Empty Rows Research Articles

Mathematics Exploration Extant in The Checker Game: A Mathematics Teaching Contribution

Aversion to mathematics shown by learners belonging to different age stages, worries and challenges mathematicians and/ or mathematics teachers to develop surveys which might improve learners´ mathematics learnings. “Thawing” recondite mathematics in several games may aid to provide a different mathematics vision. The current research article aims to identify and analyze the “concealed” mathematics through checker games played in Angola, mostly in Cuando Cubango province. The survey is placed in ethnomathematics and considering its sorts, qualitative methodology has been used supported by a half-structured interview, direct observation to picture recording. The research was conducted in the Menongue municipality (Cuando Cubango capital city). The three versions of checkers games were described (12 by 12; 10 by 10 and 8 by 8), some questions were created that guided this investigation (Why does the structure of the checkers game have the same number of rows and columns? Why do players when placing checkers pieces in the middle always leave two empty rows? Why is the sum of rows and columns equal to the even number? Why is each painted square on the checkers board corresponds to an odd number?) and, finally, some mathematical concepts involved in that game were explored (such as, for example, the notion of the Cartesian plane, diagonal lines, distance between two points, median (element of Statistics), numbers even and odd).

"Henry V": A Report on the Condition of the World

The central interest of the paper is concentrated on an online production of Henry V in 2020. The project is based on a new Polish translation by Piotr Kamiński and produced by Dariusz Rosiak, a journalist, as one of his regular Reports on the Condition of the World published on YouTube. Realised as a reading performance by three actors in front of an empty row of chairs, the production brings an innovative and revealing interpretation of the play, breaking new ground in the Polish reception of Shakespeare’s histories. The paper offers a brief review of the presence of history plays in Polish reception and introductory information on Rosiak’s YouTube channel and Kamiński’s translation as a background to a critical analysis of the production and its relevance to the here and now of our world.

Factors Influencing Jajar Legowo Innovation Decisions: (Case Study Of Budi Sepakat Farmer Group, Koto Tangah District, Padang City)

This study aims to describe the diffusion of legowo jar innovation in the Budi Sepakat farmer group and find out the factors that influence the decision of legowo jajar innovation in the Budi Agree farmer group, Koto Tangah District, Padang City. This research method uses qualitative and descriptive quantitative with a case study approach in Budi Sepakat's farmer group. The analysis of the first objective data was carried out by interactive analysis of Miles and Huberman in [1] The data used in this study are primary data and secondary data. The results showed that the innovation of legowo rows is an innovation regarding rice planting spacing with alternating planting patterns between two or more rice planting rows and one empty row. The legowo jajar innovation was first introduced by the Department of Agriculture through the 2017 Penas event in Aceh. Communication runs smoothly with the communication channel used, namely interpersonal communication channels. This innovation was communicated in 2017 and implemented in 2021. This innovation does not oppose customs and culture and is fully supported by the community. The factors that influence farmers' decisions on legowo line innovation are the nature of successive innovations, namely: Compatibility, complexity, relative advantage, trialability, and observability. And factors that do not influence farmers' decisions on legowo line innovation are age, land area, and education.

1230. Identification of Subclinical Healthcare-Associated Clusters of Staphylococcus epidermidis in an Orthopedic Patient Population.

Abstract Background Prosthetic joint infections (PJIs) cause increased morbidity and mortality for patients. Staphylococcus epidermidis (S. epidermidis) can readily form biofilm on implanted medical devices, making this typically commensal species a common cause of PJIs. This study investigates genetic, epidemiologic, and environmental factors contributing to positive S. epidermidis joint cultures. Methods We identified S. epidermidis isolates from hip or knee cultures obtained between 2017-20 in patients with one or more prior corresponding intraarticular procedure at our hospital. Whole genome sequencing and single nucleotide polymorphism (SNP) based clonality analysis was performed using the epiXact® service at Day Zero Diagnostics, including species identification, in silico multi-locus sequence typing (MLST), phylogenomic analysis, along with genotypic assessment of the prevalence of specific antibiotic resistance and virulence genes. Additional epidemiologic review was performed to compare cluster and noncluster cases. Results Sixty phenotypically distinct S. epidermidis joint isolates were identified from 44 patients. After removal of duplicates and impure samples, 46 samples were used for genomic sequencing, and 45 were used for MLST. Four S. epidermidis strains showed phenotypic susceptibility to oxacillin yet harbored mecA, and two showed phenotypic resistance despite not having mecA (Figure 1). Notably, smr was found in all isolates. MupA positivity was not observed. We also identified six clonal clusters, all with SNP distances < 10 (Figure 2). Each cluster consisted of between 2-4 patients. Cluster isolates accounted for 14/45 (31.1%) of S. epidermidis isolates sequenced. Further epidemiologic investigation showed ties to common aspirations or operative procedures although no specific common source was identified. These subclinical clusters appear to be self-limited, suggesting benefit to common infection control practices. Phylogenetic tree of S. epidermidis population and heatmap showing the presence/absence of specific genomic features. Circle color on node tip corresponds to sequence type (MLST). Color strips (right panel) showing genomic feature (gene or marker) presence/absence inferred from WGS de novo assemblies. Green cells correspond to a full match found, and gray cells to no match found. Empty rows correspond to external reference genomes used as controls. *AMR: antimicrobial resistance; ST: sequence type; SNP distance values for all pairs of samples of matching multi-locus sequence types. Only samples belonging to matching multi-locus sequence types (MLSTs) with more than one sample are shown. Blue cells correspond to pairwise distance of < 25 SNPs indicating clonality. 13 isolates with unique MLSTs are not shown. 10 isolates were not included due to having multi-strain or multi-species contamination. *ST: sequence type; SNP: single-nucleotide polymorphism; Univariate analysis of clonal isolates versus non-clonal isolates. Samples not included in the multi-locus sequence type analysis due to contamination were excluded from the univariate analysis. *PJI: prosthetic joint infection; MSIS: Musculoskeletal Infection Society; Conclusion The majority of S. epidermidis isolated from clinical joint samples are diverse in origin, but we identified an important subset of 31% that belonged to subclinical healthcare-associated clusters. Clusters appeared to resolve spontaneously over time, suggesting benefit to routine infection control practices. Diagram of clonal isolate clusters Potential relationships and modes of transmission between clonal isolates in each cluster. *PJI: prosthetic joint infection; MSIS: Musculoskeletal Infection Society; SNP: single-nucleotide polymorphism; Disclosures Mohamad Sater, PhD, Day Zero Diagnostics: Employee|Day Zero Diagnostics: Stocks/Bonds Ian C. Herriott, Bachelor's of Science, Day Zero Diagnostics: Employee|Day Zero Diagnostics: Stocks/Bonds Miriam H. Huntley, PhD, Day Zero Diagnostics: Employee|Day Zero Diagnostics: Ownership Interest.

\u201cBlessed by the algorithm\u201d: Theistic conceptions of artificial intelligence in online discourse

“My first long haul flight that didn’t fill up and an empty row for me. I have been blessed by the algorithm ”.The phrase ‘blessed by the algorithm’ expresses the feeling of having been fortunate in what appears on your feed on various social media platforms, or in the success or virality of your content as a creator, or in what gig economy jobs you are offered. However, we can also place it within wider public discourse employing theistic conceptions of AI. Building on anthropological fieldwork into the ‘entanglements of AI and Religion’ (Singler 2017a), this article will explore how ‘blessed by the algorithm’ tweets are indicative of the impact of theistic AI narratives: modes of thinking about AI in an implicitly religious way. This thinking also represents continuities that push back against the secularisation thesis and other grand narratives of disenchantment that claim secularity occurs because of technological and intellectual progress. This article will also explore new religious movements, where theistic conceptions of AI entangle technological aspirations with religious ones.

Efficient use of sparsity by direct solvers applied to 3D controlled-source EM problems

Controlled-source electromagnetic (CSEM) surveying becomes a widespread method for oil and gas exploration, which requires fast and efficient software for inverting large-scale EM datasets. In this context, one often needs to solve sparse systems of linear equations with a large number of sparse right-hand sides, each corresponding to a given transmitter position. Sparse direct solvers are very attractive for these problems, especially when combined with low-rank approximations which significantly reduce the complexity and the cost of the factorization. In the case of thousands of right-hand sides, the time spent in the sparse triangular solve tends to dominate the total simulation time, and here we propose several approaches to reduce it. A significant reduction is demonstrated for marine CSEM application by utilizing the sparsity of the right-hand sides (RHS) and of the solutions that results from the geometry of the problem. Large gains are achieved by restricting computations at the forward substitution stage to exploit the fact that the RHS matrix might have empty rows (vertical sparsity) and/or empty blocks of columns within a non-empty row (horizontal sparsity). We also adapt the parallel algorithms that were designed for the factorization to solve-oriented algorithms and describe performance optimizations particularly relevant for the very large numbers of right-hand sides of the CSEM application. We show that both the operation count and the elapsed time for the solution phase can be significantly reduced. The total time of CSEM simulation can be divided by approximately a factor of 3 on all the matrices from our set (from 3 to 30 million unknowns, and from 4 to 12 thousands RHSs).

Coverage fluctuations in theater models

We introduce the theater model, which is the simplest variant of directed random sequential adsorption in one dimension with point source and steric interactions. Particles enter sequentially an initially empty row of L sites and adsorb irreversibly at randomly chosen places. If two particles occupy adjacent sites, they prevent further particles from passing them. A jammed configuration without available empty sites is eventually reached. More generally, we investigate the class of models parametrized by b, the number of consecutive particles needed to form a blockage. We show analytically that the occupations of different sites in jammed configurations exhibit long-range correlations obeying scaling laws, for all integers , so that the total number of particles grows as a subextensive power of L, with exponent , and keeps fluctuating even for very large systems. The exactly known relative number variance measuring this lack of self-averaging is maximal for the theater model stricto sensu (b = 2). In the special case where b = 1, so that each adsorbed particle is a blockage, the model can be mapped onto the statistics of records in sequences of random variables and of cycles in random permutations. A two-sided variant of the model is also considered. In both situations the number of particles grows only logarithmically with L, and it is self-averaging.

The Analysis of Logical Remainders in QCA: Common Practices and Extensions

Standard protocols in Qualitative Comparative Analysis (QCA) turn to counterfactual thinking to include logical remainders (the empty rows in a truth table) in the analysis of data. Portrayed as ap...

Sparse prefix sums: Constant-time range sum queries over sparse multidimensional data cubes

Prefix sums are a powerful technique to answer range-sum queries over multi-dimensional arrays in O(1) time by looking up a constant number of values in an array of size O(N), where N is the number of cells in the multi-dimensional array. However, the technique suffers from O(N) update and storage costs. Relative prefix sums address the high update costs by partitioning the array into blocks, thereby breaking the dependency between cells.In this paper, we present sparse prefix sums that exploit data sparsity to reduce the high storage costs of relative prefix sums. By building upon relative prefix sums, sparse prefix sums achieve the same update complexity as relative prefix sums. The authors of relative prefix sums erroneously claimed that the update complexity is O(N) for any number of dimensions. We show that this claim holds only for two dimensions, whereas the correct complexity for an arbitrary number of d dimensions is O(Nd−1d). To reduce the storage costs, the sparse prefix sums technique exploits sparsity in the data and avoids to materialize prefix sums for empty rows and columns in the data grid; instead, look-up tables are used to preserve constant query time. Sparse prefix sums are the first approach to achieve O(1) query time with sub-linear storage costs for range-sum queries over sparse low-dimensional arrays. A thorough experimental evaluation shows that the approach works very well in practice. On the tested real-world data sets the storage costs are reduced by an order of magnitude with only a small overhead in query time, thus preserving microsecond-fast query answering.

Biochar application for the improving soil fertility and paddy production on two systems of planting

A product of pyrolysis of residual biomass called biochar has several benefits into soil. Bio-charcoal formed by burning organic waste which will produce activated carbon and organic carbon and will be added to the soil. The purpose of this study was to evaluate biochar ability to improve soil fertility and increase the production of paddy crops with two planting systems. Legowo planting system is intermittent cropping between two or more rows of rice plants and one empty row. The research was conducted in Tanjung Garbus’s Village, Deli Serdang District with an elevation of ± 50 Meters above sea level. This research used a Factorial Split Plot Design with two factors that was treatment of planting systems as main plot (S), consist of 2 (two) stages: Jajar Legowo 2:1 and Jajar Legowo 4:1 and the sub-plot was biochar application (B) consisting of 3 levels namely, without biochar application, 25.5 ton/ha, and 50.5 ton/ha. The results showed that planting system significantly affected shoot wet weight and shoot dry weight and biochar application had a significant effect on shoot wet weight and no significant effect on shoot dry weight. The interaction showed no significant effect on all parameters.

Pengaruh Pola Tanam Terhadap Pertumbuhan Gulma dan Komponen Produksi Tanaman Padi Sawah (Oryza sativa L.)

The principle of planting system “Jajar Legowo” is to increase the plant population by adjusting the spacing so that the crop will have a row of plants interspersed by empty rows where the spacing is on the row of rows half the spacing between rows. The purpose of this study to investigate the effect of different rice cropping patterns on weed growth. The research was conducted at Gampong Lhok Iboh, Baktiya district Barat North Aceh Regency started from March to June 2017. This research used non factorial Randomized Block Design which consists factor with 2 treatments: P1 (conventional cropping pattern) and P2 (jajar legowo). Observations included the amount of dominance (%), plant height (cm), number of tillers, panicle length, number of grains per panicle, and weight of 1000 grains per plot. The results revealed that cropping pattern had an effect on weed growth and production component of paddy. Planting system “jajar legowo” 2: 1 (25cm x 25 cm x 40 cm) was much better compared to conventional cropping pattern

Atomic-Scale Structural Evolution of Rh(110) during Catalysis

We report direct observation at the atomic scale of the pressure- and temperature-dependent evolution of a model Rh(110) catalyst surface during transient and steady-state CO oxidation, using high-pressure scanning tunneling microscopy (HP-STM) and ambient-pressure X-ray photoelectron spectroscopy (AP-XPS) correlated against density functional theory (DFT) calculations. Rh(110) is susceptible to the well-known missing row (MR) reconstruction. O2 dosing produces a MR structure and an O coverage of 1/2 monolayer (ML), the latter limited by the kinetics of O2 dissociation. In contrast, CO dosing retains the (1 × 1) structure and a CO coverage of 1 ML. We show that CO dosing titrates O from the (2 × 1) structure and that the final surface state is a strong function of temperature. Adsorbed CO accelerates and O inhibits the (2 × 1) to (1 × 1) transition, an effect that can be traced to the influence of the adsorbates on the energy landscape for moving metal atoms from filled to empty rows. During simultaneous ...

Overwintering grass-clover as intercrop and moderately reduced nitrogen fertilization maintain yield and reduce the risk of nitrate leaching in an organic cauliflower (Brassica oleracea L. var. botrytis) agroecosystem

Cauliflower (Brassica oleracea L. var. botrytis) has high nitrogen (N) demand during growing, but due to its low N use efficiency and N-rich residues, it may cause N losses by leaching after harvest. A field experiment was conducted to investigate the effect of overwintering grass-clover as an intercrop and moderately reduced N fertilization on organic cauliflower yield and risk of nitrate leaching. The experiment tested sole-cropped (S) and intercropped (I) systems using a substitution design and two N fertilizer rates (180 and 230kgNha−1). To investigate the competition between cauliflower and grass-clover, cauliflower grown alone with empty grass-clover rows (Semp) and grass-clover grown alone with empty cauliflower rows (GCemp) were included. The results showed that marketable yield was maintained in the I system compared to in the S system when calculated per meter crop row, and when N fertilization was moderately reduced. The Relative Competition Index (RCI) values in the I system were lower than 0, indicating that cauliflower growth was not interfered in the I system. The ability for aboveground N accumulation in the S and I systems was similar, but the N content of cauliflower residues in the S system was 33 and 23kgha−1 higher than in the I system in 2012 and 2013, respectively. The S system had 168kgNinorgha−1 in the soil layer of 0–1.5m at the start of leaching in 2013, which was 40kgNha−1 higher than the I system. Reduced N fertilizer level led to 22kgha−1 lower soil Ninorg at the end of leaching. However, the effect of system and N level on soil residual Ninorg per unit marketable yield was not significantly different. Intercropping cauliflower with overwintering grass-clover and moderately reduced N fertilization was feasible in organic cauliflower production, with regard to maintaining marketable yield and reducing the risk of nitrate leaching in the agroecosystem.

Vietnam: A Medical Mission Diary

“Good Morning Vietnam!” I sip a chocolate mocha while gazing out French windows at a steamy Saigon street. Honestly? The chocolate mocha is instant, and the French panes are fake. I am one of 30 weary souls who traveled 27 hours with 30 suitcases of cardiac devices, equipment, and medications. Airline food was miso, fish, and dragon fruit (no wonder we saw little obesity in Asia). Three of us secured empty rows and stretched out like cats. No amount of money can buy a good night’s rest. Today we bring feeding tubes to orphans with cleft palates. If a mother in Vietnam delivers a disabled baby, there are no handouts except to orphanages. How sad that mothers are forced to allow strangers to raise their children (Figure 1). Molly B. Delaney, Member, Twin Cities Chapter 155, is ED Nurse Manager, Emergency Department, East Bank, University of Minnesota Medical Center, Minneapolis, MN.

Major index for 01-fillings of moon polyominoes

We propose a major index statistic on 01-fillings of moon polyominoes which, when specialized to certain shapes, reduces to the major index for permutations and set partitions. We consider the set F ( M , s ; A ) of all 01-fillings of a moon polyomino M with given column sum s whose empty rows are A, and prove that this major index has the same distribution as the number of north–east chains, which are the natural extension of inversions (resp. crossings) for permutations (resp. set partitions). Hence our result generalizes the classical equidistribution results for the permutation statistics inv and maj. Two proofs are presented. The first is an algebraic one using generating functions, and the second is a bijection on 01-fillings of moon polyominoes in the spirit of Foata's second fundamental transformation on words and permutations.

Structure and magnetic properties ofMn∕Pt(110)−(1×2): A joint x-ray diffraction and theoretical study

The growth of a Mn submonolayer on $\mathrm{Pt}(110)\text{\ensuremath{-}}(1\ifmmode\times\else\texttimes\fi{}2)$ was studied by surface x-ray diffraction. At room temperature, Mn fills in the empty rows of the clean substrate's missing row structure. At a coverage of 0.5 ML (monolayer), a $(1\ifmmode\times\else\texttimes\fi{}2)$ surface alloy is formed, with alternating Pt and Mn dense rows. Upon annealing (or depositing at a substrate temperature of about $570\phantom{\rule{0.3em}{0ex}}\mathrm{K}$), another surface alloy forms with a $(2\ifmmode\times\else\texttimes\fi{}1)$ symmetry. It exhibits mixed dense rows where Pt and Mn sites alternate, as in bulk ${\mathrm{Pt}}_{3}\mathrm{Mn}$. The top layer is corrugated for both the $(1\ifmmode\times\else\texttimes\fi{}2)$ and $(2\ifmmode\times\else\texttimes\fi{}1)$ surfaces, with Mn lying $0.19\ifmmode\pm\else\textpm\fi{}0.03$ and $0.16\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ above the Pt site, respectively. A ${\mathrm{Pt}}_{3}\mathrm{Mn}$-like slab forms when annealing a 3-ML-thick Mn film. The observed symmetries are at variance with the NiMn and CuMn surfaces where $c(2\ifmmode\times\else\texttimes\fi{}2)$ arrangements were found. Theoretical calculations were performed for $(1\ifmmode\times\else\texttimes\fi{}2)$, $c(2\ifmmode\times\else\texttimes\fi{}2)$, and $(2\ifmmode\times\else\texttimes\fi{}1)$ PtMn two-dimensional (2D) alloys on Pt(110). Among them, the latter was found to be the ground state. Both the $(1\ifmmode\times\else\texttimes\fi{}2)$ and $(2\ifmmode\times\else\texttimes\fi{}1)$ surface alloys form antiferromagnetic (AF) Mn chains running in the $[1\overline{1}0]$ and [001] directions, respectively. The ordering within the surface layer switches to ferromagnetic (F) for a 5-ML-thick ${\mathrm{Pt}}_{3}\mathrm{Mn}(110)$ film albeit with a surface structure quite identical to the $(2\ifmmode\times\else\texttimes\fi{}1)$ 2D case. The magnetic moment per Mn atom at the surface is close to $4\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{B}$, in all cases, among the largest values ever found in similar metal-Mn surface alloys: it is directly related to the surface corrugation and to the Mn volume as already observed for other Mn-based surface alloys. The magnetic order, F or AF, is strongly influenced by the local chemical environment of the Mn sites.

On avoiding odd partial Latin squares and r-multi Latin squares

We show that for any positive integer k ⩾ 4 , if R is a ( 2 k - 1 ) × ( 2 k - 1 ) partial Latin square, then R is avoidable given that R contains an empty row, thus extending a theorem of Chetwynd and Rhodes. We also present the idea of avoidability in the setting of partial r-multi Latin squares, and give some partial fillings which are avoidable. In particular, we show that if R contains at most nr / 2 symbols and if there is an n × n Latin square L such that δ n of the symbols in L cover the filled cells in R where 0 < δ < 1 , then R is avoidable provided r is large enough.

Routing vertex disjoint Steiner-trees in a cubic grid and connections to VLSI

Consider a planar grid of size w × n . The vertices of the grid are called terminals and pairwise disjoint sets of terminals are called nets. We aim at routing all nets in a cubic grid (above the original grid holding the terminals) in a vertex-disjoint way. However, to ensure solvability, it is allowed to extend the length and the width of the original grid to w ′ = sw and n ′ = sn by introducing s - 1 pieces of empty rows and columns between every two consecutive rows and columns containing the terminals. Hence the routing is to be realized in a cubic grid of size ( s · n ) × ( s · w ) × h . The objective is to minimize the height h. It is easy to show that the required height can be as large as h = Ω ( max ( n , w ) ) in the worst case. In this paper we show that if s ≥ 2 then a routing with height h = 6 max ( n , w ) can always be found in polynomial time. Furthermore, the constant factor ‘6’ can be improved either by increasing the value of s or by limiting the number of terminals in a net. Possible trade-offs between s and h are discussed and the various constructions presented are compared by measuring the volumes of the routings obtained.

Utility of indirect and direct selection traits for improving Striga resistance in two sorghum recombinant inbred populations

Breeding of sorghum ( Sorghum bicolor L. Moench) for resistance to the parasitic weed Striga hermonthica (Del.) Benth. has been hampered by the difficulty of evaluating host resistance in the field and lack of reliable screening techniques. Therefore, we investigated the value of various indirect and direct measures of Striga resistance as selection traits. Two sorghum recombinant inbred populations of 226 F 3:5 lines each were developed from the crosses (1) IS 9830×E 36-1 and (2) N 13×E 36-1. Striga-resistant line IS 9830 is characterized by low stimulation of Striga seed germination, whereas Striga-susceptible line E 36-1 produces germination stimulants in abundance. Line N 13 possesses “mechanical” resistance and probably also an antibiosis mechanism. Resistance was assessed in 1997 and 1998 using in vitro agar-gel assays with Striga seeds from Kenya, Mali, and Niger, pot trials in the respective three countries, and field experiments in Kenya and Mali. The agar-gel assay proved to be a useful, precise and fast indirect selection method to screen for sorghum entries with the low-stimulant character. However, correlation analysis showed that this resistance mechanism was ineffective in some environments, especially in Kenya, pointing to the necessity of field evaluation. Because of low heritability estimates and moderate to low correlations to Striga resistance under field conditions, pot screening appeared to be of limited use in breeding programs. The field trials confirmed the effectiveness of several direct measures of Striga resistance in sorghum: emerged Striga counts, Striga severity index, and area under the Striga number or severity progress curves. A two-row plot field layout with an empty row between plots, coupled with artificial infestation of test rows, lattice design and six replications offered an improved screening procedure that achieved high heritability. Significant genotype×environment interactions in the field experiments stress the importance of multi-locational trials to achieve stable Striga resistance.

Patterning of Si(001) with halogens: Surface structure as a function of the halogen chemical potential

Chlorine- and bromine-chemisorbed Si(001) surfaces at various coverages $(\ensuremath{\theta})$ are studied using first-principles density functional calculations. Different stable reconstructions are obtained for the two halogen species. At $\ensuremath{\theta}=0.5,$ Br stabilizes a $c(4\ifmmode\times\else\texttimes\fi{}2)$ reconstruction with adatoms only on next-nearest neighbor dimers, whereas Cl stabilizes a $p(4\ifmmode\times\else\texttimes\fi{}2)$ structure with alternating fully chlorinated and empty dimer rows. At $\ensuremath{\theta}=1,$ a $3\ifmmode\times\else\texttimes\fi{}2$ reconstruction consisting of dimer rows separated by missing atom rows is most stable for Br, whereas for Cl such a structure is degenerate with the conventional $2\ifmmode\times\else\texttimes\fi{}1$ reconstruction. These findings are in agreement with recent scanning tunneling microscopy experiments. They can be rationalized on the basis of a stronger steric hindrance for Br.