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Influential community search aims to find cohesive subgraphs (communities) with considerable influence. It is a fundamental graph management operator that can play a crucial role in biological network analysis, activity organization, and other real-life applications. Existing research on influential community search is mainly focused on deterministic graphs with the assumption that influences between entities are certain. This assumption is invalid in many cases because it ignores the uncertainty which is an inherent property of influence. Against this backdrop, in this paper, we introduce an uncertain influential community model, namely (k,)-influential community, based on which the influential community search problem over uncertain graphs is formulated. Furthermore, we propose an online approach by integrating a peeling-pruning strategy that can progressively refine the given uncertain graph to find the (k,)-influential communities. To further improve the search performance, two novel indexes, ICU-Index and FICU-Index, are developed to organize the (k,)-influential communities at different probabilistic intervals. The indexes decompose the probabilistic interval into multiple subintervals and based on this, the (k,)-influential communities are divided into different groups in turn. Compared with ICU-Index, FICU-Index requires considerably less space with the introduction of two optimization strategies.

Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of $k$ interval graphs, by splitting the graph in some special way. As a recent example of such an approach, the classes of $k$-thin and proper $k$-thin graphs have been introduced generalizing interval and proper interval graphs, respectively. The complexity of the recognition of each of these classes is still open, even for fixed $k \geq 2$. In this work, we introduce a subclass of $k$-thin graphs (resp. proper $k$-thin graphs), called precedence $k$-thin graphs (resp. precedence proper $k$-thin graphs). Concerning partitioned precedence $k$-thin graphs, we present a polynomial time recognition algorithm based on $PQ$-trees. With respect to partitioned precedence proper $k$-thin graphs, we prove that the related recognition problem is \NP-complete for an arbitrary $k$ and polynomial-time solvable when $k$ is fixed. Moreover, we present a characterization for these classes based on threshold graphs., 33 pages

Garside theory emerged from the study of Artin groups and their generalizations. Finite-type Artin groups admit two types of interval Garside structures corresponding to their standard and dual presentations. Concerning affine Artin groups, Digne established interval Garside structures for two families of these groups by using their dual presentations. Recently, McCammond established that none of the remaining dual presentations (except for one additional case) correspond to interval Garside structures. In this paper, shifting attention from dual presentations to other nice presentations for the affine Artin group of type A ˜ discovered by Shi and Corran–Lee–Lee, I will construct interval Garside structures related to this group. This construction is the first successful attempt to establish interval Garside structures not related to the dual presentations in the case of affine Artin groups.

Given a graph G and a set S ⊆ V ( G ) , the Δ -interval of S , [ S ] Δ , is the set formed by the vertices of S and every w ∈ V ( G ) forming a triangle with two vertices of S . If [ S ] Δ = S , then S is Δ -convex of G ; if [ S ] Δ = V ( G ) , then S is a Δ -interval set of G . The Δ -interval number of G is the minimum cardinality of a Δ -interval set and the Δ -convexity number of G is the maximum cardinality of a proper Δ -convex subset of V ( G ) . In this work, we show that the problem of computing the Δ -convexity number is W[1]-hard and NP-hard to approximate within a factor O ( n 1 − ɛ ) for any constant ɛ > 0 even for graphs with diameter 2 and that the problem of computing the Δ -interval number is NP-complete for general graphs. For the positive side, we present characterizations that lead to polynomial-time algorithms for computing the Δ -convexity number of chordal graphs and for computing the Δ -interval number of block graphs. We also present results on the Δ -hull, Δ -interval and Δ -convexity numbers concerning the three standard graph products, namely, the Cartesian, the strong and the lexicographic products, in function of these and well-studied parameters of the operands.

Reliability evaluation of multiprocessor systems is of great significance to the design and maintenance of these systems. As two generalizations of traditional edge connectivity, extra edge connectivity and component edge connectivity are two important parameters to evaluate the fault-tolerant capability of multiprocessor systems. Fast identifying the extra edge connectivity and the component edge connectivity of high order remains a scientific problem for many useful multiprocessor systems. In this article, we determine the $h$ -extra edge connectivity of the 3-ary $n$ -cube $Q_n^3$ for $h\in [1, \frac{3^n-1}{2}]$ . Specifically, we divide the interval $[1, \frac{3^n-1}{2}]$ into some subintervals and characterize the monotonicity of $\lambda _h(Q_n^3)$ in these subintervals and then deduce a recursive closed formula of $\lambda _h(Q_n^3)$ . Based on this formula, an efficient algorithm with complexity $O(\log _3\,N)$ is designed to determine the exact values of $h$ -extra edge connectivity of the 3-ary $n$ -cube $Q_n^3$ for $h\in [1, \frac{3^n-1}{2}]$ completely. Moreover, we also determine the $g$ -component edge connectivity of the 3-ary $n$ -cube $Q_n^3(n\geq 6$ ) for $1\leq g\leq 3^{\lceil \frac{n}{2}\rceil }$ .

In this article, an improved system is constructed using interval type-2 fuzzy sets (IT2FS) and a fuzzy logic controller (FLC) with non-singleton inputs. The primary purpose is to better model nutritional input uncertainty which is propagated through the Type-2 FLC. To this end, methods are proposed to (1) model nutrient uncertainty in food items, (2) extend the nutritional information of a food item using an IT2FS representation for each nutrient incorporating the uncertainty in the extension process, (3) accumulate uncertainties for IT2FS inputs using fuzzy arithmetic, and (4) build IT2FS antecedents for FLC rules based on dietary reference intakes (DRIs). These methods are then used to implement a web application for diet journaling that includes a client-side Type-2 non-singleton Interval Type-2 FLC. The produced application is then compared with the previous work and shown to be more suitable. This is the first known work on diet journaling that attempts to model uncertainty for all anticipated measurement error.

In this paper, we consider the problem of discrete-time, diffusion-based distributed parameter estimation with the agents connected via directed graphs with switching topologies and a self loop at each node. We show that, by incorporating a recently introduced dynamic regressor extension and mixing procedure to a classical gradient-descent algorithm, improved convergence properties can be achieved. In particular, it is shown that with this modification sufficient conditions for global convergence of all the estimators is that one of the sensors receives enough information to generate a consistent estimate and that this sensor is well-connected. The main feature of this result is that the excitation condition imposed on this distinguished sensor is strictly weaker than the classical persistent excitation requirement. The connectivity assumption is also very mild, requiring only that the union of the edges of all connectivity graphs over any time interval with an arbitrary but fixed length contains a spanning tree rooted at the information-rich node. In the case of non-switching topologies, this assumption is satisfied by strongly connected graphs, and not only by them

In the $\varepsilon$-Consensus-Halving problem, a fundamental problem in fair division, there are $n$ agents with valuations over the interval $[0,1]$, and the goal is to divide the interval into pieces and assign a label "$+$" or "$-$" to each piece, such that every agent values the total amount of "$+$" and the total amount of "$-$" almost equally. The problem was recently proven by Filos-Ratsikas and Goldberg [2019] to be the first "natural" complete problem for the computational class PPA, answering a decade-old open question. In this paper, we examine the extent to which the problem becomes easy to solve, if one restricts the class of valuation functions. To this end, we provide the following contributions. First, we obtain a strengthening of the PPA-hardness result of [Filos-Ratsikas and Goldberg, 2019], to the case when agents have piecewise uniform valuations with only two blocks. We obtain this result via a new reduction, which is in fact conceptually much simpler than the corresponding one in [Filos-Ratsikas and Goldberg, 2019]. Then, we consider the case of single-block (uniform) valuations and provide a parameterized polynomial time algorithm for solving $\varepsilon$-Consensus-Halving for any $\varepsilon$, as well as a polynomial-time algorithm for $\varepsilon=1/2$. Finally, an important application of our new techniques is the first hardness result for a generalization of Consensus-Halving, the Consensus-$1/k$-Division problem [Simmons and Su, 2003]. In particular, we prove that $\varepsilon$-Consensus-$1/3$-Division is PPAD-hard., Journal version. Preliminary version appeared at EC '20

Background The anion gap (AG) is often used to evaluate acid-base disorders. The reference interval for normal AG is used to differentiate between raised (gap) or normal AG (non-gap) acidosis. Historically accepted AG values may not be valid with the evolution of modern analytical techniques and the reference interval requires revalidation. Aims To determine the reference interval for AG based on current laboratory techniques. Methods During a health-screening exercise, 284 participants with no major illnesses volunteered surplus blood for analysis. The samples were tested in an internationally-accredited clinical laboratory. AG was calculated by (Na+ ) - (Cl- ) - (HCO3- ) and AGK by (Na+ ) + (K+ ) - (Cl- ) - (HCO3 - ). The reference interval was determined at 2.5th-97.5th percentiles. Analysis was further undertaken for a sub-cohort of 156 individuals with no sub-optimal health indicators. Results Median age was 35 years, BMI 23.4 kg/m2 and glomerular filtration rate 106 mL/min/1.73m2 . Median AG was 13 mmol/L and the reference interval for normal AG is 10-18 mmol/L with a 99% level of confidence. Statistically significant differences in AG were detected for sex, race, obesity and serum albumin but the difference was 1 mmol/L between subgroups. The reference interval was the same for the sub-cohort of 156 individuals. Median AGK was 17.7 mmol/L and reference interval was 14.6-22.5 mmol/L. Conclusions The AG reference interval of 10-18 mmol/L is valid for laboratories with similar reference intervals for electrolytes. Lower values expected with current laboratory techniques were not observed. The median AG of 13 mmol/L may be used to differentiate gap acidosis, non-gap acidosis or mixed acid-base disorders. This article is protected by copyright. All rights reserved.

We establish some new Opial type inequalities for interval-valued functions, and obtain some generalizations and refinements of interval Opial type inequalities derived by Costa et al. (2019) [12] . Also, some examples are presented to illustrate our results.

This brief deals with the distributed consensus observer design problem for high-order integrator multi-agent systems on directed graphs, which intends to estimate the leader states accurately in a prescribed time interval. A new kind of distributed prescribed-time observers (DPTO) on directed graphs is first formulated for the followers, which is implemented in a cascading manner. Then, the prescribed-time zero-error estimation performance of the above DPTO is guaranteed for both time-invariant and time-varying directed interaction topologies, based on strictly Lyapunov stability analysis and mathematical induction method. Finally, the practicability and validity of this new distributed observer are illustrated via a numerical simulation example.

Threat evaluation (TE) is essential in battlefield situation awareness and military decision-making. The current processing methods for uncertain information are not effective enough for their excessive subjectivity and difficulty to obtain detailed information about enemy weapons. In order to optimize TE on uncertain information, an approach based on interval Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and the interval SD-G1 (SD standard deviation) method is proposed in this article. By interval SD-G1 method, interval number comprehensive weights can be calculated by combining subjective and objective weights. Specifically, the subjective weight is calculated by interval G1 method, which is an extension of G1 method into interval numbers. And the objective weight is calculated by interval SD method, which is an extension of SD method with the mean and SD of the interval array defined in this paper. Sample evaluation results show that with the interval SD-G1 method, weights of target threat attributes can be better calculated, and the approach combining interval TOPSIS and interval SD-G1 can lead to more reasonable results. Additionally, the mean and SD of interval arrays can provide a reference for other fields such as interval analysis and decision-making.

This paper develops the numerical solution of interval type-2 fuzzy singular integro-differential equation. The theory of polynomial collocation method has been introduced to find the numerical solution of interval type-2 fuzzy singular integro-differential equation in different weighted spaces. The equation has been presented in operator form. It has been shown that the operators are bounded which are required for the convergence of the proposed method. Theorems and lemmas have been developed to show the convergence of our proposed method in type-2 fuzzy environment. A numerical algorithm for the collocation method has been presented in the numerical section. A numerical example has been examined to show the validation of our proposed method. Different types of error analysis have been examined in the form of different types of tables and figures. Also, the comparison of different types of error analysis has been examined in different weighted space.

K-mer-based methods are widely used in bioinformatics, but there are many gaps in our understanding of their statistical properties. Here, we consider the simple model where a sequence S (e.g. a genome or a read) undergoes a simple mutation process whereby each nucleotide is mutated independently with some probability r, under the assumption that there are no spurious k-mer matches. How does this process affect the k-mers of S? We derive the expectation and variance of the number of mutated k-mers and of the number of islands (a maximal interval of mutated k-mers) and oceans (a maximal interval of non-mutated k-mers). We then derive hypothesis tests and confidence intervals for r given an observed number of mutated k-mers, or, alternatively, given the Jaccard similarity (with or without minhash). We demonstrate the usefulness of our results using a few select applications: obtaining a confidence interval to supplement the Mash distance point estimate, filtering out reads during alignment by Minimap2, and rating long read alignments to a de Bruijn graph by Jabba.

The Hilbert L-matrix A s = [ a i j ( s ) ] , where a i j ( s ) = 1 / ( max ⁡ { i , j } + s ) with i , j ≥ 0 , was introduced in [3] . As a surprising property, we showed that its 2-norm is constant for s ≥ s 0 , where the critical point s 0 is unknown but relies in the interval ( 1 / 4 , 1 / 2 ) . In this note, using some delicate calculations we sharpen this result by improving the upper and lower bounds of the interval surrounding s 0 . Moreover, we establish that the same property persists for the p-norm of A s matrices.

The farm-shelter forest network is a complex grid protection system, with a windbreak that is distinctly different from that of the single shelterbelt. We selected the farm-shelter forest network of a jujube field in the Tarim Basin of northwest China and used a combination of field measurements and wind tunnel tests to determine the optimal spacing interval between principal shelterbelts. The wind speed reductive curve of the farm-shelter forest network showed a gradual wind speed tendency to stability. Therefore, a model was established based on the energy transfer balance between the upper and the lower airflows for a steady wind speed. The prediction error of the model was found to be H to 20 H, where H is the shelterbelt height, maintained more than 70% of the windbreak effect of the farm-shelter forest network. If the spacing interval between principal shelterbelts were to be increased from 10 H to 20 H, the jujube planting area would be increased by 0.54%. Therefore, a thorough consideration of the windbreak effect of each shelterbelt, the synergistic effects of shelterbelts, the windbreak effects of tall crops, and the effects of temperature and humidity in farm-shelter forest networks indicates that increasing the spacing interval will not only maintain the windbreak effect, but it will also reduce the side effects of shelterbelts, increase the planting area, favor mechanized operation, and improve planting efficiency.

An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor is presented. As an application, a sufficient condition for the positive definiteness of a sixth-order real symmetric tensor (also a homogeneous polynomial form) is obtained, which is used to judge the asymptotically stability of time-invariant polynomial systems.

Let G be a graph and I be an interval. In this paper, we present bounds for the number m G I of Laplacian eigenvalues in I in terms of structural parameters of G. In particular, we show that m G ( n − α ( G ) , n ] ≤ n − α ( G ) and m G ( n − d ( G ) + 3 , n ] ≤ n − d ( G ) − 1 , where α ( G ) and d ( G ) denote the independence number and the diameter of G, respectively. Also, we characterize bipartite graphs that satisfy m G [ 0 , 1 ) = α ( G ) . Further, in the case of triangle-free or quadrangle-free, we prove that m G ( n − 1 , n ] ≤ 1 .

This paper deals with estimation of interval controls for interval Linear Time Invariant (LTI) plants using pole placement technique. Generally, the parameters associated with LTI plant system are assumed to be crisp values, but due to the occurrence of error in experimentation, measurement or due to maintenance induced errors, the parameters are imprecise. As such, the LTI problem reduces to interval LTI. The pole placement problem is then reduced to interval algebraic equation viz. interval Diophantine equation using proper transfer function. Further, the interval Diophantine equation is transformed to Interval System of Linear Equations (ISLE) viz. interval Sylvester matrix equation. Initially, using interval arithmetic an interval algebraic approach has been applied to solve the ISLE for computing non-negative or non-positive controls. Then, another approach using Artificial Neural Network (ANN) is proposed for computing the interval controls. Further, algorithms based on sign function and ANN procedures have been discussed. Finally, the efficiency of the proposed algorithms has been verified using different order interval plants.

Continuous-time linear systems with periodic coefficients of period T are considered in this paper. We study the question of the controllability interval length of periodic systems. It is known that a controllable T-periodic system is controllable over intervals of the length kT where k is the degree of the minimal polynomial of the monodromy matrix. It is proved that this boundary kT is exact and cannot be decreased. It is proved that controllability of a T-periodic system on some interval of the length sT depends on the initial moment, in general.

The objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as $ p $-convex fuzzy-interval-valued functions ($ p $-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of $ p $-convex FIVFs, we have presented some Hermite-Hadamard type inequalities ($ H-H $ type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejér type inequality ($ H-H $ Fejér type inequality) for $ p $-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense's type inequality and Schur's type inequality for $ p $-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.

We consider the differential equation $Ju'+qu=wf$ on the real interval $(a,b)$ when $J$ is a constant, invertible skew-Hermitian matrix and $q$ and $w$ are matrices whose entries are distributions of order zero with $q$ Hermitian and $w$ non-negative. In this situation it may happen that there is no existence and uniqueness theorem for balanced solutions of a given initial value problem. We describe the set of solutions the equation does have and establish that the adjoint of the minimal operator is still the maximal operator, even though unique continuation of balanced solutions fails.

Accurately diagnosing power transformer faults is critical to improving the operational reliability of power systems. Although some researchers have made great efforts to improve the accuracy of transformer fault diagnosis, accurate diagnosis of multiple faults is still a difficult problem. In order to improve the accuracy of transformer multiple faults diagnosis, a multiple fault diagnosis method based on interval fuzzy probability is proposed. Different from the previous methods which provide single-value probability, this method use probability interval to represent the occurrence degree of various possible faults, which can objectively predict the potential faults that occurring in a transformer and provide a more reasonable explanation for the diagnosis results. In the proposed method, the interval fuzzy set is used to describe the evaluation of state variables and the interval fuzzy probability model based on interval weighted average is applied to integrate the fault information. The representative matrix of fault types based on fuzzy preference relationship is established to estimate the relative importance of each gas in the dissolved gases. The proposed method can provide the probability of probable faults in transformer, help engineers quickly determine the type and location of faults, and improve the accuracy of diagnosis and maintenance efficiency of transformer. The effectiveness of the method is verified with case studies.

UDC 517.9 We consider the second order impulsive differential equation with delays $$(Lx)(t)\equiv x''(t) + \sum\limits _{j = 1}^{p} a_j(t) x'(t-\tau_j(t)) + \sum\limits _{j = 1}^{p} b_j(t) x(t-\theta_j(t)) = f(t), \quad t \in [0, \omega], $$ $$x(t_k) = \gamma_k x(t_k-0), \quad x'(t_k) = \delta_k x'(t_k-0),\quad k = 1, 2, \ldots , r,$$ where $\gamma_k > 0,$ $\delta_k >0$ for $k = 1, 2, \ldots , r.$ In this paper, we obtain the conditions of semi-nonoscillation for the corresponding homogeneous equation on the interval $[0, \omega].$ Using these results, we formulate theorems on sign-constancy of Green's functions for two-point impulsive boundary-value problems in terms of differential inequalities.

The effects of treadmill interval training (IT) and free-fall exercise were evaluated on bone parameters including osteocyte related characteristics. Thirty-eight 4-month-old male Wistar rats were randomly divided into a control (C) group and exercise groups: IT, 10 free-fall impacts/day with a 10-s (FF10) or 20-s interval between drops (FF20), 5 days/week, for 9 weeks. We assessed bone mineral density (BMD); microarchitecture by µCT; mechanical strength by a 3-point bending test; density and occupancy of the osteocyte lacunae by toluidine blue staining; osteocalcin and NTx systemic levels by ELISA; and bone tissue Sost messenger RNA (mRNA) expression by RT-PCR. NTx levels were significantly lower in exercise groups as compared with the C group. In exercise groups the Sost mRNA expression was significantly lower than in C. Tb.N was significantly higher for IT and FF20 compared with the C group. Tb.Sp was significantly lower in FF10 compared with the C group. Both IT and FF20 were associated with higher tibial lacunar density as compared with FF10. compared with FF10, IT fat mass was lower, while tibial osteocyte lacunae occupancy and systemic osteocalcin level were higher. All exercise modes were efficient in reducing bone resorption. Both IT and free-fall impact with appropriate recovery periods, which may be beneficial for bone health and osteocyte-related characteristics. Novelty: Interval training is beneficial for bone mineral density. Exercises decreased both bone resorption and inhibition of bone formation (Sost mRNA). Longer interval recovery time favors osteocyte lacunae density.

Milling is widely used as a versatile, highly automated manufacturing process. The selection of tool and its machining conditions is an ever-present challenge inherent in the process. To provide some findings contributable for the process planning, this study focuses on ball and filleted end milling. After the path interval determinations were explained briefly, the characteristics of each procedure were revealed with experimental verifications. The results of computational procedures showed good agreement with the experimental ones. Then, predominant frictional distance and cutting speed were proposed for effective selection of machining conditions. The discussion was given based on the results obtained from the demonstrations. Moreover, the relationships to path interval were elucidated through the discussion. In conclusion, several outcomes were organized from the experimental and numerical evidences.

Calculating fractal dimension of the graph of a function not simple even for real-valued functions. While through this paper, our intention is to provide some initial theories for the dimension of the graphs of vector-valued functions. In particular, we give a fresh attempt to estimate the fractal dimension of the graph of the Katugampola fractional integral of a vector-valued continuous function of bounded variation defined on a closed bounded interval in $$\mathbb {R}.$$ We prove that dimension of the graph of a continuous vector-valued function of bounded variation is 1 and so is the dimension of the graph of its Katugampola fractional integral. Further, for a Holder continuous function, we provide an upper bound for the upper box dimension of the graph of each coordinate function of the Katugampola fractional integral of the function.

A proof of the law of the iterated logarithm for random homeomorphisms of the interval is given.

The three gap theorem asserts that for any real $\alpha $ and any positive integer $N$, the fractional parts of the sequence $0, \alpha , 2\alpha , \cdots , (N-1)\alpha $ have at most three distinct gap lengths. In this note, we extend the three gap theorem to arbitrary orbits of interval exchange transformations, and in the process, we generalize the three gap theorem and a result by Boshernitzan.

One of the phenomena of the low-dose radiation effect is the radio adaptation response which is an important part of the response of molecules, cells, and body tissues to ionizing radiation. The phenomenon of radio adaptation response is a response that occurs when changes in gene expression can be induced by exposure to low doses of radiation (

For the outcomes of multiple independent populations, a small interval hypothesis states that the maximum value of the parameters that determine the outcomes is no more than a small distance apart from the minimum value. An explicit expression is given for the probability of this hypothesis, from which related Bayes factors are obtained. Examples are given for how to obtain these Bayes factors for the ‘about equal’ hypothesis.

Background and Objective: Chitinase-3-like protein 1 (CHI3L1) is an upcoming biomarker for the diagnosis of liver fibrosis. The reference intervals (RIs) for CHI3L1 have not been established in the Pakistani population. Thus, this study aimed to determine the RIs in our population and the cut-off value for diagnosis of hepatic fibrosis. Methods: This is a cross-sectional study. A total of 408 participants (202 healthy and 206 diagnosed liver fibrosis cases) were recruited. Serum CHI3L1 level was measured on CHI3L1 kits (Proprium Biotech Co. Ltd) by manual enzyme-linked immunosorbent assay. The RIs were estimated by percentile and working normal method. Results: The distribution of CHI3L1 values showed no remarkable variation with gender and age. The 95% RI of CHI3L1 was 12.80-81.80 ng/ ml in healthy Pakistani subjects and the cut-off for the diagnosis was 102.12 ng/ml in hepatic fibrosis cases. Conclusion: The RIs in healthy adults and the cut-off for the diagnosis of hepatic fibrosis of serum CHI3L1 were determined in a selective adult Pakistani population. This will be a useful reference for further local and international studies.

Introduction: Postmortem interval (PMI) is the time lapse between death of a person and its postmortem examination i.e. autopsy. Estimating the postmortem interval (PMI) is an imperative perspective of forensic medicine. Aims & Objectives: This study was conducted to see the impact of CSF protein estimation on determination of PMI. Place and duration of study: It was an observational correlational study, conducted for one year at Department of Forensic Medicine, King Edward Medical University Lahore. Material & Methods: A total of 119 cadavers were included in this study. Chemicals used were disodium molybdate, pyrogallol, succinic acid. The minimum detectable concentration of total proteins in CSF with dye binding method using pyrogallol red was determined as 0.022g/l. Two ml of CSF was taken from each cadaver. Clear, colorless samples were taken in test tubes. Turbid and blood contained samples were not included in study. Protein concentration was determined using photospectrometry. Statistical analysis was done by SPSS-23. Quantitative variables like age were presented as mean ± SD. Qualitative variables like gender were presented as frequency and percentages. For comparison between PMI and CSF proteins concentration correlation was applied. Results: Males accounted for majority of our subjects. The mean value of proteins in CSF was 219.91± 113.121 mg/dl. The most common PMI was 11 to 20 hours. CSF proteins increased gradually over 72 hours after death. The results of present study showed a significant positive correlation between time of death and CSF proteins concentration after death. Conclusion: It is observed that as a whole protein concentration increased with increasing time of death. Hence, CSF protein concentration can be used in estimating time since death.

According to the portal Math-Net.Ru a graph of journal citation is constructed. To increase the reliability of the model, the citation time interval was chosen from 2010 to 2021, when the distribution of citation articles stabilized at the level of 3500-4500 citations per year. The structure of link aging is studied and it is shown that their half-life is equal to 8 years. Therefore, the publication date of the cited articles was limited to 2002. For the constructed citation graph, the main properties, such as a small diameter and a high density, are obtained, indicating a high level of scientific communication in the Math-Net.Ru. The absence of the “Matthew effect” as a pronounced advantage in quoting established journals in relation to less well-known ones is shown. Adequacy of the journal citation graph Math-Net.Ru as a model of scientific communication confirmed by comparing the ranking of journals in the citation graph with their SCIENCE INDEX rating in eLIBRARY.RU. A direct moderate relationship between the two rankings is shown. A number of meaningful conclusions are drawn from the analysis of the citation graph.

Introduction The regionalized nature of trauma care necessitates interfacility transfer which is vulnerable to delays given its complexity. Little is known about the interval of time a patient spends at the sending hospital prior to when the transfer is initiated—the “decision to transfer” time. This primary objective of the study was to explore the impact of patient, environmental, and institutional characteristics on decision to transfer time. Methods This was a retrospective cohort study of injured adult patients who underwent emergent interfacility transfer by a provincial critical care transport organization over a 31-month period. Quantile regression was used to evaluate the impact of patient, environmental, and institutional characteristics on the time to decision to transfer. Results A total of 1128 patients were included. The median decision to transfer time was 2.42 h and the median total transport time was 3.12 h. The following variables were associated with an increase in time to decision to transfer at the 90th percentile of time: age >75 (+2.47 h), age 66–75 (+3.70 h), age 56–65 (+1.20 h), transfer between 00:00 and 07:59 (+2.08 h), and transfer in the summer (+2.25 h). The following variables were associated with a decrease in time to decision to transfer at the 90th percentile of time: Glasgow Coma Scale 3–8 (−2.21 h), respiratory rate >30 (−2.01 h), sending site being a community hospital with Conclusion Time to decision to transfer was a sizable proportion of the patients interfacility transfer. Older patients were associated with a delay in decision to transfer as were patients transferred overnight and in the summer. These findings may be used to support the implementation of geriatric trauma triage guidelines and promote ongoing education and quality improvement initiatives to decrease delay.

A fuzzy compactum in a space X is an upper semi-continuous map f : A → [ 0 , 1 ] from a nonempty compact subspace A ⊂ X to the unit closed interval [ 0 , 1 ] such that { x ∈ A : f ( x ) > 0 } is dense in A. In this paper, we investigate the topological structure of the space K e ( X ) of fuzzy compacta of a separable metric space X with the Hausdorff metric. In particular, we prove that K e ( X ) ≈ l 2 if X is an infinite, locally compact, locally connected, connected and separable metric space.

––The Gobi-Altai, Mongolia, includes high mountain ranges that have accommodated the compressional stresses derived from the collision between the Eurasian and Indian Plates. The Gurvan Bogd, which is one of the main mountain ranges in the Gobi-Altai, is a restraining bend along the Bogd sinistral fault. Although surface ruptures did not form near the Artz Bogd during the Mw = 8.1 Gobi-Altai earthquake of 1957, it is still active, as evidenced by a growing topography (i.e., forebergs). Six foreberg ridges have formed in the foreland of the Artz Bogd, which are considered to be the result of surface deformation of alluvial fans due to thrusting. One stream has cut down to expose a foreberg tip, providing the opportunity to explore the slip evolution of the region. Here we map a growing fault structure related to blind thrusting. We identify five faulting events from an analysis of the outcrop and apply optically stimulated luminescence dating to the faulted sedimentary layers, yielding an average slip rate of 0.045 ± 0.007 m/kyr and an earthquake recurrence interval of 5.8 ± 0.5 kyr over the last ~32 kyr. Furthermore, the long-term (~600 kyr) uplift rate of the foreberg is 0.067 ± 0.007 m/kyr, as deduced by dividing the vertical displacement of the alluvial fan surface by the 10Be surface exposure ages of boulders on the fan. The discrepancy (20–30%) between these two deformation rates may be due to the different timescales they cover and an along-strike gradient in slip rate.