Maximum Distance Research Articles

An almost sure limit theorem for the maximum interpoint distance of random vectors in spaces of growing dimension

Let { p n ; n ≥ 1 } be a sequence of positive integers. Let X 1 , … , X p n be i.i.d. random vectors in ℝ n with i.i.d. components that are centered and have variance 1. Consider the maximum interpoint distance M n = max 1 ≤ i < j ≤ p n ‖ X i − X j ‖ 2 . This article presents the almost sure limit theorem for M n under the polynomial and the exponential growth regimes for the dimension. The proofs rely on the moderate deviation principle of the partial sum of i.i.d. random variables, the Chen–Stein Poisson approximation method, and Gaussian approximation techniques.

Mapping pathogenic fungi in decayed Norway spruce stands: Insights from harvester positional data

Abstract Root and butt rot caused by pathogenic fungi in the genera Heterobasidion and Armillaria is a pressing issue in managed Norway spruce forests. The disease results in financial losses for the forest owners and reduces the volume of wood that can be used in long‐lived products. Pathogenic wood decay fungi spread either with the aid of airborne spores or via mycelial growth among neighbouring trees, the latter leading to clustering (tendency of decayed trees to be in close proximity relative to their neighbouring trees) of decay‐affected trees in forests. Understanding the spatial patterns of the decay‐affected trees at the forest stand level is vital for designing management strategies to address this problem. We examined decay clustering in 273 clear‐cut Norway spruce stands in Norway using harvester‐recorded data on spatial occurrence of decayed and healthy Norway spruce trees. We tested clustering using three global‐cluster tests that account for population density and distribution, evaluating clustering without identifying specific cluster locations. The proportions of clustered and non‐clustered stands differed depending on the statistical test used for clustering assessment, resulting in overall agreement of 32.8% for clustered and 36.9% for non‐clustered. Clustered stands exhibited a median cluster distance (maximum distance between the decay‐affected trees within a cluster) of 12 m (Inter‐Quantile Range, IQR, 6–20 m) and a median of 6 (IQR 3–16) nearest neighbour trees (number of decayed trees forming a cluster), estimates comparable with prior studies focused on assessment of trees infected by mycelial spread of the same fungal individual. The decay incidence in the clustered stands was 16.24%, while the non‐clustered stands had a butt‐rot incidence of 20.97%. In clustered stands the average number of trees per hectare was higher (693) than in non‐clustered stands (553). Synthesis and applications: Our study demonstrates that Norway spruce stands display a diverse range of spatial patterns of butt rotted trees. We found that higher densities of Norway spruce trees probably facilitate the vegetative spread of pathogenic wood decay fungi, leading to clustering of decay‐affected trees. To disrupt the spread of decay fungi between tree generations, precision planting of trees other than Norway spruce around infested stumps of prior generation trees has been recommended by earlier studies. We discussed the potential of using harvester‐derived geoposition data for butt‐rotted trees upon planning and execution of forest regeneration.

ZEROES: Robust Derivative-Based Demodulation Method for Optical Camera Communication

Most of Optical Camera Communication (OCC) systems benefit from the rolling shutter mechanism of Complementary Metal-Oxide Semiconductor (CMOS) cameras to record the brightness evolution of the Light-Emitting Diode (LED) through dark and bright strips within images. While this technique enhances the maximum achievable data rate, the main difficulty lies in the demodulation of the signal extracted from images, subject to blooming effect. Thus, two main approaches were proposed to deal with this issue, using adaptive thresholds whose value evolves according to amplitude changes or detecting signal variations with the first-order derivative. As the second method is more robust, a new demodulation method based on the detection of the zeros of the first-order derivative of the extracted signal was proposed in this paper. Obtained results clearly show an improvement in the extracted signal demodulation compared to other methods, achieving a raw Bit Error Rate (BER) of 10−3 around 50 cm in a Line-Of-Sight scenario, and increasing the maximum communication distance by 43.5%, reaching 330 cm in the case of a Non-Line-Of-Sight transmission.

Performance Analysis of a Color-Code-Based Optical Camera Communication System

In this study, we present a visible light communication (VLC) system that analyzes the performance of an optical camera communication (OCC) system, utilizing a mobile phone camera as the receiver and a computer monitor as the transmitter. By creating color channels in the form of a 4 × 4 matrix within a frame, we determine the parameters that affect the successful transmission of data packets. Factors such as the brightness or darkness of the test room, the light color of the lamp in the illuminated environment, the effects of daylight when the monitor is positioned in front of a window, and issues related to dead pixels and light bleed originating from the monitor’s production process have been considered to ensure accurate data transmission. In this context, we utilized the PyCharm, Pydroid, Python, Tkinter, and OpenCV platforms for programming the transmitter and receiver units. Through the application of image processing techniques, we mitigated the effects of daylight on communication performance, thereby proposing a superior system compared to standard VLC systems that incorporate photodiodes. Additionally, considering objectives such as the maximum number of channels and the maximum distance, we regulated the sizes of the channels, the distances between the channels, and the number of channels. The NumPy library, compatible with Python–Tkinter, was employed to determine the color levels and dimensions of the channels. We investigate the effects of RGB and HSV color spaces on the data transmission rate and communication distance. Furthermore, the impact of the distance between color channels on color detection performance is discussed in detail.

Comparative Analysis of the MDORA and AODV Routing Protocols for Vehicles Operating at Constant and Variable Speeds

The primary focuses of investigation have been and continue to be strategies for traffic management at intersections and measures to enhance road safety. An essential remedy for this issue is a Vehicular Ad-hoc Network (VANET). At VANET, a variety of protocols are used to route communications between vehicles. At this research, we utilize the Multipath Dynamic Optimized Routing Algorithm (MDORA), which is an acronym for position-based maximum distance on-demand routing. By choosing the vehicle closest to the destination vehicle, this protocol has the advantage of choosing the next best jumping path, which lowers the number of hops. In two scenarios—vehicle travel at a dynamic speed and constant speed—this paper compares the MDORA and AODV protocols. three standards: Factors including the time spent on communication, the pace at which packets are delivered, and the time it takes for information to travel from one end to another, were used to assess how well the two protocols performed. Finally, a comparison of the number of missed packets between the MDORA and AODV protocols was done for moving vehicles at constant and dynamic speeds, The MDORA protocol can identify the optimal route even when cars are moving at varying speeds, resulting in minimal packet loss.

Quasi-closed diaphragm based piezoelectric micromachined ultrasonic transducer with reduced Q and stress sensitivity for in-air rangefinding

To improve the performance of the Piezoelectric Micromachined Ultrasonic Transducer (PMUT) based rangefinder and decrease its stress sensitivity, a novel design with quasi-closed structure is proposed. It adopts a circular piezoelectric composite diaphragm structure with clamped boundary, in which all the deposited stack layers in its central region are intentionally removed and additional cross-slits are created into the remaining silicon device layer. Due to the reduced mass and the enhanced thermal-viscous damping at slits, a 35.2 % decrease in quality factor Q has been achieved in the proposed PMUT when compared with the conventional design, resulting in a distinctly reduced blind area from 231.3 mm to 170.7 mm. At the same time, the proposed quasi-closed PMUT facilitates the release of accumulated stress in the device structure during fabrication and operation. As a result, an approximate 50 % reduction in frequency deviation between different as-fabricated PMUTs across the same wafer has been successfully obtained. Moreover, due to the increased linear operation range, the developed bare PMUT chip demonstrates a maximum detection distance of 3 m at the operation frequency of 71.5 kHz under 40 Vpp driving voltage. Given the advantages of lower Q, insensitivity to stress, good fabrication consistency and large linear operation range, the proposed quasi-closed PMUT design can well address the requirements on small blind area and large detection range for distance sensing applications.

Automatic Image Analysis Method as a Tool to Evaluate the Anisotropy of Autoclaved Aerated Concrete for Moisture and Heat Transport

In this article, the results of studies testing the anisotropy of autoclaved aerated concrete in terms of water and heat transport are presented. Using image analysis techniques, a study was conducted on four different samples of concrete produced in the same process. To ensure the comparability of results, the pictures were taken from a fixed distance with the same lens settings trimmed to a set size. Cross-sectional profiles of the material were examined and were arranged in two directions: perpendicular and parallel to the growth direction occurring in the autoclave. For each block, approximately 4750 objects were obtained, with an average of 2700 objects along the wall and 2050 across it. As a result of the comparative analysis, metrics concerning pores, significantly distinguishing the profile direction, were identified. These included the pore area (area), the maximum and minimum distance between points on the perimeter (Feret, MinFeret), lengths of the major and minor axes of the fitted ellipse (major, minor), and the ratio of the area of selection to its convex hull (solidity). As a reference, standard investigations were conducted for moisture transport using the time domain reflectometry setup and for thermal conductivity values using the steady-state heat flow plate apparatus.

Optimised GRS coded cooperation: sliding relay selection design and improved joint decoding

ABSTRACT In this paper, the novel optimised generalised Reed-Solomon coded cooperative (OGRSCC) scheme is developed with a flexible selection of the code length and information dimension. In the OGRSCC scheme, two GRS codes with different dimensions are deployed at the source and relay, respectively, where the information symbols of the relay are dependent on those of the source. At the relay, different symbol selections may contribute to distinct joint codes at the destination. As a result, to achieve a maximum free distance (FD) and the optimised weight distribution of the final code, the global search method is first proposed to obtain the optimal selection pattern. However, as the code grows longer, its complexity rises dramatically. To make the selection more practical, the low-complexity sliding search method is then investigated to obtain the local optimal symbol selection pattern. Monte-Carlo simulated results indicate the OGRSCC scheme with two selection methods demonstrates almost identical performance. Furthermore, based on this special selection method and the unique algebraic structure of GRS code, the improved joint decoding algorithm is first proposed to boost the overall system performance. In addition, the theoretical upper bound is analysed, verifying the effectiveness of the proposed OGRSCC scheme. Numerical simulations reveal that the proposed OGRSCC scheme outperforms its corresponding non-cooperative scheme by a gain of over 3.2 dB and its existing comparable schemes by a margin of approximately more than 4 dB at high signal-to-noise ratio (SNR), respectively.

7284 Ablation of hexose-6-phosphate dehydrogenase in mice causes skeletal muscle atrophy and dramatically impairs exercise capacity

Abstract Disclosure: M. Zogg: None. A.D. Grötsch: None. J. Birk: None. P. Pelczar: None. J. Bouitbir: None. A. Odermatt: None. Hexose-6-phosphate dehydrogenase (H6PD) catalyzes the first two steps of the pentose-phosphate pathway (PPP) within the endoplasmic reticulum (ER), generating the redox equivalent NADPH. It has been shown that mice lacking H6PD develop defects mainly in skeletal muscles [1]. Nevertheless, the mechanisms underlying the myopathy in H6PD KO mice is unknown. Here, we further assessed muscle responses to H6PD deficiency and aimed to uncover the mechanisms that may cause myopathy in mice. We conducted a detailed characterization of the muscle structure and function as well as energy metabolism in oxidative and glycolytic muscles of H6PD KO mice. At the age of 15 weeks, H6PD KO mice displayed lower body weight than WT mice, despite similar food and water intake. Grip strength was significantly lower in H6PD KO than in WT mice. This was associated with decreased weight of the mixed (gastrocnemius, quadriceps) and fast fiber type rich muscles of the hind leg (extensor digitorum longus, tibialis anterior) in H6PD KO animals. Atrogin1 and Murf1 mRNA expression, markers of atrophy, increased only in the white (glycolytic) quadriceps. In this context, fast-twitch fibers in WT mice displayed higher H6pd mRNA expression than slow-twitch fibers. Electron microscopy analysis of red and white gastrocnemius muscles displayed the presence of large intramyofibrillar vacuoles, and morphologic changes of the sarcoplasmic reticulum and mitochondria in H6PD KO muscle. Metabolically, H6PD KO muscles presented an accumulation of glycogen granules and significantly decreased mRNA expression of glucose transporter Glut4, glucose-6-phosphate transporter G6pt and glycogen phosphorylase Pygm. The exercise capacity, measured by maximal running distance, decreased by more than 50% in H6PD KO mice. Upon exercise, both WT and H6PD KO animals were able to mobilize the majority of glycogen stored in their muscles. However, immediately after exercise, there was a significant increase in plasma lactate and glucose levels in H6PD KO animals. Disturbances in glucose metabolism were further supported by in vitro experiments using stable C2C12 H6PD KO myoblasts, revealing a shift in basal state mitochondrial fuel oxidation usage from glucose to fatty acid and glutamine in metabolic dependency assays. In conclusion, our findings revealed that H6PD seems to play a key role in proper function and energy metabolism of skeletal muscles.

Validation of an Artificial Intelligence-Based Prediction Model Using 5 External PET/CT Datasets of Diffuse Large B-Cell Lymphoma.

The aim of this study was to validate a previously developed deep learning model in 5 independent clinical trials. The predictive performance of this model was compared with the international prognostic index (IPI) and 2 models incorporating radiomic PET/CT features (clinical PET and PET models). Methods: In total, 1,132 diffuse large B-cell lymphoma patients were included: 296 for training and 836 for external validation. The primary outcome was 2-y time to progression. The deep learning model was trained on maximum-intensity projections from PET/CT scans. The clinical PET model included metabolic tumor volume, maximum distance from the bulkiest lesion to another lesion, SUVpeak, age, and performance status. The PET model included metabolic tumor volume, maximum distance from the bulkiest lesion to another lesion, and SUVpeak Model performance was assessed using the area under the curve (AUC) and Kaplan-Meier curves. Results: The IPI yielded an AUC of 0.60 on all external data. The deep learning model yielded a significantly higher AUC of 0.66 (P < 0.01). For each individual clinical trial, the model was consistently better than IPI. Radiomic model AUCs remained higher for all clinical trials. The deep learning and clinical PET models showed equivalent performance (AUC, 0.69; P > 0.05). The PET model yielded the highest AUC of all models (AUC, 0.71; P < 0.05). Conclusion: The deep learning model predicted outcome in all trials with a higher performance than IPI and better survival curve separation. This model can predict treatment outcome in diffuse large B-cell lymphoma without tumor delineation but at the cost of a lower prognostic performance than with radiomics.

Quantum Entanglement in Nonlinear Coupler with Raman Process

This paper examines the possible quantum entanglement generated in a coupler system consisting of two waveguides, where one waveguide is nonlinear and Raman-active, while the other waveguide only undergoes linear processes. The analytical-perturbative method is employed to investigate the production of entangled states in the given system. The Hillery-Zubairy criterion is employed to examine the possible quantum entanglement between the two fundamental pump modes propagating in both waveguides. We explore the generation of quantum entanglement under different initial conditions and critical design parameters. The simulation results suggest a continuous entanglement that remains until a particular distance of interaction is reached. As the linear coupling parameter increases, the relationship between the maximum reachable distance for entanglement and the degree of entanglement becomes more complex. The study reveals that entanglement experiences significant fluctuations when there is a substantial frequency mismatch between the modes.

A modified Fuvar fusion algorithm based on adaptive end-member selection for hyperspectral remote sensing images

ABSTRACT A significant strategy for achieving a balance between spatial and spectral resolution is to combine hyperspectral remote sensing images with low spatial resolution and multispectral remote sensing images with high spatial resolution. For the issues of spectrum distortion and lack of the ability of gaining high frequency information when the Fuvar algorithm employs the Vertex Component Analysis (VCA) technique, this thesis presents a modified Fuvar (MFuvar) algorithm that utilizes the Maximum Distance Analysis (MDA) method instead of the VCA approach. The two subsets from the hyperspectral remote sensing image of GF-5 and the multispectral remote sensing image of Sentinel-2A, representing different land cover types were used as test data. The spectral fidelity and the ability of gaining high frequency information were assessed by using visual and statistical analysis. Fused images are compared with eight fusion methods, including SFIMHS, GLPHS, MAPSMM, CNMF, Hysure, SpaFusion, LTTR, and Fuvar, respectively. The results show that the MFuvar algorithm can keep the best balance between spectral fidelity and the ability of gaining high frequency information, and it is generally better than the compared eight algorithms. And it fulfils the automatic selection of end elements without manual intervention and increases the efficiency of algorithm operation.

Diffusion Mechanism of Variable-Rate Grouting in Water Prevention and Control of Coal Mine

Regional grouting treatment is an effective technical means to prevent mine water disasters, and the grouting effect is affected by many factors. In actual grouting engineering, the single constant-rate grouting method is often transformed into a variable-parameter grouting process. However, research on grouting rates has been insufficient. This investigation focused on the issue of “the diffusion law of variable-rate grouting slurry in regional governance”. Methods such as theoretical analysis, numerical simulation, and field verification were used to evaluate the diffusion mechanism of variable-rate fracture grouting. The results indicated that the key parameters of variable-rate grouting, such as slurry diffusion distance and grouting pressure, were affected by the grouting rate. The decrease in the grouting rate reduced the migration speed of the slurry and the grouting pressure. The time for constant-velocity grouting and variable-velocity grouting to reach the same diffusion distance was 60 s and 108 s, respectively, which can be achieved with lower grouting pressure. When the grouting rate was 7.5 L/min and 30 L/min, the maximum grout diffusion distance was 2.81 m and 5.64 m, respectively, which required greater grouting pressure. The slurry diffusion rate decreased with the reduction in the grouting rate. Under the same diffusion distance conditions, variable-rate grouting took longer than constant high-rate grouting. In variable-rate grouting, the grouting pressure decreased stepwise with the grouting rate, with a final pressure drop of 77.4%. In grouting practice, the innovative use of the rate-reducing grouting method can greatly reduce the final grouting pressure under the premise of changing the slurry diffusion distance less, which can not only ensure the stability of surrounding rock but also reduce the cost of high-pressure grouting and the risk of grouting operation. The investigation results can provide scientific guidance for ground grouting renovation projects in deep coal mine water hazard areas.

Is naloxone where it needs to be? Using spatial analytics to examine equitable distribution of community-based naloxone sites

BackgroundOne of the most effective harm reduction services for preventing opioid overdose deaths is naloxone. Given the ongoing opioid crisis, which has led to a surge in overdose deaths across the country, expanding access to naloxone is critical. Community-based naloxone distributions sites in Palm Beach County can increase access to naloxone. However, several rural and disadvantaged regions rarely have any type of access to naloxone. The purpose of this descriptive paper is to examine the spatial distribution of and evaluate equitable accessibility to community-based naloxone sites in Palm Beach County. MethodsWe examined health equity in the distribution of community-based naloxone sites using a mixed-methods approach with ArcGIS Pro version 3.0, which is a geographic information system (GIS) software used for mapping, spatial analysis, and data visualization. ResultsThe Belle Glade region was identified as the location most adversely affected with health inequities and limited accessibility to naloxone distribution sites, as it ranked in the 100 % percentile for all social vulnerability index (SVI) themes. The 30-minute drive-time area calculated a county service area of 1885.3 km2 (km2), which covers about 34 % of the 478.0 km2 land area of census tracts. Drive-time areas did not account for periods of heavier traffic such as during rush hour. Maximum distances during heavier traffic may be smaller, thus decreasing accessibility to naloxone distribution sites. ConclusionThere is a need for effective policy-led strategies tailored to expanding our understanding of the challenges that are experienced by the individuals in need of naloxone and encountered by the distribution sites themselves, as accessible naloxone is crucial for preventing nonfatal and fatal overdoses and ensuring timely emergency responses in vulnerable communities.

DNA barcoding and cryptic diversity in fishes from the Ili River Valley in China, Xinjiang.

The Ili River Valley, located in the northwest of China, serves as a vital repository for fish genetic resources. Its extensive water network and diverse climate have given rise to a unique fish composition and endemic species. In this study, we collected the cytochrome c oxidase subunit I (COI) sequences from 660 fish specimens in the Ili River Valley. The effectiveness of DNA barcoding in identifying fish species in the area was assessed by examining genetic distances, constructing phylogenetic trees, and performing ABGD (Automatic Barcode Gap Discovery) analyses, among other methods. In total, 20 species were identified, including one unidentified species (Silurus sp.). Except for Silurus asotus and Hypophthalmichthys molitrix (only one sample), the maximum intraspecific genetic distance among the remaining species was smaller than the minimum interspecific distance, which proves that the species exhibit obvious barcode gaps. In the Neighbor-Joining trees, 20 species formed separate monophyletic branches. According to ABGD analysis, 660 sequences were categorized into 19 Operational Taxonomic Units, with Silurus sp. and S. asotus grouped into a single OTU. The Silurus in this study exhibits shared haplotypes and significant genetic divergence, suggesting the potential presence of cryptic species. Furthermore, the nucleotide diversity across all species fell below the threshold level, indicating that the local fish population is gradually declining. In conclusion, this study has demonstrated the effectiveness of DNA barcoding in identifying fish species in the Ili River Valley, providing valuable data to support the conservation of local fish resources.

Large, but Dispersal-Limited Populations of the Marsh Fritillary Euphydryas aurinia Persist on Abandoned Military Training Areas Three Decades After the End of the Cold War.

Military training areas can host important biodiversity, due to the preservation of diverse, nutrient-poor historical cultural landscapes and an insect-friendly disturbance regime. In Europe, many training areas were abandoned after the end of the cold war in 1991 and the withdrawal of the Allied and Soviet forces. Many of these are now protected areas, and current management strategies vary from rewilding to active habitat management such as grazing or mowing. In a capture-release-recapture approach, marking 2418 individuals, we assessed the population size and movement patterns of the dry ecotype of the Marsh Fritillary Euphydryas aurinia Rottemburg 1775 on three former military training areas in Germany that varied in size and management (natural succession, mowing, and sheep-/goat grazing). Euphydryas aurinia is a rare and declining butterfly species listed in Annex II of the European Union Habitats Directive. Jolly-Seber models revealed a large population of ca. 19,000 individuals on the largest study site and a smaller population at a second site, whereas recapture rates were too low to predict the population size reliably at a third site. Population densities were 190-194 butterflies ha-1 at the unmanaged, large site and 56-71 butterflies ha-1 at a smaller site grazed with sheep. Thirty-nine percent of the recapture events occurred within the same 1-ha-study plot. The average minimum flight distance between the study plots was 313 m for males and 328 m for females. The maximum lifetime flight distance was 1237 m within 3 days. No dispersal was detected between study sites. Thirty years after cessation of the military use, the large former training site still held what likely is one of the largest populations of the species dry ecotype in Central Europe, including in areas where management ceased already in 1991. This suggests remarkable persistence of the species in areas without regular management, contrary to current opinion. However, regular flight distances seem not to be sufficient to connect the isolated habitat patches. It remains unknown how long the large population at the abandoned military area will persist without active habitat management. Careful, but active habitat management and restoration of habitat connectivity should thus be considered.

Effect of energy on the interface morphologies and tensile-shear properties of the electromagnetic pulse welding T2/SS304 joints

This investigation focused on the effect that electromagnetic pulse welding (EMPW) of copper (T2) and stainless steel (SS304) dissimilar materials with various discharge energies, which is interfacial morphology and tensile-shear properties of the joints. The results showed that the interface of T2/SS304 dissimilar material joints treated with EMPW exhibits a typical waveform morphology. The maximum wave peak distance reaches 36 μm (39 kJ), and the distance between peak and trough reaches 6 μm (37 kJ, 39 kJ). The tensile-shear properties of the joints were better than those of the base material, with the fracture mode changing from interfacial fracture (35 kJ) to base mental fracture (37 kJ, 39 kJ), and the maximum tensile-shear of the joints was 11.1 kN (39 kJ). The wave spacing after fracture was extended up to 3 μm.

Four new families of NMDS codes with dimension 4 and their applications

For an [n,k,d]q linear code C, the singleton defect of C is defined by S(C)=n−k+1−d. When S(C)=S(C⊥)=1, the code C is called a near maximum distance separable (NMDS) code, where C⊥ is the dual code of C. NMDS codes have important applications in finite projective geometries, designs and secret sharing schemes. In this paper, we present four new constructions of infinite families of NMDS codes with dimension 4 and completely determine their weight enumerators. As an application, we also determine the locality of the dual codes of these NMDS codes and obtain four families of distance-optimal and dimension-optimal locally recoverable codes.

Generating efficient circulant-like MDS matrices for implementation

The exploration of maximal distance separable codes (MDS codes) has been a longstanding focus in error-correcting code theory and holds significant relevance in cryptography. Numerous approaches have been investigated for constructing MDS matrices, including deriving them from MDS codes, utilizing Hadamard matrices, Cauchy matrices, Vandermonde matrices, circulant matrices, circulant-like matrices, among others. However, a major challenge for cryptography designers is finding MDS matrices with low implementation cost. In this paper, we propose algorithms for generating efficient circulant-like MDS matrices of size , and for implementation. Subsequently, we evaluate the fixed points, the number of XOR operations of the proposed MDS matrices, and compare them with MDS matrices of other well-known ciphers. These proposed MDS matrices can become promising candidates for many cryptographic algorithms in the future.

Lossless Approximate Pattern Matching: Automated Design of Efficient Search Schemes.

This study introduces a pioneering approach to automate the creation of search schemes for lossless approximate pattern matching. Search schemes are combinatorial structures that define a series of searches over a partitioned pattern. Each search specifies the processing order of these parts and the cumulative lower and upper bounds on the number of errors in each part of the pattern. Together, these searches ensure the identification of all approximate occurrences of a search pattern within a predefined limit of k errors. While existing literature offers designed schemes for up to k = 4 errors, designing search schemes for larger k values incurs escalating computational costs. Our method integrates a greedy algorithm and a novel Integer Linear Programming (ILP) formulation to design efficient search schemes for up to k = 7 errors. Comparative analyses demonstrate the superiority of our ILP-optimal schemes over alternative strategies in both theoretical and practical contexts. Additionally, we propose a dynamic scheme selection technique tailored to specific search patterns, further enhancing efficiency. Combined, this yields runtime reductions of up to 53% for higher k values. To facilitate search scheme generation, we present Hato, an open-source software tool (AGPL-3.0 license) employing the greedy algorithm and utilizing CPLEX for ILP solving. Furthermore, we introduce Columba 1.2, an open-source lossless read-mapper (AGPL-3.0 license) implemented in C++. Columba surpasses existing state-of-the-art tools by identifying all approximate occurrences of 100,000 Illumina reads (150 bp) in the human reference genome within 24 seconds (maximum edit distance of 4) and 75 seconds (maximum edit distance of 6) using a single CPU core. Notably, our study showcases Columba's capability to align 100,000 reads of length 50, with high error rates and up to an edit distance of 7, in a mere 2 hours and 15 minutes. This achievement is unmatched by other lossless aligners, which require over 3 hours for edit distance 5 alignments. Moreover, Columba exhibits a mapping rate four times higher than that of a lossy tool for this dataset.