Start Point Research Articles

Surgical Tattoos in Infrared: A Dataset for Quantifying Tissue Tracking and Mapping.

Quantifying performance of methods for tracking and mapping tissue in endoscopic environments is essential for enabling image guidance and automation of medical interventions and surgery. Datasets developed so far either use rigid environments, visible markers, or require annotators to label salient points in videos after collection. These are respectively: not general, visible to algorithms, or costly and error-prone. We introduce a novel labeling methodology along with a dataset that uses said methodology, Surgical Tattoos in Infrared (STIR). STIR has labels that are persistent but invisible to visible spectrum algorithms. This is done by labelling tissue points with IR-fluorescent dye, indocyanine green (ICG), and then collecting visible light video clips. STIR comprises hundreds of stereo video clips in both in vivo and ex vivo scenes with start and end points labelled in the IR spectrum. With over 3,000 labelled points, STIR will help to quantify and enable better analysis of tracking and mapping methods. After introducing STIR, we analyze multiple different frame-based tracking methods on STIR using both 3D and 2D endpoint error and accuracy metrics. STIR is available at https://dx.doi.org/10.21227/w8g4-g548.

A topical reappreasal on use of repetitive Transcranial Magnetic Stimulation in elderly patients with postischemic stroke statuses - a systematic literature review

Abstract: Introduction: Stroke is a cerebrovascular disease with an impressive potential of disabil-ity, (multi)morbidity, and mortality among elderly patients. After stroke, a series of seque-lae represents a dynamic challenge for rehabilitation, especially for improving motor, cognitive and depressive disorders (1,2). Repetitive Transcranial Magnetic Stimulation (rTMS) is a non-invasive, painless, neuromodulations and neurostimulation method, which uses electromagnetic induction to administer repeated trains of pulses, with thera-peutic, diagnostic and research purposes (3–5). Method: We performed a systematic literature review of the related literature using a widely international accepted method - Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA)(6), by searching, filtering, and selecting profile documen-tary material. Combinations/syntaxes of keywords were searched in the following interna-tional databases: Elsevier(7), PubMed(8), PMC(9), PEDro(10), in ISI indexed journals by Web of Knowledge/Science(11) during 1/01/2019-31/12/2021. Besides the 9 articles selected to enhance our related knowledge base we have also used some works freely identified in the literature. Results and discussions: 9 articles satisfied all the previous filtering criteria/ PRISMA steps and were selected for qualitative and detailed analysis. The benefits of rTMS, aiming to bring further insight into the responsiveness of motor deficit, depression, and cognitive impairment of the treatment, and through the favorable dynamic progress of the scores of the quantification scales used: HAMD-17/ HDRS, Hamilton Depression Scale; MMSE, Mini-Mental State Examination; MoCA, Montreal Cognitive Assesment; SCWT, Stroop Color-Word Interference Test; WAIS, Wechsler Adult Intelligence Scale; NIHSS, National Institutes of Health Stroke Scale; Barthel Index Score; ADL, Activities of Daily Living; mRS, modified Rankin Scale; FIM, Functional Independence Measures. Conclusions: Through this systematic review, we wish to present the perspective of the successful use of rTMS among elderly patients. We also intend for this work to be the start-ing point in the development of a doctoral study, which will include post-stroke sequelae, such as motor deficits, depressive and cognitive disorders, and through which we will strengthen scientific confidence in the tolerability and effectiveness of this type of stimula-tion for this segment of age.

ANDClust: An Adaptive Neighborhood Distance‐Based Clustering Algorithm to Cluster Varying Density and/or Neck‐Typed Datasets

AbstractAlthough density‐based clustering algorithms can successfully define clusters in arbitrary shapes, they encounter issues if the dataset has varying densities or neck‐typed clusters due to the requirement for precise distance parameters, such as eps parameter of DBSCAN. These approches assume that data density is homogenous, but this is rarely the case in practice. In this study, a new clustering algorithm named ANDClust (Adaptive Neighborhood Distance‐based Clustering Algorithm) is proposed to handle datasets with varying density and/or neck‐typed clusters. The algorithm consists of three parts. The first part uses Multivariate Kernel Density Estimation (MulKDE) to find the dataset's peak points, which are the start points for the Minimum Spanning Tree (MST) to construct clusters in the second part. Lastly, an Adaptive Neighborhood Distance (AND) ratio is used to weigh the distance between the data pairs. This method enables this approach to support inter‐cluster and intra‐cluster density varieties by acting as if the distance parameter differs for each data of the dataset. ANDClust is tested on synthetic and real datasets to reveal its efficiency. The algorithm shows superior clustering quality in a good run‐time compared to its competitors. Moreover, ANDClust could effectively define clusters of arbitrary shapes and process high‐dimensional, imbalanced datasets may have outliers.

Boronic acid inhibitors of penicillin-binding protein 1b: serine and lysine labelling agents

Penicillin-binding proteins (PBPs) contribute to bacterial cell wall biosynthesis and are targets of antibacterial agents. Here, we investigated PBP1b inhibition by boronic acid derivatives. Chemical starting points were identified by structure-based virtual screening and aliphatic boronic acids were selected for further investigations. Structure–activity relationship studies focusing on the branching of the boron-connecting carbon and quantum mechanical/molecular mechanical simulations showed that reaction barrier free energies are compatible with fast reversible covalent binding and small or missing reaction free energies limit the inhibitory activity of the investigated boronic acid derivatives. Therefore, covalent labelling of the lysine residue of the catalytic dyad was also investigated. Compounds with a carbonyl warhead and an appropriately positioned boronic acid moiety were shown to inhibit and covalently label PBP1b. Reversible covalent labelling of the catalytic lysine by imine formation and the stabilisation of the imine by dative N–B bond is a new strategy for PBP1b inhibition.

Systematic Analysis of the MIO-forming Residues of Aromatic Ammonia Lyases.

Aromatic ammonia lyases (AALs) and tyrosine/phenylalanine ammonia mutases (TAM/PAM) are 3,5-dihydro-5-methylidene-4H-imidazol-4-one (MIO)-dependent enzymes. Usually, the MIO moiety is autocatalytically formed from the tripeptide Ala-Ser-Gly (ASG) and acts as an electrophile during the enzymatic reaction. However, the MIO-forming residues (ASG) have some diversity in this enzyme class. In this work, a systematic investigation on the variety of MIO-forming residues was carried out using in-depth sequence analyses. Several protein clusters of AAL-like enzymes with unusual MIO-forming residues such as ACG, TSG, SSG, and CSG were identified, including two novel histidine ammonia lyases and one PAM with CSG and TSG residues, respectively, as well as three novel ergothioneine trimethylammonia lyases without MIO motif. The mutagenesis of common MIO-groups confirmed the function of these MIO variants, which provides good starting points for future functional prediction and mutagenesis research of AALs.

Development of an Artificial Intelligence-Based Image Recognition System for Time-Sequence Analysis of Tracheal Intubation.

Total intubation time (TIT) is an objective indicator of tracheal intubation (TI) difficulties. However, large variations in TIT because of diverse initial and end targets make it difficult to compare studies. A video laryngoscope (VLS) can capture images during the TI process. By using artificial intelligence (AI) to detect airway structures, the start and end points can be freely selected, thus eliminating the inconsistencies. Further deconstructing the process and establishing time-sequence analysis may aid in gaining further understanding of the TI process. We developed a time-sequencing system for analyzing TI performed using a #3 Macintosh VLS. This system was established and validated on 30 easy TIs performed by specialists and validated using TI videos performed by a postgraduate-year (PGY) physician. Thirty easy intubation videos were selected from a cohort approved by our institutional review board (B-ER-107-088), and 6 targets were labeled: the lip, epiglottis, laryngopharynx, glottic opening, tube tip, and a black line on the endotracheal tube. We used 887 captured images to develop an AI model trained using You Only Look Once, Version 3 (YOLOv3). Seven cut points were selected for phase division. Seven experts selected the cut points. The expert cut points were used to validate the AI-identified cut points and time-sequence data. After the removal of the tube tip and laryngopharynx images, the durations between 5 identical cut points and sequentially identified the durations of 4 intubation phases, as well as TIT. The average and total losses approached 0 within 150 cycles of model training for target identification. The identification rate for all cut points was 92.4% (194 of 210), which increased to 99.4% (179 of 180) after the removal of the tube tip target. The 4 phase durations and TIT calculated by the AI model and those from the expert exhibited strong Pearson correlation (phase I, r = 0.914; phase II, r = 0.868; phase III, r = 0.964; and phase IV, r = 0.949; TIT, r = 0.99; all P < .001). Similar findings were obtained for the PGY's observations (r > 0.95; P < .01). YOLOv3 is a powerful tool for analyzing images recorded by VLS. By using AI to detect the airway structures, the start and end points can be freely selected, resolving the heterogeneity resulting from the inconsistencies in the TIT cut points across studies. Time-sequence analysis involving the deconstruction of VLS-recorded TI images into several phases should be conducted in further TI research.

Partitioning climate uncertainty in ecological projections: Pacific oysters in a hotter Europe

Projections of the range expansions of marine species are critical if we are to anticipate and mitigate the impacts of climate change on marine ecosystems. However, most projections do not assess the level of uncertainty of future changes, which brings their usefulness for scenario planning and ecosystem management into question. For the overall climate system, these uncertainties take three forms: scenario uncertainty, climate model uncertainty and internal climate variability. Critically, internal variability, a measure of how natural variability affects future climate projections, has largely been ignored in ecological studies. Here we use an ensemble modelling approach for the non-native Pacific oyster in Europe to understand the impact of these uncertainties. Future Pacific oyster recruitment was projected using a model that relates recruitment to cumulative and instantaneous heat exposure. Model projections were carried out for four climate change scenarios: SSP1 2.6, SSP2 4.5, SSP3 7.0 and SSP5 8.5. In each scenario an ensemble of over twenty climate models was used. The impact of internal variability in climate models was assessed by using five climate models which were available with multiple pre-industrial starting points. We find that model uncertainty within SSP1 2.6 is higher than the differences between SSP1 2.6 and SSP 4.5, but it is unclear if overall scenario uncertainty is greater than climate model uncertainty due to its subjective nature. Comparisons of scenario projections indicate that future recruitment areas of Pacific oysters under the SSP5 8.5 scenario could be more than twice as high as in the low emissions SSP1 2.6 scenario. Importantly, the ensemble showed that near-term changes in Pacific oysters are highly uncertain due to internal variability, which is of a similar magnitude to climate model uncertainty on a 20-year timescale. Our results show that it is critical to think about the future in terms of potential scenarios and not individual projections.

BI-RRT*: An improved path planning algorithm for secure and trustworthy mobile robots systems

The optimal RRT in elliptic space sampling (Informed-RRT*) is an extension of RRT that provides asymptotic optimality, however, it experiences gradual progress and close to obstacles. In the paper, we propose a novel path planning algorithm guided bidirectional Informed-RRT* (BI-RRT*), that introduces extension range, dual-direction exploration, and refinement in trajectory design. The growth range refers to maintaining an additional area from the obstacle to enhance the dependability of the path through preventing impacts. Bidirectional search is a search strategy using both start and target points for a initial solution. Smoothing improves path robustness by using cubic spline. Furthermore, simulation tests for the BI-RRT* algorithm are executed, and the efficacy of the suggested algorithm is confirmed through its application in a robot operating system (ROS). Simulations and experimental tests verify that the proposed algorithm improves the path planning capability. We emphasize the importance of safety, privacy, and reliability in the deployment of AI systems. Our algorithm ensures that the planned paths maintain a safe distance from obstacles, reducing the risk of collisions. Additionally, we prioritize privacy by adhering to data protection regulations and implementing secure communication protocols within the AI system. Moreover, we have applied rigorous testing and validation processes to enhance the reliability of our algorithm, ensuring consistent and accurate path planning outcomes.

Identification of small-molecule binding sites of a ubiquitin-conjugating enzyme-UBE2T through fragment-based screening.

UBE2T is an attractive target for drug development due to its linkage with several types of cancers. However, the druggability of ubiquitin-conjugating E2 (UBE2T) is low because of the lack of a deep and hydrophobic pocket capable of forming strong binding interactions with drug-like small molecules. Here, we performed fragment screening using 19 F-nuclear magnetic resonance (NMR) and validated the hits with 1 H-15 N-heteronuclear single quantum coherence (HSQC) experiment and X-ray crystallographic studies. The cocrystal structures obtained revealed the binding modes of the hit fragments and allowed for the characterization of the fragment-binding sites. Further screening of structural analogues resulted in the identification of a compound series with inhibitory effect on UBE2T activity. Our current study has identified two new binding pockets in UBE2T, which will be useful for the development of small molecules to regulate the function of this protein. In addition, the compounds identified in this study can serve as chemical starting points for the development of UBE2T modulators.

Sensitivity Analysis of Start Point of Extreme Daily Rainfall Using CRHUDA and Stochastic Models

Forecasting extreme precipitation is one of the basic actions of warning systems in Latin America and the Caribbean (LAC). With thousands of economic losses and severe damage caused by floods in urban areas, hydrometeorological monitoring is a priority in most countries in the LAC region. The monitoring of convective precipitation, cold fronts, and hurricane tracks are the most demanded technological developments for early warning systems in the region. However, predicting and forecasting the onset time of extreme precipitation is a subject of life-saving scientific research. Developed in 2019, the CRHUDA (Crossing HUmidity, Dew point, and Atmospheric pressure) model provides insight into the onset of precipitation from the Clausius–Clapeyron relationship. With access to a historical database of more than 600 storms, the CRHUDA model provides a prediction with a precision of six to eight hours in advance of storm onset. However, the calibration is complex given the addition of ARMA(p,q)-type models for real-time forecasting. This paper presents the calibration of the joint CRHUDA+ARMA(p,q) model. It is concluded that CRHUDA is significantly more suitable and relevant for the forecast of precipitation and a possible future development for an early warning system (EWS).

Formation of tourism law in Slovakia and some of its divergences in relation to Czech law

Attempts to codify the issue of tourism appeared in Slovakia and the Czech Republic almost simultaneously with attempts to formulate and follow a purposeful state policy in this area. We can trace this effort in Slovakia to the years of the Second World War, while in the Czechoslovak context it was connected to the previous pre-war period. Just as there are common starting points, the same are the decisive stimuli that led to the initiation of the process of gradual legal regulation of tourism in the 1990s. Given the initially identical legal starting points and the same social challenges and needs, the observed development reached remarkably different results in both countries, not only in terms of the quantity and complexity of legislation, but the differences are noticeable even deeper, already in the formulation of state interests and goals in this promising economic sector. The paper tries to define the entirety of tourism law, characterize its current form in Slovakia and indicate the reasons for the divergent development in both countries.

Creating inspiration by developing digital mood boards in student teams

Mood boards have notable potential to serve as inspirational tools in design. However, we still do not fully understand how mood boards are created utilizing material found online in collaborative educational settings. The purpose of our study is to deepen our understanding of both team design and the creation of shared digital mood boards through a qualitative analysis on how three student teams created shared mood boards using computers, and how they gathered inspirational material from the Web. We discuss how the creation of a shared mood board is a complex process, including deepening and broadening cycles, where a key idea is either explained more thoroughly, or then expanded with additional, related ideas. In relation to mood board ideas, the teams decided the specific keywords to be used to gather images online, balancing the design constraints, with an intuitive yet systematic way of working. We encourage to acknowledge a digitally created mood board as a collaborative method for creating meaningful starting points for designing, and for finding inspiration outside the direct design problem. Our study provides information which is beneficial for developing pedagogies that include collaboration and the use of online inspirational material.Keywords: team ideation; mood board; sources of inspiration; online material; metaphor; design education

Combined In-Solution Fragment Screening and Crystallographic Binding-Mode Analysis with a Two-Domain Hsp70 Construct.

Heat shock protein 70 (Hsp70) isoforms are key players in the regulation of protein homeostasis and cell death pathways and are therefore attractive targets in cancer research. Developing nucleotide-competitive inhibitors or allosteric modulators, however, has turned out to be very challenging for this protein family, and no Hsp70-directed therapeutics have so far become available. As the field could profit from alternative starting points for inhibitor development, we present the results of a fragment-based screening approach on a two-domain Hsp70 construct using in-solution NMR methods, together with X-ray-crystallographic investigations and mixed-solvent molecular dynamics simulations. The screening protocol resulted in hits on both domains. In particular, fragment binding in a deeply buried pocket at the substrate-binding domain could be detected. The corresponding site is known to be important for communication between the nucleotide-binding and substrate-binding domains of Hsp70 proteins. The main fragment identified at this position also offers an interesting starting point for the development of a dual Hsp70/Hsp90 inhibitor.

Development and implementation of Concept-Test questions in abstract algebra

In tertiary mathematics courses, students often have difficulties acquiring an understanding of the mathematical concepts covered. One approach to address this problem is to implement so-called Concept-Tests. These are multiple-choice questions whose distractors represent common problems and misconceptions related to the concepts. While there exist lots of such questions for calculus, Concept-Test questions focusing on basic concepts of abstract algebra are still rare, although previous research has shown that students have many problems with these. We therefore developed such questions for important concepts of basic group and ring theory in the years 2020–2022. In this paper, we first want to present the questions and the developmental process. Furthermore, we want to present an empirical study investigating to what extent the questions helped students in a proof-oriented abstract algebra course to acquire an understanding of the concepts covered. This study especially indicates that the developed Concept-Test questions provided good starting points for conceptual changes.

Thermodynamics and electronic structure of adsorbed and intercalated plumbene in graphene/hexagonal SiC heterostructures

Graphene-covered hexagonal SiC substrates have been frequently discussed to be appropriate starting points for epitaxial overlayers of Xenes, such as plumbene, or even their deposition as intercalates between graphene and SiC. Here, we investigate, within density functional theory, the plumbene deposition for various layer orderings and substrate terminations. By means of total energy studies we demonstrate the favorization of the intercalation versus the epitaxy for both C-terminated and Si-terminated 4H-SiC substrates. These results are explained in terms of chemical bonding and by means of layer-resolved projected band structures. Our results are compared with available experimental findings.

Path planning for robots in preform weaving based on learning from demonstration

AbstractA collision-free path planning method is proposed based on learning from demonstration (LfD) to address the challenges of cumbersome manual teaching operations caused by complex action of yarn storage, variable mechanism positions, and limited workspace in preform weaving. First, by utilizing extreme learning machines (ELM) to autonomously learn the teaching data of yarn storage, the mapping relationship between the starting and ending points and the teaching path points is constructed to obtain the imitation path with similar storage actions under the starting and ending points of the new task. Second, an improved rapidly expanding random trees (IRRT) method with adaptive direction and step size is proposed to expand path points with high quality. Finally, taking the spatical guidance point of imitation path as the target direction of IRRT, the expansion direction is biased toward the imitation path to obtain a collision-free path that meets the action yarn storage. The results of different yarn storage examples show that the ELM-IRRT method can plan the yarn storage path within 2s–5s when the position of the mechanism changes in narrow spaces, avoiding tedious manual operations that program the robot movements, which is feasible and effective.

Connecting an Offshore Dry Air Stratospheric Intrusion with the Outbreak of Soberanes Fire 2016

Abstract This study investigates the connection between the arrival of dry stratospheric air and the Soberanes Fire (2016). The Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT) and Goddard Earth Observing System Forward Processing model (GEOS-FP) are used for back-trajectories and offshore deep stratospheric intrusion in conjunction with the ignition and outbreak of the fire. The back-trajectory analysis indicates that most air reaching the vertical column was critically dry, exhibiting relative humidity values below 10%. As the fire ignited, dry air arrived from due west at heights of 1–3 km about 24 h prior. During the overnight fire growth, dry air arrived from the northwest to north-northwest at heights of 3.5–5.5 km 48–72 h prior. The synoptic and GEOS-FP analyses demonstrate offshore mid-to-low stratospheric intrusion. On 21 July 2016, an enclosed upper-level low approached the California–Oregon border along the northwesterly subtropical jet stream hours before the fire outbreak. The GEOS-FP results of potential vorticity, specific humidity, and ozone along the back-trajectories to the west and northwest of the fire suggest a stratospheric intrusion event into the mid-to-low troposphere at the back-trajectory start points, and vertical velocity indicates sinking motion. The specific humidity analyzed at the arrival time shows the transport of the abnormally dry air to the Soberanes Fire. Results suggest a connection between dry stratospheric air transported to the Soberanes Fire at ignition and overnight accelerated growth, supported by a dark bank in satellite water vapor imagery. The prediction of low-level transport of dry stratospheric air to the coastal communities could help to predict the occurrence of wildfire outbreaks, or periods of accelerated fire growth.

A Modified Approach to the Rack Generation of Beveloid Gears

The purpose of this paper is to present an easier and more efficient method for the determination of the geometry of a bevelled gear tooth. Based on a method that provides an easier way for the rack generation of involute helical gears, the mathematical model of a beveloid gear is studied. The mathematical procedure for developing two-dimensional cross-sections has been extended to three-dimensional gear models. A computer programme is developed to obtain generating and generated surfaces. The proposed algorithm is compared with the previous studies for verification and validation. The results demonstrate that the coordinates obtained from the given method are nearly the same on the start and end points of the main gear parts, such as the involute and root fillets regions. Also, between the limits, the values can be considered acceptable. A coordinate deviation of the gear profile has been observed in the mathematical model, because of the profile shift. Modifications have been developed in the equations to eliminate these cases. The main advantage of the proposed method is to obtain mathematical models without carrying out some of the calculation steps used in previous studies. Eventually, this feature will provide an easier and faster method to develop computer-aided models of the beveloid gear types.

Development of Location-Data-Based Orchard Passage Map Generation Method

Currently, pest control work using speed sprayers results in increasing numbers of safety accidents such as worker pesticide poisoning and rollover of vehicles during work. To address this, there is growing interest in autonomous driving technology for speed sprayers. To commercialize and rapidly expand the use of self-driving speed sprayers, an economically efficient self-driving speed sprayer using a minimum number of sensors is essential. This study developed an orchard passage map using location data acquired from positioning sensors to generate autonomous driving paths, without installing additional sensors. The method for creating the orchard passage map presented in this study was to create paths using location data obtained by manually driving the speed sprayer and merging them. In addition, to apply the orchard passage map when operating autonomously, a method is introduced for generating an autonomous driving path for the work start point movement path, work path, and return point movement path.

Path Planning in a Weighted Planar Subdivision Under the Manhattan Metric

In this paper, we consider the problem of path planning in a weighted polygonal planar subdivision. Each polygon has an associated positive weight which shows the cost of path per unit distance of movement in that polygon. The goal is to find a minimum cost path under the Manhattan metric for two given start and destination points. First, we propose an O(n2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^2)$$\\end{document} time and space algorithm to solve this problem, where n is the total number of vertices in the subdivision. Then, we improve the time and space complexity of the algorithm to O(nlog2n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n \\log ^2 n)$$\\end{document} and O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n \\log n)$$\\end{document}, respectively, by applying a divide and conquer approach. We also study the case of rectilinear regions in three dimensions and show that the minimum cost path under the Manhattan metric is obtained in O(n2log3n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ O(n^2 \\log ^3 n) $$\\end{document} time and O(n2log2n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ O(n^2 \\log ^2 n) $$\\end{document} space.