Quantitative Version Research Articles

Stability estimates for the magnetic Schrödinger operator with partial measurements

In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset in Rn with n≥3, from measurements on open subsets of its boundary. This inverse problem is associated with a magnetic Schrödinger operator. Our estimates are quantitative versions of the uniqueness results obtained by D. Dos Santos Ferreira, C.E. Kenig, J. Sjöstrand and G. Uhlmann in [13]. The moduli of continuity are of logarithmic type.

FACTORS AFFECTING THE DELAY OF THE LONG SEGMENT SCHEME ROAD MAINTENANCE PROJECT IN CENTRAL SULAWESI PROVINCE

Road maintenance is a road handling activity in the form of prevention, maintenance, and repair so that it continues to function optimally to serve traffic. The long segment road maintenance scheme is divided into effective and non-effective scopes. The effective scope of the implementation period is determined by the specific terms of the contract, and the non-effective scope ends December 31 of the current year. Implementation control is determined in the schedule. The project is considered critical if it is minus (-10%) for period I and minus (-5%) for period II. If it is critical, control is carried out by conducting a Show Cause Meeting (SCM). The non-effective scope applies performance indicators (IK) in the first 90 days. Financial sanctions are imposed on service providers if minus (-5%) is in the critical (late) category. The purpose of this study is to determine the factors that have a positive and significant effect on project delays. The method used is descriptive quantitative analysis method and Smart PLS version 3 analysis tool, with a sample size of 82 respondents. The results of the study (T-statistics), human resource factor (0.161), financial factor (3.400), material factor (0.024), equipment factor (2.097), and implementation method factor (2.144), had a significant effect if T-statistic > 1, 96, the dependent variable is the delay in the long segment scheme project in Central Sulawesi Province.

High-Dimensional Central Limit Theorems for Homogeneous Sums

This paper develops a quantitative version of de Jong’s central limit theorem for homogeneous sums in a high-dimensional setting. More precisely, under appropriate moment assumptions, we establish an upper bound for the Kolmogorov distance between a multi-dimensional vector of homogeneous sums and a Gaussian vector so that the bound depends polynomially on the logarithm of the dimension and is governed by the fourth cumulants and the maximal influences of the components. As a corollary, we obtain high-dimensional versions of fourth-moment theorems, universality results and Peccati–Tudor-type theorems for homogeneous sums. We also sharpen some existing (quantitative) central limit theorems by applications of our result.

A quantitative constant rank theorem for quasiconcave solutions to fully nonlinear elliptic equations

We investigate the fully nonlinear elliptic equations F(D2u,Du,u,x)=0, which satisfy the structural condition previously posed by Bianchini-Longinetti-Salani in 2009. By establishing a novel differential inequality, we prove a weak Harnack inequality for the principal curvatures of the level surfaces of the solutions. This result is indeed a quantitative version of the constant rank theorem showed by Guan-Xu in 2013.

A map of neurofilament light chain species in brain and cerebrospinal fluid and alterations in Alzheimer's disease.

Neurofilament light is a well-established marker of both acute and chronic neuronal damage and is increased in multiple neurodegenerative diseases. However, the protein is not well characterized in brain tissue or body fluids, and it is unknown what neurofilament light species are detected by commercial assays and whether additional species exist. We developed an immunoprecipitation-mass spectrometry assay using custom antibodies targeting various neurofilament light domains, including antibodies targeting Coil 1A/1B of the rod domain (HJ30.13), Coil 2B of the rod domain (HJ30.4) and the tail region (HJ30.11). We utilized our assay to characterize neurofilament light in brain tissue and CSF of individuals with Alzheimer’s disease dementia and healthy controls. We then validated a quantitative version of our assay and measured neurofilament light concentrations using both our quantitative immunoprecipitation-mass spectrometry assay and the commercially available immunoassay from Uman diagnostics in individuals with and without Alzheimer’s disease dementia. Our validation cohort included CSF samples from 30 symptomatic amyloid-positive participants, 16 asymptomatic amyloid-positive participants, 10 symptomatic amyloid-negative participants and 25 amyloid-negative controls. We identified at least three major neurofilament light species in CSF, including N-terminal and C-terminal truncations, and a C-terminal fragment containing the tail domain. No full-length neurofilament light was identified in CSF. This contrasts with brain tissue, which contained mostly full-length neurofilament and a C-terminal tail domain fragment. We observed an increase in neurofilament light concentrations in individuals with Alzheimer’s disease compared with healthy controls, with larger differences for some neurofilament light species than for others. The largest differences were observed for neurofilament light fragments including NfL165 (in Coil 1B), NfL324 (in Coil 2B) and NfL530 (in the C-terminal tail domain). The Uman immunoassay correlated most with NfL324. This study provides a comprehensive evaluation of neurofilament light in brain and CSF and enables future investigations of neurofilament light biology and utility as a biomarker.

Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics

We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of the form q(x1,⋯,xn)=m, where q is a non-degenerate integral quadratic form in n⩾3 variables and m is a non-zero integer. This gives asymptotic formulas for the density of integral points taking coprime polynomial values, which is a quantitative version of the arithmetic purity of strong approximation property off infinity for affine quadrics.

A Quantification of a Besicovitch Non-linear Projection Theorem via Multiscale Analysis

The Besicovitch projection theorem states that if a subset E of the plane has finite length in the sense of Hausdorff measure and is purely unrectifiable (so its intersection with any Lipschitz graph has zero length), then almost every orthogonal projection of E to a line will have zero measure. In other words, the Favard length of a purely unrectifiable 1-set vanishes. In this article, we show that when linear projections are replaced by certain non-linear projections called curve projections, this result remains true. In fact, we go further and use multiscale analysis to prove a quantitative version of this Besicovitch non-linear projection theorem. Roughly speaking, we show that if a subset of the plane has finite length in the sense of Hausdorff and is nearly purely unrectifiable, then its Favard curve length is very small. Our techniques build on those of Tao, who in (Proc Lond Math Soc 98:559–584, 2009) proves a quantification of the original Besicovitch projection theorem.

Convergence rates of RLT and Lasserre-type hierarchies for the generalized moment problem over the simplex and the sphere

We consider the generalized moment problem (GMP) over the simplex and the sphere. This is a rich setting and it contains NP-hard problems as special cases, like constructing optimal cubature schemes and rational optimization. Using the reformulation-linearization technique (RLT) and Lasserre-type hierarchies, relaxations of the problem are introduced and analyzed. For our analysis we assume throughout the existence of a dual optimal solution as well as strong duality. For the GMP over the simplex we prove a convergence rate of O(1/r) for a linear programming, RLT-type hierarchy, where r is the level of the hierarchy, using a quantitative version of Pólya’s Positivstellensatz. As an extension of a recent result by Fang and Fawzi (Math Program, 2020. https://doi.org/10.1007/s10107-020-01537-7) we prove the Lasserre hierarchy of the GMP (Lasserre in Math Program 112(1):65–92, 2008. https://doi.org/10.1007/s10107-006-0085-1) over the sphere has a convergence rate of O(1/r^2). Moreover, we show the introduced linear RLT-relaxation is a generalization of a hierarchy for minimizing forms of degree d over the simplex, introduced by De Klerk et al. (J Theor Comput Sci 361(2–3):210–225, 2006).

The proof of a formula concerning the asymptotic behavior of the reciprocal sum of the square of multiple-angle Fibonacci numbers

Let (F_{n})_{n} be the Fibonacci sequence defined by F_{n+2}=F_{n+1}+F_{n} with F_{0}=0 and F_{1}=1. In this paper, we prove that for any integer mgeq 1 there exists a positive constant C_{m} for which limn→∞{(∑k=n∞1Fmk2)−1−(Fmn2−Fm(n−1)2+(−1)mnCm)}=0.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\lim_{n\\to \\infty } \\Biggl\\{ \\Biggl( \\sum_{k=n}^{ \\infty } \\frac{1}{F_{mk}^{2}} \\Biggr)^{-1} - \\bigl(F_{mn}^{2}-F_{m(n-1)}^{2}+(-1)^{mn}C_{m} \\bigr) \\Biggr\\} =0. $$\\end{document} Furthermore, we show that C_{m} tends to 2/5 as mto infty (indeed, we provide quantitative versions of the previous results as well as an explicit form for C_{m}). This confirms some questions proposed by Lee and Park [J. Inequal. Appl. 2020(1):91 2020].

The Erdős-Hajnal conjecture for three colors and triangles

Erdős and Szekeres's quantitative version of Ramsey's theorem asserts that in every 2-edge-coloring of Kn there is a monochromatic clique on at least 12log⁡n vertices. The famous Erdős-Hajnal conjecture claims that forbidding fixed colorings on subgraphs ensures much larger monochromatic cliques. Specifically, the most general, multi-color version of the conjecture states that for any fixed integers k,s and any s-edge-coloring c of Kk, there exists ε>0 such that in any s-edge-coloring of Kn that avoids c there is a clique on at least nε vertices, using at most s−1 colors. The conjecture is open in general, though a few partial results are known.Here, we focus on quantitative aspects of this conjecture in the case when k=3 and s=3, and when there are several forbidden subgraph colorings. More precisely, for a family H of triangles, each edge-colored with colors from {r,b,y}, Forb(n,H) denotes the family of edge-colorings of Kn using colors from {r,b,y} and containing none of the colorings from H. Let h2(n,H) be the maximum q such that any coloring from Forb(n,H) has a clique on at least q vertices using at most two colors. We provide bounds on h2(n,H) for all families H consisting of at most three triangles. For most of them, our bounds are asymptotically tight. This, in particular, extends a result of Fox, Grinshpun, and Pach, who determined h2(n,H) for H consisting of a rainbow triangle. In addition, we prove that for some H, h2(n,H) corresponds to certain classical Ramsey numbers, smallest independence number in graphs of given odd girth, or some other natural graph theoretic parameters.

The relative Mishchenko–Fomenko higher index and almost flat bundles II: Almost flat index pairing

This is the second part of a series of papers which bridges the Chang–Weinberger–Yu relative higher index and geometry of almost flat Hermitian vector bundles on manifolds with boundary. In this paper, we apply the description of the relative higher index given in part I to establish the relative version of the Hanke–Schick theorem, which relates the relative higher index with the index pairing of K-homology cycles and almost flat relative vector bundles. We also deal with the quantitative version and the dual problem of this theorem.

A note on the Nash equilibria of some multi-player reachability/safety games

<p style='text-indent:20px;'>In this short note we study a class of multi-player, turn-based games with deterministic state transitions and reachability / safety objectives (this class contains as special cases "classic" two-player reachability and safety games as well as multi-player and ""stay–in-a-set" and "reach-a-set" games). Quantitative and qualitative versions of the objectives are presented and for both cases we prove the existence of a deterministic and memoryless Nash equilibrium; the proof is short and simple, using only Fink's classic result about the existence of Nash equilibria for <i>multi-player discounted stochastic games</i></p>

On a Berry-Esseen type limit theorem for Boolean convolution

We obtain a sharp estimate of the speed of convergence in the Boolean central limit theorem for measures with finite sixth moment. The main tool is a quantitative version of the Stieltjes-Perron inversion formula.

Quantifications of boundedly complete and shrinking bases

In the present paper, we’ll introduce quantities measuring how far a (Schauder) basis is from being boundedly complete or shrinking. These quantities will be proved to really measure nonbounded completeness or nonshrinkingness of bases by investigating many bases. As applications, they will be used to prove quantitative versions of the well-known relationships between shrinking bases and boundedly complete bases due to R. C. James.

SELF-INFLICTED FIREARM INJURIES AS COMPARED TO THE ACCIDENTAL FIREARM INJURY; A COMPARATIVE ANALYTICAL STUDY TO DETERMINE THE COMMONEST SITE OF NON-SUICIDAL SELF-INFLICTED INJURIES

Objective: To determine the commonest site of non-suicidal self-inflicted firearm wound in comparison with accidental firearm wounds.
 Study Design: Cross sectional study.
 Place and Duration of Study: Combined Military Hospitals Jhelum, Bannu & Kharian, from Nov 2014 to Nov 2018.
 Methodology: Sixty-four patients with firearm injuries were observed. All the participants were males between the ages of 18- 60 years. The injuries were determined to be either self-inflicted or accidental by an independent committee. The participants’ replies and responses were assessed by dividing them into five main domains by using quantitative software SPSS version 20. Variables involving demographic characteristics of participants such as age, occupation, marital and socioeconomic status, were associated with mental health variables such as psychological stress, previous history of self-harm and clinical psychiatric illness.
 Result: Fifteen subjects were found to have self-inflicted injuries and 50 had accidental injuries. There was a marked preference for left foot and left lower limb as a site for non-suicidal self-inflicted injuries (94.6%) as compared to other sites (left upper extremity 1.8%, chest 1.8% and right lower extremity 1.8%).
 Conclusions: Left lower limb and left foot was a more common site for self-injury as compared to the other sites.

Ultradifferentiable extension theorems: A survey

We survey ultradifferentiable extension theorems, i.e., quantitative versions of Whitney’s classical extension theorem, with special emphasis on the existence of continuous linear extension operators. The focus is on Denjoy–Carleman classes for which we develop the theory from scratch and discuss important related concepts such as (non-)quasianalyticity. It allows us to give an efficient and, to a fair extent, elementary introduction to Braun–Meise–Taylor classes based on their representation as intersections and unions of Denjoy–Carleman classes.

Social Selection and the Evolution of Maladaptation.

Evolution by natural selection is often viewed as a process that inevitably leads to adaptation or an increase in population fitness over time. However, maladaptation, an evolved decrease in fitness, may also occur in response to natural selection under some conditions. Social selection, which arises from the effects of social partners on fitness, has been identified as a potential cause of maladaptation, but we lack a general rule identifying when social selection should lead to a decrease in population mean fitness. Here we use a quantitative genetic model to develop such a rule. We show that maladaptation is most likely to occur when social selection is strong relative to nonsocial selection and acts in an opposing direction. In this scenario, the evolution of traits that impose fitness costs on others may outweigh evolved gains in fitness for the individual, leading to a net decrease in population mean fitness. Furthermore, we find that maladaptation may also sometimes occur when phenotypes of interacting individuals negatively covary. We outline the biological situations where maladaptation in response to social selection can be expected, provide both quantitative genetic and phenotypic versions of our derived result, and suggest what empirical work would be needed to test it. We also consider the effect of social selection on inclusive fitness and support previous work showing that inclusive fitness cannot suffer an evolutionary decrease. Taken together, our results show that social selection may decrease population mean fitness when it opposes individual-level selection, even as inclusive fitness increases.

The Sometimes Context-Specific Habituation: Theoretical Challenges to Associative Accounts.

Simple SummaryWhen a stimulus occurs repeatedly without significant consequences, animals tend to decrease their responses to that stimulus. This phenomenon, known as habituation, can be explained by a class of theories that posit that expected events are less effective in provoking their responses than unexpected events. According to Allan Wagner’s priming theory, one of the ways this expectation might happen is via associative learning between the stimulus and the context in which stimulation occurred. In this article, we summarize a few theoretical complexities that derive from this approach along with some relevant empirical questions that remain open to further research.A substantial corpus of experimental research indicates that in many species, long-term habituation appears to depend on context–stimulus associations. Some authors have recently emphasized that this type of outcome supports Wagner’s priming theory, which affirms that responding is diminished when the eliciting stimulus is predicted by the context where the animal encountered that stimulus in the past. Although we agree with both the empirical reality of the phenomenon as well as the principled adequacy of the theory, we think that the available evidence is more provocative than conclusive and that there are a few nontrivial empirical and theoretical issues that need to be worked out by researchers in the future. In this paper, we comment on these issues within the framework of a quantitative version of priming theory, the SOP model.

A rigidity result for metric measure spaces with Euclidean heat kernel

We prove that a metric measure space equipped with a Dirichlet form admitting an Euclidean heat kernel is necessarily isometric to the Euclidean space. This helps us providing an alternative proof of Colding’s celebrated almost rigidity volume theorem via a quantitative version of our main result. We also discuss the case of a metric measure space equipped with a Dirichlet form admitting a spherical heat kernel.

PENGARUH LOKASI WISATA DAN BAURAN PROMOSI TERHADAP MINAT BERKUNJUNG PADA OBJEK WISATA CROCO LITYRE WATERPARK DESA SUNGAI LALA KECAMATAN SUNGAI LALA KABUPATEN INDRAGIRI HULU

This research was conducted at the tourist attraction Croco Lityre Waterpark Sungai Lala Village, Sungai Lala District, Indragiri Hulu Regency. This study aims to determine the effect of tourism location and promotion mix on interest in visiting the Croco Lityre Waterpark tourism object, Sungai Lala Village, Sungai Lala District, Indragiri Hulu Regency. This research uses quantitative descriptive analysis method and SPSS version 26 . The population in this study are all visitors who are visiting Croco Lityre Waterpark in 2020 with a total of 4.123 people. Sampling was determined by accidental sampling technique and obtained a total sample of 98 respondents. Data collection techniques through questionnaires. The types and sources of data used are primary data and secondary data. From the data analysis which includes validity test, reliability test, classical assumption test, simple regression analysis, multiple regression analysis, coefficient of determination test, and significance test with t test (partial) and f test (simultaneous). The results of this study indicate that the results of the first t test hypothesis testing, tourist sites on visiting interest are t count (5,261) > t table (1,66088) which means that tourist locations have a significant effect on visiting interest. The two promotion mixes on visiting interest are t count (8,041) > t table (1.66088) which means that the promotion mix has a significant effect on visiting interest. The results of the calculated f test (35,648) > f table (3.09) which means that the tourist location and the promotion mix simultaneously affect the interest in visiting the Croco Lityre Waterpark tourist attraction, Sungai Lala Village, Sungai Lala District, Indragiri Hulu Regency