The Complexity and Expressive Power of Limit Datalog

Motivated by applications in declarative data analysis, in this article, we study Datalog Z —an extension of Datalog with stratified negation and arithmetic functions over integers. This language is known to be undecidable, so we present the fragment of limit Datalog Z programs, which is powerful enough to naturally capture many important data analysis tasks. In limit Datalog Z , all intensional predicates with a numeric argument are limit predicates that keep maximal or minimal bounds on numeric values. We show that reasoning in limit Datalog Z is decidable if a linearity condition restricting the use of multiplication is satisfied. In particular, limit-linear Datalog Z is complete for Δ 2 EXP and captures Δ 2 P over ordered datasets in the sense of descriptive complexity. We also provide a comprehensive study of several fragments of limit-linear Datalog Z . We show that semi-positive limit-linear programs (i.e., programs where negation is allowed only in front of extensional atoms) capture coNP over ordered datasets; furthermore, reasoning becomes coNEXP-complete in combined and coNP-complete in data complexity, where the lower bounds hold already for negation-free programs. In order to satisfy the requirements of data-intensive applications, we also propose an additional stability requirement, which causes the complexity of reasoning to drop to EXP in combined and to P in data complexity, thus obtaining the same bounds as for usual Datalog. Finally, we compare our formalisms with the languages underpinning existing Datalog-based approaches for data analysis and show that core fragments of these languages can be encoded as limit programs; this allows us to transfer decidability and complexity upper bounds from limit programs to other formalisms. Therefore, our article provides a unified logical framework for declarative data analysis which can be used as a basis for understanding the impact on expressive power and computational complexity of the key constructs available in existing languages.

SUPG-YZβ formulation for solving convection-dominated steady linear reaction-convection-diffusion equations

In this computational study, stabilized finite element solutions of convection-dominated steady linear reaction-convection-diffusion equations are examined. Although the standard Galerkin finite element method (GFEM) is one of the most robust, efficient, and reliable methods for many engineering simulations, it suffers from instability issues in solving convection-dominated problems. To this end, this work deals with a stabilized version of the standard GFEM, called the streamline-upwind/Petrov-Galerkin (SUPG) formulation, to overcome the instability issues in solving such problems. The stabilized formulation is further supplemented with YZβ shock-capturing to provide additional stability around sharp gradients. A comprehensive set of test computations is provided to compare the results obtained by using the GFEM, SUPG, and SUPG-YZβ formulations. It is observed that the GFEM solutions involve spurious oscillations for smaller values of the diffusion parameter, as expected. These oscillations are significantly eliminated when the SUPG formulation is employed. It is also seen that the SUPG-YZβ formulation provides better solution profiles near steep gradients, in general.

Hg2+ Detection with Rational Design of DNA-Templated Fluorescent Silver Nanoclusters

Atomically precise silver nanoclusters (AgNCs) are small nanostructures consisting of only a few atoms of silver. The combination of AgNCs with cytosine-rich single-stranded oligonucleotides results in DNA-templated silver nanoclusters (DNA-AgNCs). DNA-AgNCs are highly luminescent and can be engineered with reproducible and unique fluorescent properties. Furthermore, using nucleic acids as templates for the synthesis of AgNCs provides additional practical benefits by expanding optical activity beyond the visible spectral range and creating the possibility for color tunability. In this study, we explore DNA oligonucleotides designed to fold into hairpin-loop (HL) structures which modulate optical properties of AgNCs based on the size of the loop containing different number of cytosines (HL-CN). Depending on the size of the loop, AgNCs can be manufactured to have either single or multiple emissive states. Such hairpin-loop structures provide an additional stability for AgNCs and further control over the base composition of the loop, allowing for the rational design of AgNCs’ optical properties. We demonstrate the potential of AgNCs in detecting Hg2+ by utilizing the HL-C13 design and its variants HL-T2C11, HL-T4C9, and HL-T6C7. The replacement of cytosines with thymines in the loop was intended to serve as an additional sink for mercury ions extending the detectable range of Hg2+. While AgNC@HL-T0C13 exhibits an interpretable quenching curve, AgNC@HL-T6C7 provides the largest detectable range of Hg2+. The results presented herein suggest that it is possible to use a rational design of DNA-AgNCs based on the composition of loop sequence in HL structures for creating biosensors to detect heavy metals, particularly Hg2+.

Distal-Ulna Stump Stability: The Role of Distal Interosseous Membrane: Myth or Reality? Anatomical Research

Background Distal-ulna stump (DUS) instability often occurs when performing a distal radioulnar joint (DRUJ) arthroplasty. Recent studies suggest that the distal interosseous membrane (DIOM) reinforces the triangular fibrocartilage complex, providing additional stability to the DRUJ. The aim of this study was to determine whether the DIOM stabilizes the ulnar stump. Methods Twenty fresh-frozen random forearms were dissected. The presence of a distal oblique bundle (DOB) was recorded and measured. The radius was fixed to a vise and the ulna kept free. The DRUJ was fixed with a lag screw. A bone slice was removed by transverse ulna osteotomies 10 and 15 mm proximal to the DRUJ. A 10-N force was applied to the ulna in dorsal and volar directions. Displacements were measured. The DIOM was then transected, and maneuvers and measurements were repeated and compared. Results A distinct distal membrane was present in 70% and a cord-like DOB in 30%. The mean length was 29 mm. Its origin was proximal to the sigmoid notch; its insertion was on the distal third of the ulna, at its lateral border. This attachment is comprised between 39 and 48 mm proximal to the ulnocarpal joint. Initial displacements averaged 22 mm dorsally and 13 mm volarly. After DIOM transection, ulnar translocation increased to 31 mm dorsally and 19 mm volarly. Conclusion In DRUJ arthroplasties, the DIOM does not appear to be a stabilizer of the DUS beneath a useful threshold. Its retaining effect occurs only after an initial 22-mm dorsal displacement, which we consider not clinically admissible. Therefore, in DRUJ arthroplasties, some augmentation might be advisable.

An Uncommon Trauma: Hoffa's Fracture Associated with Tibial Avulsion Fracture of the Posterior Cruciate Ligament

BackgroundSince Hoffa fractures are usually the result of high-energy injuries, many additional accompanying injuries have been described. This is the first paper representing the lateral condyle Hoffa fracture accompanying tibial avulsion fracture of the posterior cruciate ligament (PCL).Case PresentationA 42-years-old male presented with swelling and instability in his left knee after falling during parachute landing. He was diagnosed with simultaneous Letenneur Type I lateral condyle Hoffa fracture and tibial avulsion fracture of the PCL. He was operated on with a single posterior incision for both fractures. Multiple cannulated lag screws were used for the fixation of the Hoffa fracture, and a buttress plate was used for additional stability. PCL avulsion fracture was fixed with a cannulated screw with a washer. The patient was allowed for full-weight-bearing and range of motion at the sixth week after the operation. No complications occurred during follow-up.ConclusionCare should be taken in terms of additional injuries that may accompany Hoffa fractures. The posterior approach allows easy access to both fractures with a single incision. Using a buttress plate after the fixation of the Hoffa fracture with multiple lag screws provides additional stability.

The study of the curvature of the axis of the processed shaft when based in the centers using a steady rest

This paper presents the analysis and results of the study of a two-stage shaft fixed in dead centers and a rest device. Cutting forces act on the shaft, causing a bending moment. The analysis of the curvature of the axis of the workpiece, processed on a lathe when based in the centers, using a rest device, is carried out. The formula of elastic displacement of the workpiece axis at the place of the resulting cutting force is obtained. Diagrams of the stresses of the shaft axis displacements are constructed and a conclusion is made. The analysis showed that the greatest deflection is at the point of the cutting forces acting on the shaft. The quality of the part obtained after processing is characterized by accuracy. The parts mating in the product and, as a result, the overall reliability depends on how accurately the size and shape of the part will be maintained during processing. Parts with length of 10 to 12 times larger than the diameter are bent under the action of their own weight and cutting forces, as a result of which they get a barrel-like shape. It is possible to eliminate this by applying special devices for the machine. When processing long nonrigid workpieces, the tools, jigs and fixtures must evenly distribute the clamping force over the surface of the part. These conditions are well provided by technological equipment with pneumatic, hydraulic clamping devices, as well as with various collet clamps, split bushings, diaphragm or cartridges. When processing long non-rigid shafts, rest devices are used. The rest device plays the role of the main or secondary support when working with workpieces; it creates support for large, long parts during processing. It helps to avoid the risk of damage and deformation of the workpiece or the cutting elements of the machine, by giving the workpiece additional stability

Do substrate roughness and gap distance impact gap-bridging strategies in arboreal chameleons?

Chameleons are well equipped for an arboreal lifestyle, having “zygodactylous” hands and feet as well as a fully prehensile tail. However, to what degree tail use is preferred over autopod prehension has been largely neglected. Using an indoor experimental set-up, where chameleons had to cross gaps of varying distances, we tested the effect of substrate diameter and roughness on tail use in Chamaeleo calyptratus. Our results show that when crossing greater distances, C. calyptratus is more likely to use its tail for additional stability. The animals were able to cross greater distances (up to 1.75 times the shoulder-hip length) on perches with a rougher surface. We saw that depending on the distance of the gap, chameleons would change how they use their prehensile tails when crossing. With shorter gaps the tails either do not touch, or only touch the perch without coiling around it. With larger distances the tails are fully coiled around the perch, and with the largest distances additionally they reposition the hind legs, shifting them towards the end of the perch. Males were able to cross relatively greater distances than females, likely due to their larger size and strength.

Improved Isolation Procedures for Okadaic Acid Group Toxins from Shellfish (Mytilus edulis) and Microalgae (Prorocentrum lima)

Okadaic acid (OA) group toxins may accumulate in shellfish and can result in diarrhetic shellfish poisoning when consumed by humans, and are therefore regulated. Purified toxins are required for the production of certified reference materials used to accurately quantitate toxin levels in shellfish and water samples, and for other research purposes. An improved procedure was developed for the isolation of dinophysistoxin 2 (DTX2) from shellfish (M. edulis), reducing the number of purification steps from eight to five, thereby increasing recoveries to ~68%, compared to ~40% in a previously reported method, and a purity of >95%. Cell densities and toxin production were monitored in cultures of Prorocentrum lima, that produced OA, DTX1, and their esters, over ~1.5 years with maximum cell densities of ~70,000 cells mL−1 observed. Toxin accumulation progressively increased over the study period, to ~0.7 and 2.1 mg L−1 of OA and DTX1 (including their esters), respectively, providing information on appropriate harvesting times. A procedure for the purification of OA and DTX1 from the harvested biomass was developed employing four purification steps, with recoveries of ~76% and purities of >95% being achieved. Purities were confirmed by LC-HRMS, LC-UV, and NMR spectroscopy. Additional stability observations led to a better understanding of the chemistry of these toxins.

SEASONAL CHANGES IN THE VALUE OF THE RESISTANCE COEFFICIENT OF THE LANDSLEND

The results of calculating the stability of a landslide-prone slope located on the river bank are presented. Additional stability studies were carried out due to the fact that, according to the results of slope calculations using various “compartments” methods, based on the construction of circular cylindrical sliding surfaces, the slope is in a stable state (tables are given containing the numerical values of the safety factors). However, in the spring-autumn period, local landslides occur on the slope. Therefore, new calculations of slope stability were carried out using a method based on the analysis of the stress state of the soil massif, which allows one to take into account the "weighing" effect of groundwater when it rises and the decrease in the strength properties of the constituent soils when they are soaked. This method is formalized in a computer program developed with the participation of one of the authors; the program has a certificate of state registration. Calculations have established that an increase in the level of groundwater to the maximum possible value reduces the values of the safety factors along the considered sliding lines by 5.9-21 %. It is shown that if the numerical values of the safety factors obtained by the methods of circular cylindrical sliding surfaces are reduced by 21 %, then some of their values will be very close to unity or even less, which resolves the above contradiction. When calculating the stability of landslide-prone soil masses, in which seasonal fluctuations of groundwater are possible, one should take into account the "weighing" effect of groundwater at the maximum level of their rise, a decrease in the physical and mechanical (strength) characteristics of soils due to their soaking and, preferably, the destabilizing effect of hydraulic heads.