority Groups

Research shows that ethnic minority candidates often face an electoral penalty at the ballot box. In this study, we argue that this penalty depends on both candidate and voter characteristics, and that pro-minority policy positions incur a greater penalty than a candidate’s ethnic background itself. Using a conjoint experiment embedded in a panel study of British voters, we investigate the relative contributions of candidate ethnicity, policy positions, affirmative action, and voter attitudes to this electoral penalty. We find that although Pakistani (Muslim) candidates are penalized directly for their ethnicity, black Caribbean candidates receive on average the same levels of support as white British ones. However, black Caribbean candidates suffer conditional discrimination where they are penalized if they express support for pro-minority policies, and all candidates are penalized for having been selected through an affirmative action initiative. We also find that some white British voters are more inclined to support a black Caribbean candidate than a white British one, all else being equal. These voters (one quarter of our sample) have cosmopolitan views on immigration, and a strong commitment to anti-prejudice norms. However, despite efforts across parties to increase the ethnic diversity of candidates for office, many voters’ preferences continue to pose barriers toward descriptive and substantive representation of ethnic minority groups

Monadic Datalog Containment on Trees

We show that the query containment problem for monadic datalog on finite unranked labeled trees can be solved in 2-fold exponential time when (a) considering unordered trees using the axes child and descendant, and when (b) considering ordered trees using the axes firstchild, nextsibling, child, and descendant. When omitting the descendant-axis, we obtain that in both cases the problem is EXPTIME-complete.Comment: This article is the full version of an article published in the proccedings of the 8th Alberto Mendelzon Workshop (AMW 2014

On a nonlinear partial differential algebraic system arising in technical textile industry: Analysis and numerics

In this paper we explore a numerical scheme for a nonlinear fourth order system of partial differential algebraic equations that describes the dynamics of slender inextensible elastica as they arise in the technical textile industry. Applying a semi-discretization in time, the resulting sequence of nonlinear elliptic systems with the algebraic constraint for the local length preservation is reformulated as constrained optimization problems in a Hilbert space setting that admit a solution at each time level. Stability and convergence of the scheme are proved. The numerical realization is based on a finite element discretization in space. The simulation results confirm the analytically predicted properties of the scheme.Comment: Abstract and introduction are partially rewritten. The numerical study in Section 4 is completely rewritte

Household Survey Panels: How Much Do Following Rules Affect Sample Size?

In household panels, typically all household members are surveyed. Because household composition changes over time, so-called following rules are implemented to decide whether to continue surveying household members who leave the household (e.g. former spouses/partners, grown children) in subsequent waves. Following rules have been largely ignored in the literature leaving panel designers unaware of the breadth of their options and forcing them to makead hoc decisions. In particular, to what extent various following rules affect sample size over time is unknown. From an operational point of view such knowledge is important because sample size greatly affects costs. Moreover, the decisionof whom to follow has irreversible consequences as finding household members who moved out years earlier is very difficult. We find that household survey panels implement a wide variety of following rules but their effect on sample size is relatively limited. Even after 25 years, the rule "follow only wave 1 respondents" still captures 85% of the respondents of the rule "follow everyone who can be traced back to a wave 1 household through living arrangements". Almost all of the remaining 15% live in households of children of wave 1 respondents who have grown up (5%) and in households of former spouses/partners (10%). Unless attrition is low, there is no danger of an ever expanding panel because even wide following rules do not typically exceed attrition.Survey panels, Survey methodology

The succinctness of first-order logic on linear orders

Succinctness is a natural measure for comparing the strength of different logics. Intuitively, a logic L_1 is more succinct than another logic L_2 if all properties that can be expressed in L_2 can be expressed in L_1 by formulas of (approximately) the same size, but some properties can be expressed in L_1 by (significantly) smaller formulas. We study the succinctness of logics on linear orders. Our first theorem is concerned with the finite variable fragments of first-order logic. We prove that: (i) Up to a polynomial factor, the 2- and the 3-variable fragments of first-order logic on linear orders have the same succinctness. (ii) The 4-variable fragment is exponentially more succinct than the 3-variable fragment. Our second main result compares the succinctness of first-order logic on linear orders with that of monadic second-order logic. We prove that the fragment of monadic second-order logic that has the same expressiveness as first-order logic on linear orders is non-elementarily more succinct than first-order logic

Do ethnic minority candidates mobilise ethnic minority voters? Mostly not.

All major political parties in the UK have made efforts to increase the number of ethnic minority candidates that stand under their label for election, with Labour’s Sadiq Khan aiming to be become the first Muslim Mayor of London after May of this year. Here, Nicole Martin argues that the idea that ethnic minority candidates mobilise ethnic minority voters in great number isn’t necessarily borne out by the evidence

Why Black Lives (Must) Matter at UK

As a university committed to creating inclusive learning environments, we must remember that our pedagogical practices and philosophies are not crafted in insolation from our social, political, and cultural environments. The psychic and emotional injury spurred by the events of the summer of 2016 will continue to reverberate across campus as we move into the fall semester. When we boldly address the lingering effects of trauma through our pedagogical practices, we demonstrate how the campus actively creates space for the civic development of students, staff, faculty, and administration