Degree spectra for transcendence in fields

We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e. degrees above an arbitrary fixed $\Delta^0_2$ degree. In other cases, these spectra may be characterized by the ability to enumerate an arbitrary $\Sigma^0_2$ set. This is the first proof that a computable field can fail to have a computable copy with a computable transcendence basis

Emotion Differentiation as a Protective Factor Against Nonsuicidal Self-Injury in Borderline Personality Disorder

Evidence that nonsuicidal self-injury (NSSI) serves a maladaptive emotion regulation function in borderline personality disorder (BPD) has drawn attention to processes that may increase risk for NSSI by exacerbating negative emotion, such as rumination. However, more adaptive forms of emotion processing, including differentiating broad emotional experiences into nuanced emotion categories, might serve as a protective factoragainst NSSI. Using an experience-sampling diary, the present study tested whether differentiation of negative emotion was associated with lower frequency of NSSI acts and urges in 38 individuals with BPD who reported histories of NSSI. Participants completed a dispositional measure of rumination and a 21-day experience-sampling diary, which yielded an index of negative emotion differentiation and frequency of NSSI acts and urges. A significant rumination by negative emotion differentiation interaction revealed that rumination predicted higher rates of NSSI acts and urges in participants with difficulty differentiating their negative emotions. The results extend research on emotion differentiation into the clinical literature and provide empirical support for clinical theories that suggest emotion identification and labeling underlie strategies for adaptive self-regulation and decreased NSSI risk in BPD

Monolithic microwave integrated circuits: Interconnections and packaging considerations

Monolithic microwave integrated circuits (MMIC's) above 18 GHz were developed because of important potential system benefits in cost reliability, reproducibility, and control of circuit parameters. The importance of interconnection and packaging techniques that do not compromise these MMIC virtues is emphasized. Currently available microwave transmission media are evaluated to determine their suitability for MMIC interconnections. An antipodal finline type of microstrip waveguide transition's performance is presented. Packaging requirements for MMIC's are discussed for thermal, mechanical, and electrical parameters for optimum desired performance

Identification of Mental States and Interpersonal Functioning in Borderline Personality Disorder

Atypical identification of mental states in the self and others has been proposed to underlie interpersonal difficulties in borderline personality disorder (BPD), yet no previous empirical research has directly examined associations between these constructs. We examine 3 mental state identification measures and their associations with experience-sampling measures of interpersonal functioning in participants with BPD relative to a healthy comparison (HC) group. We also included a clinical comparison group diagnosed with avoidant personality disorder (APD) to test the specificity of this constellation of difficulties to BPD. When categorizing blended emotional expressions, the BPD group identified anger at a lower threshold than did the HC and APD groups, but no group differences emerged in the threshold for identifying happiness. These results are consistent with enhanced social threat identification and not general negativity biases in BPD. The Reading the Mind in the Eyes Test (RMET) showed no group differences in general mental state identification abilities. Alexithymia scores were higher in both BPD and APD relative to the HC group, and difficulty identifying one’s own emotions was higher in BPD compared to APD and HC. Within the BPD group, lower RMET scores were associated with lower anger identification thresholds and higher alexithymia scores. Moreover, lower anger identification thresholds, lower RMET scores, and higher alexithymia scores were all associated with greater levels of interpersonal difficulties in daily life. Research linking measures of mental state identification with experience-sampling measures of interpersonal functioning can help clarify the role of mental state identification in BPD symptoms

An Improved Bound for First-Fit on Posets Without Two Long Incomparable Chains

It is known that the First-Fit algorithm for partitioning a poset P into chains uses relatively few chains when P does not have two incomparable chains each of size k. In particular, if P has width w then Bosek, Krawczyk, and Szczypka (SIAM J. Discrete Math., 23(4):1992--1999, 2010) proved an upper bound of ckw^{2} on the number of chains used by First-Fit for some constant c, while Joret and Milans (Order, 28(3):455--464, 2011) gave one of ck^{2}w. In this paper we prove an upper bound of the form ckw. This is best possible up to the value of c.Comment: v3: referees' comments incorporate

Parameterized Complexity of the k-anonymity Problem

The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization that has been recently proposed is the $k$-anonymity. This approach requires that the rows of a table are partitioned in clusters of size at least $k$ and that all the rows in a cluster become the same tuple, after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is known to be APX-hard even when the records values are over a binary alphabet and $k=3$, and when the records have length at most 8 and $k=4$ . In this paper we study how the complexity of the problem is influenced by different parameters. In this paper we follow this direction of research, first showing that the problem is W[1]-hard when parameterized by the size of the solution (and the value $k$). Then we exhibit a fixed parameter algorithm, when the problem is parameterized by the size of the alphabet and the number of columns. Finally, we investigate the computational (and approximation) complexity of the $k$-anonymity problem, when restricting the instance to records having length bounded by 3 and $k=3$. We show that such a restriction is APX-hard.Comment: 22 pages, 2 figure

Multidimensional Binary Vector Assignment problem: standard, structural and above guarantee parameterizations

In this article we focus on the parameterized complexity of the Multidimensional Binary Vector Assignment problem (called \BVA). An input of this problem is defined by $m$ disjoint sets $V^1, V^2, \dots, V^m$, each composed of $n$ binary vectors of size $p$. An output is a set of $n$ disjoint $m$-tuples of vectors, where each $m$-tuple is obtained by picking one vector from each set $V^i$. To each $m$-tuple we associate a $p$ dimensional vector by applying the bit-wise AND operation on the $m$ vectors of the tuple. The objective is to minimize the total number of zeros in these $n$ vectors. mBVA can be seen as a variant of multidimensional matching where hyperedges are implicitly locally encoded via labels attached to vertices, but was originally introduced in the context of integrated circuit manufacturing. We provide for this problem FPT algorithms and negative results ($ETH$-based results, $W$[2]-hardness and a kernel lower bound) according to several parameters: the standard parameter $k$ i.e. the total number of zeros), as well as two parameters above some guaranteed values.Comment: 16 pages, 6 figure

Dimension Spectra of Lines

This paper investigates the algorithmic dimension spectra of lines in the Euclidean plane. Given any line L with slope a and vertical intercept b, the dimension spectrum sp(L) is the set of all effective Hausdorff dimensions of individual points on L. We draw on Kolmogorov complexity and geometrical arguments to show that if the effective Hausdorff dimension dim(a, b) is equal to the effective packing dimension Dim(a, b), then sp(L) contains a unit interval. We also show that, if the dimension dim(a, b) is at least one, then sp(L) is infinite. Together with previous work, this implies that the dimension spectrum of any line is infinite

Systems of Linear Equations over F2\mathbb{F}_2 and Problems Parameterized Above Average

In the problem Max Lin, we are given a system $Az=b$ of $m$ linear equations with $n$ variables over $\mathbb{F}_2$ in which each equation is assigned a positive weight and we wish to find an assignment of values to the variables that maximizes the excess, which is the total weight of satisfied equations minus the total weight of falsified equations. Using an algebraic approach, we obtain a lower bound for the maximum excess. Max Lin Above Average (Max Lin AA) is a parameterized version of Max Lin introduced by Mahajan et al. (Proc. IWPEC'06 and J. Comput. Syst. Sci. 75, 2009). In Max Lin AA all weights are integral and we are to decide whether the maximum excess is at least $k$, where $k$ is the parameter. It is not hard to see that we may assume that no two equations in $Az=b$ have the same left-hand side and $n={\rm rank A}$. Using our maximum excess results, we prove that, under these assumptions, Max Lin AA is fixed-parameter tractable for a wide special case: $m\le 2^{p(n)}$ for an arbitrary fixed function $p(n)=o(n)$. Max $r$-Lin AA is a special case of Max Lin AA, where each equation has at most $r$ variables. In Max Exact $r$-SAT AA we are given a multiset of $m$ clauses on $n$ variables such that each clause has $r$ variables and asked whether there is a truth assignment to the $n$ variables that satisfies at least $(1-2^{-r})m + k2^{-r}$ clauses. Using our maximum excess results, we prove that for each fixed $r\ge 2$, Max $r$-Lin AA and Max Exact $r$-SAT AA can be solved in time $2^{O(k \log k)}+m^{O(1)}.$ This improves $2^{O(k^2)}+m^{O(1)}$-time algorithms for the two problems obtained by Gutin et al. (IWPEC 2009) and Alon et al. (SODA 2010), respectively