Mn Log Research Articles

Association between blood heavy metal exposure levels and risk of metabolic dysfunction associated fatty liver disease in adults: 2015-2020 NHANES large cross-sectional study.

The relationships between heavy metals and fatty liver, especially the threshold values, have not been fully elucidated. The objective of this research was to further investigate the correlation between blood heavy metal exposures and the risk of Metabolic dysfunction Associated Fatty Liver Disease (MAFLD) in adults. Laboratory data on blood metal exposure levels were obtained from National Health and Nutrition Examination Survey (NHANES) data for the period 2015 to 2020 for a cross-sectional study in adults. Associations between blood levels of common heavy metals and the risk of MAFLD in adults were analyzed using multifactorial logistic regression and ranked for heavy metal importance using a random forest model. Finally, thresholds for important heavy metals were calculated using piecewise linear regression model. In a multifactorial logistic regression model, we found that elevated levels of selenium (Se) and manganese (Mn) blood exposure were strongly associated with the risk of MAFLD in adults. The random forest model importance ranking also found that Se and Mn blood exposure levels were in the top two positions of importance for the risk of disease in adults. The restricted cubic spline suggested a non-linear relationship between Se and Mn blood exposure and adult risk of disease. The OR (95% CI) for MAFLD prevalence was 3.936 (2.631-5.887) for every 1 unit increase in Log Mn until serum Mn levels rose to the turning point (Log Mn = 1.10, Mn = 12.61 μg/L). This correlation was not significant (p > 0.05) after serum Mn levels rose to the turning point. A similar phenomenon was observed for serum Se levels, with a turning point of (Log Se = 2.30, Se = 199.55 μg/L). Blood heavy metals, especially Se and Mn, are significantly associated with MAFLD in adults. They have a non-linear relationship with a clear threshold.

Online load balancing with general reassignment cost

We investigate a semi-online variant of load balancing with restricted assignment. In this problem, we are given n jobs, which need to be processed by m machines with the goal to minimize the maximum machine load. Since strong lower bounds rule out any competitive ratio of o(log⁡n), we may reassign jobs at a certain job-individual cost. We generalize a result by Gupta, Kumar, and Stein (SODA 2014) by giving a O(log⁡log⁡mn)-competitive algorithm with constant amortized reassignment cost.

Trigeminal sensory modulatory effects of galcanezumab and clinical response prediction.

Galcanezumab, a monoclonal antibody against calcitonin gene-related peptide, is an emerging migraine preventative. We hypothesized that the preventive effects are conveyed via the modulation of somatosensory processing and that certain sensory profiles may hence be associated with different clinical responses. We recruited migraine patients (n = 26), who underwent quantitative sensory tests over the right V1 dermatome and forearm at baseline (T0), 2 to 3 weeks (T1) and 1 year (T12) after monthly galcanezumab treatment. The clinical response was defined as a reduction of ≥30% in headache frequency based on the headache diary. Predictors for clinical response were calculated using binary logistical regression models. After galcanezumab (T1 vs T0), the heat pain threshold (°C, 44.9 ± 3.4 vs 43.0 ± 3.3, P = 0.013) and mechanical pain threshold (log mN, 1.60 ± 0.31 vs 1.45 ± 0.26, P = 0.042) were increased exclusively in the V1 dermatome but not the forearm. These changes were immediate, did not differ between responders and nonresponders, and did not last in 1 year of follow-up (T12 vs T0). However, baseline heat pain threshold (OR: 2.13, 95% CI: 1.08-4.19, P = 0.029) on the forearm was a robust predictor for a clinical response 3 months later. In summary, our data demonstrated that galcanezumab modulates pain thresholds specifically in the V1 dermatome, but this modulation is short-lasting and irrelevant to clinical response. Instead, the clinical response may be determined by individual sensibility even before the administration of medication.

On the Length of Shortest Strings Accepted by Two-way Finite Automata

Given a two-way finite automaton recognizing a non-empty language, consider the length of the shortest string it accepts, and, for each n ≥ 1, let f(n) be the maximum of these lengths over all n-state automata. It is proved that for n-state two-way finite automata, whether deterministic or nondeterministic, this number is at least Ω(10n/5) and less than (2nn+1), with the lower bound reached over an alphabet of size Θ(n). Furthermore, for deterministic automata and for a fixed alphabet of size m ≥ 1, the length of the shortest string is at least e(1+o(1))mn(log n− log m).

Umbilical Cord Blood Metal Mixtures and Birth Size in Bangladeshi Children.

Background:Studies have evaluated environmental exposure to toxic metals such as arsenic (As), cadmium (Cd), manganese (Mn), or lead (Pb) on birth size; however, information on potential effects of exposures to metal mixtures is limited.Objectives:We assessed the association between metal mixtures (As, Cd, Mn, Pb) in umbilical cord blood and neonate size in Bangladeshi children.Methods:In this birth cohort study, pregnant women who were of age with an ultrasound-confirmed singleton pregnancy of gestation were recruited from two Bangladesh clinics between 2008 and 2011. Neonate size metrics were measured at the time of delivery. Metals in cord blood were measured using inductively coupled plasma mass spectrometry. We employed multivariable linear regression and Bayesian kernel machine regression (BKMR) to estimate associations of individual metals and metal mixtures with birth size parameters.Results:Data from 1,088 participants was assessed. We found a significant negative association between metal mixture and birth length and head circumference when all metal concentrations were above the 60th and 55th percentiles, respectively, compared with the median. An interquartile range (IQR) increase in log Cd concentration {log[Cd (in micrograms per deciliter)] } was associated with a 0.13-standard deviation (SD) decrease in mean birth length (95% CI: , ) and a 0.17-SD decrease in mean head circumference (95% CI: , ), based on linear regression models adjusted for covariates and the other metals. An IQR increase in log Mn concentration {log[Mn (in micrograms per deciliter)] } was associated with a 0.07-SD decrease in mean birth weight (95% CI: , 0.002).Discussion:Metal mixtures in cord blood were associated with reduced birth size in Bangladeshi children. Results from linear regression models adjusted and the BKMR mixtures analyses suggest adverse effects of Cd and Mn, as individual metal exposures, on birth size outcomes. https://doi.org/10.1289/EHP7502

On a Routing Open Shop Problem on Two Nodes with Unit Processing Times

The Routing Open Shop Problem deals with $$n $$ jobs located in the nodes of an edge-weighted graph $$G=(V,E) $$ and $$m $$ machines that are initially in a special node calleddepot. The machines must process all jobs in arbitrary order so that each machine processes at most one job at any one time and each job is processed by at most one machine at any one time. The goal is to minimize the makespan; i.e., the time when the last machine returns to the depot. This problem is known to be NP-hard even for the two machines and the graph containing only two nodes. In this article we consider the particular case of the problem with a $$2$$ -node graph, unit processing time of each job, and unit travel time between every two nodes. The conjecture is made that the problem is polynomially solvable in this case; i.e., the makespan depends only on the number of machines and the loads of the nodes and can be calculated in time $$O(\log mn) $$ . We provide some new bounds on the makespan in the case of $$m = n $$ depending on the loads distribution.

Fast Exponentially Convergent Solution of Electromagnetic Scattering From Multilayer Concentric Magnetodielectric Cylinders by the Spectral Integral Method

The multilayer surface integral equations (SIEs) for electromagnetic scattering by infinitely long magnetodielectric cylinders with an arbitrary number of layers are derived and solved by the spectral integral method (SIM). Singularity subtraction for the 2-D Green's function is used to enhance the computation accuracy and achieve exponential convergence. The final matrix equation after discretization is formed in the Fourier spectral domain rather than the spatial domain, which greatly expedites the SIM solution by accelerating the convolution via the fast fourier transform (FFT) algorithm. A recursive method is proposed to solve the spectral integral equations instead of using an iterative method to lower the computation complexity. Numerical examples for ordinary multilayer cylinders and invisibility cloak cylinders are presented to validate the SIM results by comparing the total fields, scattered fields, and radar cross section (RCS) to analytical solutions or finite-element simulations. They verify that the recursive solution has a complexity of O(MN log N) for an M-layer cylinder with N discrete points on each interface. Meanwhile, the SIM outperforms the analytical method because only the 0th-order and 1st-order special functions (Bessel functions and Hankel functions) are used in the SIM but higher-order functions are necessary for the analytical method to maintain the accuracy.

Quantum speedup of twin support vector machines

We devise new quantum algorithms that exponentially speeds up the training and prediction procedures of twin support vector machines (TSVM). To train TSVMs using quantum methods, we demonstrate how to prepare the desired input states according to classical data, and these states are used in the quantum algorithm for the system of linear equations. In the prediction process, we employ a quantum circuit to estimate the distances from a new sample to the hyperplanes and then make a decision. The proposed quantum algorithms can learn two non-parallel hyperplanes and classify a new sample by comparing the distances from the sample to the two hyperplanes in $O(\log mn)$ time, where $m$ is the sample size and $n$ is the dimension of each data point. In contrast, the corresponding classical algorithm requires polynomial time for both the training and prediction procedures.

A Simpler and Faster Strongly Polynomial Algorithm for Generalized Flow Maximization

We present a new strongly polynomial algorithm for generalized flow maximization that is significantly simpler and faster than the previous strongly polynomial algorithm [34]. For the uncapacitated problem formulation, the complexity bound O ( mn ( m + n log n )log ( n 2 / m )) improves on the previous estimate by almost a factor O ( n 2 ). Even for small numerical parameter values, our running time bound is comparable to the best weakly polynomial algorithms. The key new technical idea is relaxing the primal feasibility conditions. This allows us to work almost exclusively with integral flows, in contrast to all previous algorithms for the problem.

Low-Complexity Linear Equalization for OTFS Modulation

In this letter, we propose low-complexity linear equalizers for orthogonal time frequency space (OTFS) modulation that exploit the structure of the effective channel matrix in OTFS. The proposed approach exploits the block circulant nature of the OTFS channel matrix to achieve significant complexity reduction. For an $N\times M$ OTFS system, where $N$ and $M$ are the number of Doppler and delay bins, respectively, the proposed approach gives exact minimum mean square error (MMSE) and zero-forcing (ZF) solutions with just $\mathcal {O}(MN \log MN)$ complexity, while MMSE and ZF solutions using the traditional matrix inversion approach require $\mathcal {O}(M^{3}N^{3})$ complexity. The proposed approach can provide low complexity initial solutions for local search techniques to achieve enhanced bit error performance.

Randomized nonlinear model order reduction methods for large dynamical problems with explicit time integration

AbstractProjection‐based nonlinear model order reduction (MOR) often involves the computation of a truncated singular value decomposition (SVD) of a snapshot matrix A ∈ ℝm×n, m≥n, computed from training simulations, where only the first k basis vectors are retained. A can however become very large in case of detailed models with a large number of degrees of freedom (DoFs), or when many snapshots are present. This is often the case for explicit FEM simulations of industrial problems. Computing the SVD can then become problematic, as most widely used SVD algorithms for MOR have an asymptotic complexity of 𝒪(mn2 ) [1]. Randomized algorithms can alternatively be used to compute only the k most significant basis vectors. Such methods only scale with 𝒪(mnk) or even 𝒪(mn log(k)) [2]. We present a modified hybrid randomized incremental algorithm for efficient reduced basis (RB) computation with low memory requirements, and apply the method to a large‐scale example problem. The results show that the hybrid algorithm is capable of efficiently computing a RB even for very large problems at a manageable computational effort.

A tractable discrete fractional programming: application to constrained assortment optimization

In this note, we consider a discrete fractional programming in light of a decision problem where limited number of indivisible resources are allocated to several heterogeneous projects to maximize the ratio of total profit to total cost. For each project, both profit and cost are solely determined by the amount of resources allocated to it. Although the problem can be reformulated as a linear program with $$O(m^2 n)$$O(m2n) variables and $$O(m^2 n^2)$$O(m2n2) constraints, we further show that it can be efficiently solved by induction in $$O(m^3 n^2 \log mn)$$O(m3n2logmn) time. In application, this method leads to an $$O(m^3 n^2 \log mn)$$O(m3n2logmn) algorithm for assortment optimization problem under nested logit model with cardinality constraints (Feldman and Topaloglu, Oper Res 63: 812---822, 2015).

Efficient hierarchical identity based encryption scheme in the standard model over lattices

Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only (dm 2 + mn) log q bits and whose message-ciphertext expansion factor is only log q, where d is the maximum hierarchical depth and (n, m, q) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2dm 2 + mn +m) log q. To reduce the message-ciphertext expansion factor of the proposed scheme to log q, the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m 2 bits of plaintext are encrypted into m 2 log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.

Laguerre–Galerkin methods with reduced sum-products

The always stable solution of time-domain integral equations by plain implementation of the classical marching-on-in-degree (MOD) methods demands O(M2N3) operations, where M and N are, respectively, the spatial and temporal degrees of freedom. Diverse caching and basis reordering approaches are first explored to reduce the number of matrix–vector multiplications necessary to compute the right hand side of the MOD system. The new schemes primarily eliminate the existing O(N) innermost vector summations on all past polynomial orders. This complexity reduction facilitates the usage of FFT approaches to accelerate the calculation of existing temporal convolutions. In an additive secondary stage, the recursive time convolution products of the Toeplitz block aggregates of the retarded interaction matrices are expedited by array multiplications in spectral domain. When the translation invariancy on time-order indices are placed on the outermost possible nested Toeplitz levels due to the space shift invariancy, the overall computational complexities and memory requirements can be further reduced to O(MNlog(MN)) and O(MN), respectively.

A note on scheduling jobs with equal processing times and inclusive processing set restrictions

We consider the problem of scheduling n jobs on m parallel machines with inclusive processing set restrictions. Each job has a given release date, and all jobs have equal processing times. The objective is to minimize the makespan of the schedule. Li and Li (2015) have developed an O(n2+mn log n) time algorithm for this problem. In this note, we present a modified algorithm with an improved time complexity of O(min{m, log n} ⋅ n log n).

On the number of matroids

We consider the problem of determining mn, the number of matroids on n elements. The best known lower bound on mn is due to Knuth (1974) who showed that log log mn is at least n − 3/2 log n−O(1). On the other hand, Piff (1973) showed that log log mn ≤ n − log n + log log n + O(1), and it has been conjectured since that the right answer is perhaps closer to Knuth's bound.We show that this is indeed the case, and prove an upper bound on log log mn that is within an additive 1 + o(1) term of Knuth's lower bound. Our proof is based on using some structural properties of non-bases in a matroid together with some properties of independent sets in the Johnson graph to give a compressed representation of matroids.

On Sub-determinants and the Diameter of Polyhedra

We derive a new upper bound on the diameter of a polyhedron $$P = \{x {\in } {\mathbb {R}}^n :Ax\le b\}$$ P = { x ? R n : A x ≤ b } , where $$A \in {\mathbb {Z}}^{m\times n}$$ A ? Z m × n . The bound is polynomial in $$n$$ n and the largest absolute value of a sub-determinant of $$A$$ A , denoted by $$\Delta $$ Δ . More precisely, we show that the diameter of $$P$$ P is bounded by $$O(\Delta ^2 n^4\log n\Delta )$$ O ( Δ 2 n 4 log n Δ ) . If $$P$$ P is bounded, then we show that the diameter of $$P$$ P is at most $$O(\Delta ^2 n^{3.5}\log n\Delta )$$ O ( Δ 2 n 3.5 log n Δ ) . For the special case in which $$A$$ A is a totally unimodular matrix, the bounds are $$O(n^4\log n)$$ O ( n 4 log n ) and $$O(n^{3.5}\log n)$$ O ( n 3.5 log n ) respectively. This improves over the previous best bound of $$O(m^{16}n^3(\log mn)^3)$$ O ( m 16 n 3 ( log m n ) 3 ) due to Dyer and Frieze (Math Program 64:1---16, 1994).

A decomposition for in-place matrix transposition

We describe a decomposition for in-place matrix transposition, with applications to Array of Structures memory accesses on SIMD processors. Traditional approaches to in-place matrix transposition involve cycle following, which is difficult to parallelize, and on matrices of dimension m by n require O(mn log mn) work when limited to less than O(mn) auxiliary space. Our decomposition allows the rows and columns to be operated on independently during in-place transposition, reducing work complexity to O(mn), given O(max(m, n)) auxiliary space. This decomposition leads to an efficient and naturally parallel algorithm: we have measured median throughput of 19.5 GB/s on an NVIDIA Tesla K20c processor. An implementation specialized for the skinny matrices that arise when converting Arrays of Structures to Structures of Arrays yields median throughput of 34.3 GB/s, and a maximum throughput of 51 GB/s. Because of the simple structure of this algorithm, it is particularly suited for implementation using SIMD instructions to transpose the small arrays that arise when SIMD processors load from or store to Arrays of Structures. Using this algorithm to cooperatively perform accesses to Arrays of Structures, we measure 180 GB/s throughput on the K20c, which is up to 45 times faster than compiler-generated Array of Structures accesses. In this paper, we explain the algorithm, prove its correctness and complexity, and explain how it can be instantiated efficiently for solving various transpose problems on both CPUs and GPUs.

Volume based expression of soil variables: Good descriptor of soil-plant interrelationships

This research compared the gravimetric method of expression of soil nutrient concentration with actual soil volume based expression in terms of yield response using rubber as a test crop. A rubber plantation (planted in year 1989 under a NPK fertilizer trial) was investigated. The experiment was laid out with thirteen treatments in three replications in a randomized block design planted with rubber (Clone RRII 105) at a spacing of 4.9 × 4.9 m. Twenty-four trees formed the main plot and 8 trees were used for measurements of plant related and soil parameters. The treatments included selected combinations of N, P and K; three rates of N (30, 60 and 90 kg ha-1 year-1), two rates of P (30 and 60 kg ha-1 year-1) and two rates of elemental potassium (20 and 40 kg ha-1 year-1) and a control (without fertilizer application). Urea, rock phosphate and muriate of potash were applied as source of elements, N, P and K, respectively. All the nutrients were supplied in two equal splits during April-May and September-October every year. During August 1999, soil samples were collected from all the 39 plots from a depth of 0 to 30 cm. From all these plots rubber latex yield data were also recorded simultaneously at the time of soil sampling. Results revealed that soils vary in plant exploitable actual soil volume (ASV) and its contents. However soil nutrients are not widely expressed on volume basis and gravimetric expression can be misleading when ASV is not known. Soils had different descriptive statistics of variables when expressed in both ways. No gravimetric variables were correlated with rubber yield while volumetric Ca correlated significantly (r = 0.576**). Path analysis showed that log P, log Ca, Mg, log Mn and log Fe had prominent direct effects (0.521, 0.944, 0.454, -0.595 and -0.735, respectively) and variable indirect effects through other variables. However, log Ca only yielded significant correlation with yield even after partial neutralization of direct effect with indirect effects. Path analysis revealed prominent interactions through indirect effects although some correlations (sum of direct and indirect effects) were insignificant and described 57% variability indicating the scope for inclusion of other variables to describe yield. The study provided a lead indicating the merit of volumetric expression over gravimetric expression to explore further as these observations are of practical significance in soils with spatially varied contents of coarse fragments. Key words: Actual soil volume, expression, nutrient content, path analysis, rubber latex yield.

Robust Free Space Computation for Curved Planar Bodies

We present a free space computation algorithm for two planar bodies bounded by line segments and circular arcs. The computational complexity is O(((mn)2+k)log(mn)) with m and n the number of boundary curves of the two bodies, and with k the number of configurations with three pairs of curves in contact. Although k is in O((mn)3), mild input restrictions reduce it to O(mn). We develop a robust implementation that is accurate, is fast, and handles degenerate input.