Formulas vs. Circuits for Small Distance Connectivity

We give the first super-polynomial separation in the power of bounded-depth boolean formulas vs. circuits. Specifically, we consider the problem Distance $k(n)$ Connectivity, which asks whether two specified nodes in a graph of size $n$ are connected by a path of length at most $k(n)$. This problem is solvable (by the recursive doubling technique) on {\bf circuits} of depth $O(\log k)$ and size $O(kn^3)$. In contrast, we show that solving this problem on {\bf formulas} of depth $\log n/(\log\log n)^{O(1)}$ requires size $n^{\Omega(\log k)}$ for all $k(n) \leq \log\log n$. As corollaries: (i) It follows that polynomial-size circuits for Distance $k(n)$ Connectivity require depth $\Omega(\log k)$ for all $k(n) \leq \log\log n$. This matches the upper bound from recursive doubling and improves a previous $\Omega(\log\log k)$ lower bound of Beame, Pitassi and Impagliazzo [BIP98]. (ii) We get a tight lower bound of $s^{\Omega(d)}$ on the size required to simulate size-$s$ depth-$d$ circuits by depth-$d$ formulas for all $s(n) = n^{O(1)}$ and $d(n) \leq \log\log\log n$. No lower bound better than $s^{\Omega(1)}$ was previously known for any $d(n) \nleq O(1)$. Our proof technique is centered on a new notion of pathset complexity, which roughly speaking measures the minimum cost of constructing a set of (partial) paths in a universe of size $n$ via the operations of union and relational join, subject to certain density constraints. Half of our proof shows that bounded-depth formulas solving Distance $k(n)$ Connectivity imply upper bounds on pathset complexity. The other half is a combinatorial lower bound on pathset complexity

Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms $\R^3$, \bbS^3 and \bbH^3. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.Comment: 18 pages, revised versio

Constant mean curvature surfaces of any positive genus

We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus $g \geq 1$, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.Comment: 14 pages, 10 figure

An O(n^3)-Time Algorithm for Tree Edit Distance

The {\em edit distance} between two ordered trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this paper, we present a worst-case $O(n^3)$-time algorithm for this problem, improving the previous best $O(n^3\log n)$-time algorithm~\cite{Klein}. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems (which is interesting in its own right), together with a deeper understanding of the previous algorithms for the problem. We also prove the optimality of our algorithm among the family of \emph{decomposition strategy} algorithms--which also includes the previous fastest algorithms--by tightening the known lower bound of $\Omega(n^2\log^2 n)$~\cite{Touzet} to $\Omega(n^3)$, matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds of $\Theta(n m^2 (1 + \log \frac{n}{m}))$ when the two trees have different sizes $m$ and~$n$, where $m < n$.Comment: 10 pages, 5 figures, 5 .tex files where TED.tex is the main on

Appearance investment and intimacy: direct and indirect effects in the context of romantic relationships

Physical appearance is highly valued in Western society and has the potential to impact many domains of personal life, including romantic relationships. This study examined the direct effect of appearance investment on intimacy and indirect effects through perfectionist self-presentation presentation and relationship mindfulness, utilizing a Structural Equation Model approach. Appearance schemas are cognitive generalizations about the importance of physical appearance within one’s self-concept and contribute to cognitive and behavioral investment in appearance. Concern for appearance influences how individuals interact with others and process the world around them, thus it has the potential to influence relationship health. However, no study to date has investigated how appearance investment relates to key components of relationship functioning, such as intimacy, nor the mechanisms for these relations. We collected self-report data from 220 adults who were in a current romantic relationship and living in the United States. Findings showed that higher concern for appearance is negatively associated with intimate behavior through the mechanism of presenting as perfect within the relationship. This study illustrates the importance of examining how appearance investment may impact intimacy within romantic relationships, as well as the factors that mediate this relationship, providing implications for future research and social and interventional implications. © The Author(s) 2024

Vesuvianite From Pajsberg, Sweden, and the Role of Be In the Vesuvianite Structure

Vesuvianite from Pajsberg, Sweden contains about one atom of Mn, based on 50 cations per formula unit, and small amounts of Be, B, and As. Optical absorption analysis suggests that the Mn is predominantly or entirely trivalent. Crystal-structure analysis indicates that Mn is housed at the general octahedral site Y3, which exhibits only minor distortion from ideal octahedral symmetry. Arsenic is housed at Y2 and Z2, and the formula derived from electron microprobe and LA-ICP-MS analyses suggests minor substitution of Al for Si, also at Z2. Beryllium and B are at T1, between the edge-sharing trimers Y3Y2Y3, as is the case for B in the boron-dominant vesuvianite species wiluite. The total content at T1 is interpreted as 0.82Be, 0.34B, and 0.037Fe^(3+)

Senior Capstone Team Formation Based on Project Interest: Team Selection by Students Compared to Team Selection by Instructors

Assigning teams in large courses is logistically challenging and students are sometimes unhappy with their assigned team. This is exacerbated when the project work extends over multiple terms and teams have unique projects. Giving students some agency in team and project selection is one way to improve their project experience. This paper examines two key questions: (a) What is the best way to incorporate student interests into the team-forming process? (b) What impact does the team-forming process have on the student experience throughout the project? We consider two different approaches to giving students agency in the team formation / project selection process that have been implemented in our capstone course. One approach has faculty forming teams outside of class based on student surveys of project interests, skills, time availability, and team preferences. The alternative method enables students to form their own teams in a dynamic faculty-guided setting: Students place nametags on their top project posters, speak with other interested students, and move their nametags as needed until each project had teams with the appropriate size and skillset. Teams formed using these two approaches have completed a full year-long senior design project experience. Throughout these experiences, we collected data to help answer our two key questions. We used student surveys about the experience and the class, peer feedback on team dynamics, focus group discussions, and faculty observations. The results are inconclusive: The differences between the two approaches are small, indicating that either approach could be used to enable student agency in the team-forming process

Parameterized complexity of DPLL search procedures

We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a Prover-Delayer game which models the running time of DPLL procedures and we establish an information-theoretic method to obtain lower bounds to the running time of parameterized DPLL procedures. We illustrate this technique by showing lower bounds to the parameterized pigeonhole principle and to the ordering principle. As our main application we study the DPLL procedure for the problem of deciding whether a graph has a small clique. We show that proving the absence of a k-clique requires n steps for a non-trivial distribution of graphs close to the critical threshold. For the restricted case of tree-like Parameterized Resolution, this result answers a question asked in [11] of understanding the Resolution complexity of this family of formulas

Camaronesite, [Fe^(3+)(H_2O)_2(PO_3OH)]_2(SO_4)•1-2H_2O, a new phosphate-sulfate from the Camarones Valley, Chile, structurally related to taranakite

Camaronesite (IMA 2012-094), [Fe^(3+)(H_2O)_2(PO_3OH)]_2(SO_4)•1-2H_2O, is a new mineral from near the village of Cuya in the Camarones Valley, Arica Province, Chile. The mineral is a low-temperature, secondary mineral occurring in a sulfate assemblage with anhydrite, botryogen, chalcanthite, copiapite, halotrichite, hexahydrite, hydroniumjarosite, pyrite, römerite, rozenite and szomolnokite. Lavender-coloured crystals up to several mm across form dense intergrowths. More rarely crystals occur as drusy aggregates of tablets up to 0.5 mm in diameter and 0.02 mm thick. Tablets are flattened on {001} and exhibit the forms {001}, {104}, {015} and {018}. The mineral is transparent with white streak and vitreous lustre. The Mohs hardness is 2½, the tenacity is brittle and the fracture is irregular, conchoidal and stepped. Camaronesite has one perfect cleavage on {001}. The measured and calculated densities are 2.43(1) and 2.383 g/cm^3, respectively. The mineral is optically uniaxial (+) with ω = 1.612(1) and ε = 1.621(1) (white light). The pleochroism is O (pale lavender) > E (colourless). Electron-microprobe analyses provided Fe_2O_331.84, P_2O_529.22, SO_315.74, H_2O 23.94 (based on O analyses), total 100.74 wt.%. The empirical formula (based on 2 P a.p.f.u.) is: Fe_(1.94)(PO_3OH)_2(S_(0.96)O_4)(H_2O)_4•1.46H_2O. The mineral is slowly soluble in concentrated HCl and extremely slowly soluble in concentrated H_2SO_4. Camaronesite is trigonal, R32, with cell parameters:a = 9.0833(5), c = 42.944(3) Å, V = 3068.5(3) Å3 and Z = 9. The eight strongest lines in the X-ray powder diffraction pattern are [d_(obs) Å (I)(hkl)]: 7.74(45)(101), 7.415(100)(012), 4.545(72)(110), 4.426(26)(018), 3.862(32)(021,202,116), 3.298(93)(027,119), 3.179(25)(208) and 2.818(25)(1•1•12,125). In the structure of camaronesite (R_1 = 2.28% for 1138 F_o > 4σF), three types of Fe octahedra are linked by corner sharing with (PO_3OH) tetrahedra to form polyhedral layers perpendicular to c with composition [Fe^(3+)(H_2O)_2(PO_3OH)]. Two such layers are joined through SO_4 tetrahedra (in two half-occupied orientations) to form thick slabs of composition [Fe^(3+)(H_2O)_2(PO_3OH)]_2(SO_4). Between the slabs are partially occupied H_2O groups. The only linkages between the slabs are hydrogen bonds. The most distinctive component in the structure consists of two Fe octahedra linked to one another by three PO_4 tetrahedra yielding an [Fe_2(PO_4)_3] unit. This unit is also the key component in the sodium super-ionic conductor (NASICON) structure and has been referred to as the lantern unit. The polyhedral layers in the structure of camaronesite are similar to those in the structure of taranakite. The Raman spectrum exhibits peaks consistent with sulfate, phosphate, water and OH groups

Delimitation of Neonectria and Cylindrocarpon (Nectriaceae, Hypocreales, Ascomycota) and related genera with Cylindrocarpon-like anamorphs

Neonectria is a cosmopolitan genus and it is, in part, defined by its link to the anamorph genus Cylindrocarpon. Neonectria has been divided into informal groups on the basis of combined morphology of anamorph and teleomorph. Previously, Cylindrocarpon was divided into four groups defined by presence or absence of microconidia and chlamydospores. Molecular phylogenetic analyses have indicated that Neonectria sensu stricto and Cylindrocarpon sensu stricto are phylogenetically congeneric. In addition, morphological and molecular data accumulated over several years have indicated that Neonectria sensu lato and Cylindrocarpon sensu lato do not form a monophyletic group and that the respective informal groups may represent distinct genera. In the present work, a multilocus analysis (act, ITS, LSU, rpb1, tef1, tub) was applied to representatives of the informal groups to determine their level of phylogenetic support as a first step towards taxonomic revision of Neonectria sensu lato. Results show five distinct highly supported clades that correspond to some extent with the informal Neonectria and Cylindrocarpon groups that are here recognised as genera: (1) N. coccinea-group and Cylindrocarpon groups 1 & 4 (Neonectria/Cylindrocarpon sensu stricto); (2) N. rugulosa-group (Rugonectria gen. nov.); (3) N. mammoidea/N. veuillotiana-groups and Cylindrocarpon group 2 (Thelonectria gen. nov.); (4) N. radicicola-group and Cylindrocarpon group 3 (Ilyonectria gen. nov.); and (5) anamorph genus Campylocarpon. Characteristics of the anamorphs and teleomorphs correlate with the five genera, three of which are newly described. New combinations are made for species where their classification is confirmed by phylogenetic data