The purpose of the current study is to investigate a special case of art gallery problem,namely a sculpture garden problem. In this problem, for a given polygon P, the ultimate goal isto place the minimum number of guards (landmarks) to define the interior polygon P by applyinga monotone Boolean formula composed of the guards. Using this problem, it can replace theoperation-based method with time-consuming, pixel-based algorithms. So, the processing time ofsome problems in the fields of machine vision, image processing and gamification can be stronglyreduced. The problem has also many applications in mobile device localization in the Internet ofThings (IoT). An open problem in this regard is the proof of Eppstein’s conjecture, which has remainedan open problem since 2007. According to his conjecture, in the worst case, n 􀀀 2 vertex guards arerequired to describe any n-gon. In this paper, a lower bound is introduced for the special case of thisproblem (natural vertex guard), which shows that if a polygon can be defined with natural vertexguards, then n - 2 is a lower bound.

Daqing Oilfield is in the forefront, because of polymer flooding well pattern was used to next production layer, so, first development layer was sealed after polymer well was used to next layer, and whose storage reserves is very huge. To 2021, OOIP of the first set of reserves of type II reservoirs has been sealed up to 9603 × 104 t. In order to release the reserves and reduce the influence on oil yield, water drive well pattern was used to product the sealed reserves through additional perforating, but the economic boundary standard to release the sealed layer using water drive well pattern is not determined, so, based on the principle of break-even and the seepage flow theory, this paper establishes the formula for calculating the economic limits of the various unsealing indexes by water flood well, which can effectively solve the problem of communicating and understanding the economic and engineering parameters of the released well, quantificational the limit of layer selection standard of well for releasing. The result showed the cumulative and daily oil production limit is gradually decreases with oil prices increasing, and vertically, the limit is increases with the input-output ratio (ROI) increases. FWHP of oil well b1-40-527 is 0.4 Mpa, well spacing is 300 m, oil well radius is 0.1 m, viscosity is 8.8 mPa. s, production time of 300 d, density of 0.86 g/cm3, when ROI is 1:2, the lower limit of the cumulative oil raised production is 206.9 t and daily increasing oil floor is 0.69 t/d, the minimum released effective thickness is 8.4 m as oil price is 60 $/BBL, meanwhile, the lower limit of the cumulative oil raised production is 421.4 t and daily increasing oil floor is 1.4 t/d when oil price is 40 $/BBL. After increasing the thickness of released layer according the limit, it is verified by actual data, that the increasing oil production of daily and accumulated reached to the calculation minimum limit after thickness increased by re-unsealing. The fluid production daily of the well b1-40-527 was 41.41 t/d and oil production was 1.53 t/d, water cut was 96.3% before the well releasing, then, the well was released firstly in July 2021, total effective thickness released is 6.6 m, after the released, the daily oil production was 1.92 t/d, the daily water cut was 96.3%, and oil production daily increased is 0.39 t/d, which is lower than the requirement of 0.79 t with oil price is 60 $/BBL and ROI is 1:2, therefore, the lower permeability layers were added, the total released thickness is to 10.7 m, which meets the requirement of unsealing, and the daily fluid production of the well b1-40-527 was to 67.79 t/d, the daily oil production was 3.2 t/d, the daily water cut was 95.3%, daily oil production increased was by 1.25 t/d, water cut decreased is 1.0%, and the releasing measure is valid still now.

This paper is concerned with transparent boundary conditions (TBCs) for the time-dependent Schrödinger equation in one and two dimensions. Discrete TBCs are introduced in the numerical simulations of whole space problems in order to reduce the computational domain to a finite region. Since the discrete TBC for the Schrödinger equation includes a convolution w.r.t. time with a weakly decaying kernel, its numerical evaluation becomes very costly for large-time simulations. As a remedy we construct approximate TBCs with a kernel having the form of a finite sum-of-exponentials, which can be evaluated in a very efficient recursion. We prove stability of the resulting initial-boundary value scheme, give error estimates for the considered approximation of the boundary condition, and illustrate the efficiency of the proposed method on several examples.

The general behavior of the nuclear equation of state (EOS), relevant for the description of neutron stars (NS), is studied within a Bayesian approach applied to a set of models based on a density-dependent relativistic mean-field description of nuclear matter Malik et al 2022. The EOS is subjected to a minimal number of constraints based on nuclear saturation properties and the low-density pure neutron matter EOS obtained from a precise next-to-next-to-next-to-leading order (N$^{3}$LO) calculation in chiral effective field theory ($\chi$EFT). The number of final sample parameters corresponding to the posterior sets is around fourteen thousand. We present five EOSs among them, namely DDBl, DDBm, DDBu1, DDBu2, and DDBx. The DDBl, DDBm, DDBu2 were chosen so that the radius of the 1.4$M_\odot$ star has the lower limit, a medium value, and the upper limit of the 90% CI for the conditional probabilities $P(R|M)$. We have also included DDBu1 that has a slightly lower $R_{1.4}$ than the upper limit but lies completely inside the 90% CI for the conditional probabilities $P(R|M)$. The DDBx is the one that predicts a maximum mass of 2.5$M_\odot$ and has the following nuclear matter properties, $K_0=300$ MeV, $J_{sym,0}=30$ MeV and $L_{sym,0}=39$ MeV.

We also release our entire sets of ~14K NS matter EOS. All the EOSs are for NS core and starting baryon density is 0.04 fm$^{-3}$. One needs to add their own choice of crust EOS for the star properties calculation. The uncertainty in star properties for the choice of the different crust has been discussed in Section 2.1 of the manuscript (arxiv: 2201.12552).

To extract the entire sets of ~14K NS matter EOS files, one needs to follow the steps,
1) unzip DDB_EOS_14K.zip
----------------------------Note-------------------------------------
All the eos files have three columns baryon density (fm-3), energy density (MeV.fm-3), and pressure (MeV.fm-3). The starting density is 0.04 fm-3, as it is NS core eos. One needs to add their own choice of crust eos in order to calculate NS properties. 
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The global probiotic infant formula market is experiencing robust growth, driven by increasing awareness of gut health's importance in infant development and the rising prevalence of infant gut-related disorders. Parents are increasingly seeking formulas that promote a healthy gut microbiome, leading to higher demand for products enriched with probiotics. This trend is further fueled by advancements in probiotic research, resulting in more effective and targeted formulations. The market is segmented by various factors including probiotic strains used, formula type (powdered, liquid), and distribution channels (online, offline). Major players like Enfamil, Similac, Nestlé Health Science, and Bellamy's Organic are heavily invested in research and development, leading to product innovation and increased market competition. The market's CAGR, while not specified, can be reasonably estimated at 7-9% based on industry trends and the growth observed in related sectors like infant nutrition and functional foods. This growth is anticipated to continue throughout the forecast period (2025-2033), driven by increasing disposable incomes in developing economies and rising health consciousness among parents globally. However, market growth faces challenges. Regulatory hurdles and varying standards across different regions present a significant restraint. Moreover, the high cost of production and stringent quality control measures associated with probiotic infant formula can limit accessibility, particularly in lower-income demographics. Furthermore, concerns about the long-term effects of probiotic supplementation in infants require ongoing research and transparency to maintain consumer confidence. Despite these challenges, the overall market outlook remains positive, with considerable scope for growth through strategic partnerships, increased product diversification, and targeted marketing campaigns emphasizing the health benefits of probiotic infant formula. The market is expected to witness consolidation in the coming years, with larger players acquiring smaller companies to enhance their market share and product portfolio.

The Mathematica notebook (extension "nb"), which requires as input the three text files with lists, containing a total of 3909 x 4 numbers, calculates the inverse of the exponential integral Ei[x]. The method and all details are provided in the manuscript "Numerical calculation of the inverse of the exponential integral Ei(x) with a quartic polynomial". The PDF file is the "printed" Mathematica notebook, for inspection of the algorithm without the software. Each entry in the list files with the calculated interval limits consists of four numbers, that represent the exponential integral of the lower limits, the exponential integral of the upper limits, the X0s, and the exponential integral of the X0s; in the case of logarithmic transformation (x >= 10), the natural logarithm of the first two numbers is taken. In the filenames, "Neg" stands for "negative", "Pos" for "positive, and "Eps11" refers to epsilon = 10^-11.

AL refers to the axial length, CCT to the central corneal thickness, ACD to the external phakic anterior chamber depth measured from the corneal front apex to the front apex of the crystalline lens, LT to the central thickness of the crystalline lens, R1 and R2 to the corneal radii of curvature for the flat and steep meridians, Rmean to the average of R1 and R2, PIOL to the refractive power of the intraocular lens implant, and SEQ to the spherical equivalent power achieved 5 to 12 weeks after cataract surgery.

Abstract Background: Simplified projected aortic valve area (EOAproj) is a valuable echocardiographic parameter in the evaluation of low flow low gradient aortic stenosis (LFLG AS). Its widespread use in clinical practice is hampered by the laborious process of flow rate (Q) calculation. Objetive: This study proposes a less burdensome, alternative method of Q calculation to be incorporated in the original formula of EOAproj and measures the agreement between the new proposed method of EOAproj calculation and the original one. Methods: Retrospective observational single-institution study that included all consecutive patients with classic LFLG AS that showed a Q variation with dobutamine infusion ≥ |15|% by both calculation methods. Results: Twenty-two consecutive patients with classical LFLG AS who underwent dobutamine stress echocardiography were included. Nine patients showed a Q variation with dobutamine infusion calculated by both classical and alternative methods ≥ |15|% and were selected for further statistical analysis. Using the Bland-Altman method to assess agreement we found a systematic bias of 0,037 cm2 (95% CI 0,004 - 0,066), meaning that on average the new method overestimates the EOAproj in 0,037 cm2 compared to the original method. The 95% limits of agreement are narrow (from -0,04 cm2 to 0,12 cm2), meaning that for 95% of individuals, EOAproj calculated by the new method would be between 0,04 cm2 less to 0,12 cm2 more than the EOAproj calculated by the original equation. Conclusion: The bias and 95% limits of agreement of the new method are narrow and not clinically relevant, supporting the potential interchangeability of the two methods of EOAproj calculation. As the new method requires less additional measurements, it would be easier to implement in clinical practice, promoting an increase in the use of EOAproj.

NMR calculation statistics for an ensemble of the 20 lowest energy structures of REF54–155 bound to ICP27103–138.

Explorative data of corneal thickness at the apex (CCT) and at the thinnest point of the cornea (TCT) in terms of mean, standard deviation, median and the lower (2.5% quantile) and upper boundary (97.5% quantile) of the 95% confidence interval. In the left block we displayed the mean values for the 3 repeat measurements (indicated by (.)m), and on the right block the deviations of the 3 repeat measurements from the mean value (indicated by (.)d). Table cells in bold letters indicate the within-subject standard deviations Sw. The portion of repeat measurements outside the clinically relevant threshold of ±5 micron from the mean value is shown in the last row.

Human breathing is crucial for studying indoor environments and human health. Computational Fluid Dynamics (CFD) is a key tool for simulating human respiration. To enhance the accuracy of CFD simulations and reduce computation time, a new simulation strategy for human respiration is proposed in this paper. The effects of steady versus unsteady boundary conditions on simulation results were examined. For the unsteady boundary, sinusoidal exhalation velocities and non-inhalation gas were assumed, while the steady boundary involved constant velocities during both exhalation and inhalation phases. The jet center trajectory under different boundary conditions was analyzed and compared with experimental data. Additionally, variations in pollutant dispersion near the mouth under the two boundary conditions were discussed. Furthermore, the paper compared the calculation accuracy, calculation time and memory occupied by a single turbulence model or switching flow character models in human respiration simulation. Differences in exhaled gas vorticity and jet penetration depth across different flow models were identified. Finally, combined with the non-iterative algorithm, the optimal strategy of human respiration simulation was proposed. Results show that under the comprehensive consideration of calculation accuracy, calculation time and memory occupancy, using sinusoidal expiratory boundary conditions combined with the PISO algorithm, with the RNG k-ε model during expiratory phase, and switching into the laminar flow during inspiratory phase, is the optimal strategy of simulating human breathing.

SD refers to the standard deviation, 2.5% quantile and 97.5% quantile to the lower and upper boundary of the 95% confidence interval, and IQR to the interquartile range as the difference between the 75% and the 25% quantile. Formula constant optimisation was performed to minimise the sum of squared prediction errors PE. Situation A) refers to the ‘classical’ formulae with standard nK/nC values, with situation B) the formula constants and nK/nC in the main part of the formula were varied for optimisation, with situation C) the formula constants and nK/nC in the main part of the formula were varied to minimise for PE and the PE trend error over corneal radius, and with situation D) a standard optimisation was performed using the nK/nC value from situation B) derived from the other dataset in terms of a cross-validation.

We obtained families of generalized van der Waals equations characterized by an even number n = 2, 4, 6 and a continuous free parameter, which is tunable for a critical compressibility factor. Each equation features two adjacent critical points which have a common critical temperature Tc and arbitrarily two close critical densities. The critical phase transitions are naturally two-sided: the critical exponents are αP=γP=23 and βP=δ−1=13 for T > Tc and αP=γP=nn+1 and βP=δ−1=1n+1 for T < Tc. In contrast with the original van der Waals equation, our novel equations all reduce consistently to the classical ideal gas law in the low-density limit. We tested our formulas against the NIST data for 11 major molecules and showed agreements better than the original van der Waals equation, not only near to the critical points but also in low-density regions.

The number of CFU in the TBLN could not be quantified for all rabbits at 24h and 36h, due to the CFU being too numerous to count after plating. This is why we only have a lower bound for the number of CFU for some of the rabbits at these times. For the rabbits that died before the time point at which they were scheduled to be sacrificed, we assume that if they had survived then their CFU measurement would have been greater than the highest measurement observed for a surviving animal, which was CFU in the TBLN and CFU in the blood. These data were obtained during the study published by Gutting et al. [22]