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In statistics, probability theory, and computer science, a derangement, !n, is known to be a basic problem that computes total ways of rearranging n ∈ N items such that a result contains no item i that stands in the same position as it did in the input. Formally, the derangement problem has a problem instance of a finite collection C = {(x1,y1), .∙∙., (xn,yn)}, ∣C∣ = n. With this formulation, !n is a total number of qualified collections C' where C' contains n members of (xi,yj) where i ≠ j and every Xi and yj (1 ≤ i,j < n) must show up exactly once in C'. In this article, we present a dynamic programming algorithm that computes !n and its justification. We also provide a discussion about extending the limitation of the problem with an objective to cover a general case where we have a finite set of variables a1, a2∙∙∙∙ak rather than the traditional scenario that has only two variables: x and y. [ABSTRACT FROM AUTHOR]

Copyright of Naturaliste Canadien is the property of La Societe Provancher and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A matching point in compositions and words is an extension to these objects of the well-studied concept of fixed points in permutations. The equivalent of the derangement problem is solved here by providing a formula for the number of compositions of n having no matching points, and showing that the number of words with no matching points tends to zero as (the length of the word) n tends to infinity. We also find formulae for the average number of matching points in both words and compositions. [ABSTRACT FROM AUTHOR]

Objective: This review aimed to systematically analyse the influence of clinical variables, diagnostic parameters and the overall image acquisition process on automation and deep learning in TMJ disorders. Methods: Articles were screened in late 2022 according to a predefined eligibility criteria adhering to the PRISMA protocol. Eligible studies were extracted from databases hosted by MEDLINE, EBSCOHost, Scopus, PubMed and Web of Science. Critical appraisals were performed on individual studies following Nature Medicine's MI‐CLAIM checklist while a combined appraisal of the image acquisition procedures was conducted using Cochrane's GRADE approach. Results: Twenty articles were included for full review following eligibility screening. The average experience possessed by the clinical operators within the eligible studies was 13.7 years. Bone volume, trabecular number and separation, and bone surface‐to‐volume ratio were clinical radiographic parameters while disc shape, signal intensity, fluid collection, joint space narrowing and arthritic changes were successful parameters used in MRI‐based deep machine learning. Entropy was correlated to sclerosis in CBCT and was the most stable radiomic parameter in MRI while contrast was the least stable across thermography and MRI. Adjunct serum and salivary biomarkers, or clinical questionnaires only marginally improved diagnostic outcomes through deep learning. Substantial data was classified as unusable and subsequently discarded owing to a combination of suboptimal image acquisition and data augmentation procedures. Inadequate identification of the participant characteristics and multiple studies utilising the same dataset and data acquisition procedures accounted for serious risks of bias. Conclusion: Deep‐learned models diagnosed osteoarthritis as accurately as clinicians from 2D and 3D radiographs but, in comparison, performed poorly when detecting disc disorders from MRI datasets. Complexities in clinical classification criteria; non‐standardised diagnostic parameters; errors in image acquisition; cognitive, contextual or implicit biases were influential variables that generally affected analyses of inflammatory joint changes and disc disorders. [ABSTRACT FROM AUTHOR]

The probability that a random permutation in Sn is a derangement is well known to be Xn j=0 (-1)j 1/j! . In this paper, we consider the conditional probability that the (k+1)st point is fixed, given there are no fixed points in the first k points. We prove that when n 6= 3 and k 6= 1, this probability is a decreasing function of both k and n. Furthermore, it is proved that this conditional probability is well approximated by 1 n-k/n²(n-1) . Similar results are also obtained about the more general conditional probability that the (k + 1)st point is fixed, given that there are exactly d fixed points in the first k points. [ABSTRACT FROM AUTHOR]

In [2] the third author studied arithmetic properties of a class of sequences that generalize the sequence of derangements. The aim of the following paper is to disprove two conjectures stated in [2]. The first conjecture regards the set of prime divisors of their terms. The latter one is devoted to the order of magnitude of considered sequences. [ABSTRACT FROM AUTHOR]

We study fixed points in integer partitions viewed, respectively, as weakly increasing or weakly decreasing structures. A fixed point is a point with value i in position i. We also study matching points in weakly decreasing partitions. These are defined as positions where the partition and its reverse have the same size parts. From the generating functions, we also obtain asymptotic estimates as n → ∞ of some of the above statistics. [ABSTRACT FROM AUTHOR]

We give two simple combinatorial proofs directly on derangements to the well-known identity d n = n d n - 1 + (- 1) n of derangement numbers. Inversion properties on derangements are given. Partial i n v q -analogues are established. [ABSTRACT FROM AUTHOR]

We investigate properties of random mappings whose core is composed of derangements as opposed to permutations. Such mappings arise as the natural framework for studying the Screaming Toes game described, for example, by Peter Cameron. This mapping differs from the classical case primarily in the behaviour of the small components, and a number of explicit results are provided to illustrate these differences. [ABSTRACT FROM AUTHOR]

We consider a sequence of four variable polynomials by refining Stieltjes's continued fraction for Eulerian polynomials. Using combinatorial theory of Jacobi-type continued fractions and bijections, we derive various combinatorial interpretations in terms of permutation statistics for these polynomials, which include special kinds of descents and excedances in a recent paper of Baril and Kirgizov. As a byproduct, we derive several equidistribution results for permutation statistics, which enables us to confirm and strengthen a recent conjecture of Vajnovszki and also to obtain several companion permutation statistics for two bistatistics in a conjecture of Baril and Kirgizov. [ABSTRACT FROM AUTHOR]

We use generating functions to account for alphabetic points (or the lack thereof) in compositions and words. An alphabetic point is a value j such that all the values to its left are not larger than j and all the values to its right are not smaller than j. We also provide the asymptotics for compositions and words which have no alphabetic points, as the size tends to infinity. This is achieved by the construction of upper and lower bounds which converge to each other, and in the latter case by probabilistic arguments. [ABSTRACT FROM AUTHOR]

Neck of femur fracture is a common consequence of falls in the elderly with a large burden of morbidity and mortality. Derangement in liver function tests (LFTs) is frequently seen in elderly people with neck of femur (NOF) fracture in the peri-operative period and can indicate serious and treatable underlying pathology as well as prognosis. On admission, raised alkaline phosphatase (ALP) levels with normal gamma-glutamyl transferase (GGT) suggest underlying bone pathology such as osteomalacia or Paget's disease but do not confirm or exclude osteoporosis. ALP can also be raised by non-bone pathology such as congestive cardiac failure and chronic kidney disease. LFT derangement in cardiac failure is associated with poorer prognosis. Post-operatively, ALP levels rise after the first week with a peak at 3–4 weeks and then fall thereafter. The rate at which they fall may help indicate bone healing in trochanteric fractures. Derangement in other LFTs is commonly due to hepatic injury; causes include trauma, alcohol, and viral hepatitis. There are also iatrogenic causes including surgery and commonly prescribed medication such as beta-lactam antibiotics, non-steroidal anti-inflammatories, and paracetamol. The differential diagnosis for deranged LFTs in the elderly peri-operatively is wide; however, most causes can be elicited through careful history and examination with occasional need for further investigations. [ABSTRACT FROM AUTHOR]

In this article we obtain the generating function of the sequence P(n; j), the number of j-permutations of n objects. We consider two applications. Our method, which employs integration by parts, gives an integral representation for the difference (e -- en) n!, where en = Σnj=0 1/j! denote the truncated expansion of the number e. By using this integral representation weobtain a sharp double sided inequality concerning the difference (e -- en) n!, and also we compute some moments of it. As the second application, we provide a recurrence method to compute power weighted sums concerning P(n, j), and also alternating power weighted sums of P(n; j) in terms of the number of derangements. [ABSTRACT FROM AUTHOR]

OBJECTIVES To evaluate the relationship between diuretic use, serum electrolyte concentrations, and supplementation requirements in infants admitted to the neonatal intensive care unit. METHODS This was a single-center retrospective cohort study conducted in a freestanding children's hospital Level IV NICU. Data were collected for all infants younger than 6 months, admitted to the NICU between January 2015 and May 2017, who received 2 or more consecutive doses of furosemide, chlorothiazide, hydrochlorothiazide, and/or hydrochlorothiazide/spironolactone. The primary outcome was the composite of the incidence of electrolyte abnormalities and/or electrolyte supplementation requirement within 30 days of diuretic exposure. RESULTS A total of 72 patients met inclusion criteria, with a median gestational age of 30 weeks. Overall, 92% of patients exposed to diuretics experienced derangement in at least 1 serum electrolyte and/or required electrolyte supplementation during diuretic therapy. Patients born at 36 to 41 weeks' gestational age, receiving thiazide diuretics, experienced a significantly lower rate of the primary outcome (37%, p ≤ 0.001). The most common electrolytes affected by diuretic use were potassium and bicarbonate, with the highest incidence of the primary outcome for potassium occurring in patients receiving furosemide (p = 0.0196). Last, the median total daily dose of chlorothiazide in patients with an adverse event was 15 mg/kg/day, compared with 10 mg/kg/day in patients without an adverse event (p = 0.0041). CONCLUSIONS Use of diuretics in young infants is likely to cause electrolyte derangements and/or require electrolyte supplementation. Patients born at earlier gestational ages may be at higher risk for developing such adverse effects. ABBREVIATIONS GA, gestational age; GFR, glomerular filtration rate; IV, intravenous; NICU, neonatal intensive care unit; PN, parenteral nutrition [ABSTRACT FROM AUTHOR]

Background: The prevalence and cost of hip osteoarthritis (OA) is rising. Mechanical diagnosis and therapy (MDT) is an orthopedic classification and treatment system based on mechanical and symptomatic response to repeated and sustained end-range movements. There has been no investigation of the association between MDT and patients diagnosed with hip OA. Case Description: This case report presents a 71-year-old female diagnosed with hip OA and matching the currently accepted clinical prediction rule (CPR) for symptomatic hip OA. The patient was classified and treated by a Diplomat of MDT and co-examiner using MDT. Outcomes: Short- and long-term (13 months) outcomes were excellent, demonstrating rapid abolishment of symptoms and improvement in function in 5 visits over 21 days. The patient demonstrated the ability to prevent and manage reoccurrence of symptoms independently; nevertheless, she received a total hip replacement which was not in accordance with current guidelines and recommendations. Conclusion: This case report raises questions about whether or not pathologies traditionally associated with the etiology of hip OA are actually at fault. Moreover, it raises questions about the utility of special tests and CPRs typically utilized to identify those structures. The case report provides preliminary evidence from one patient that MDT may be capable of providing effective short- and long-term outcomes in the management of hip OA. [ABSTRACT FROM AUTHOR]

To assess the frequency of TMJ Arthrocentesis among patients of different age groups and genders by an institution based retrospective study. A retrospective cross-sectional cohort study was conducted using the patient records from the Department of Oral and Maxillofacial Surgery from June 2019-March 2020, and details of the patients were collected by Non-probability sampling. Among a sample size of 87 patients who had reported for TMJ pain and disorders, 20 patients had undergone TMJ Arthrocentesis as treatment and were included in the study. The data collected was analysed for gender, age, difference in mouth opening. Statistical analysis was done using SPSS Version 20. Chi square statistical test for significance was used. 60% patients subjected to TMJ Arthrocentesis were females (12 patients) and they were predominantly of the age group below 35 years of age (50% - 10 patients). It was also noticed that patients less than 35 years of age had an immediate improvement in mouth opening less than 5mm, and only 26.67% of the female patients had a mouth opening greater than 5mm. The prevalence of TMJ Arthrocentesis was predominant among female patients under the age of 35 years. [ABSTRACT FROM AUTHOR]

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Let D h , E k and F α be sets of size h , k , α respectively, with k ≤ h . We define a strongly widened derangement to be a permutation of D h ∪ E k ∪ F α such that the elements of D h are not fixed and the elements of E k cannot occupy a site originally occupied by an object of the same type or by an object of F α . We show a connection between strongly widened derangements and generalized Laguerre polynomials that provides a generalization, for integer values of α , of Even and Gillis (Math Proc Camb Philos Soc, 79:135–143, 1976) different from the one presented in Foata and Zeilberger (SIAM J Discrete Math, 1:425–433, 1988). [ABSTRACT FROM AUTHOR]

Copyright of Ri-vista: Ricerche per la progettazione del paesaggio is the property of Firenze University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Introduction: Sacroiliac Joint (SIJ) is a familiar nociceptive source of Low Back Pain (LBP). Patients with SIJ pain commonly present with tenderness around the Posterior Superior Iliac Spine (PSIS) which can be recorded by using pressure pain algometer. Mechanical Diagnosis and Therapy (MDT) is a manual therapy technique which uses repetitive movements to assess and treat the dysfunction. MDT is found to be effective in treating SIJ pain; however, its effect on Pain Pressure Threshold (PPT) is not yet determined. Aim: To determine the effect of Mechanical Diagnosis and Therapy on Pain Pressure Threshold in Sacroiliac Joint pain. Materials and Methods: A total of 25 subjects with unilateral LBP of age group 20-65 years participated in the study. Subjects with the direction of preference, pain around the PSIS, positive on two out of four pain provocation tests were included in the study. These patients were given 30 repetitions of either anterior or posterior rotation of the innominate, for four sessions. PPT and Visual Analogue Scale (VAS) were used to measure the effect of treatment. Data were analysed by using paired t-test. Results: There was a significant improvement seen (p<0.01) in PPT and VAS after four consecutive sessions of treatment. Conclusion: A significant statistical difference was seen in PPT and VAS with p-value <0.01 at the end of four sessions of MDT treatment. The study suggests that MDT can be used effectively in managing SIJ tenderness around the PSIS and pain. However, future studies should focus on comparing MDT with a control group or with other manual therapy techniques. [ABSTRACT FROM AUTHOR]

Copyright of Osjecki Matematicki List is the property of Osjecki Matematicki List and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This is the third in a series of four papers in which we prove a conjecture made by Boston et al. and Shalev that the proportion of derangements (fixed point free elements) is bounded away from zero for transitive actions of finite simple groups on a set of size greater than one. This paper treats the case of primitive subspace actions. It is also shown that if the dimension and codimension of the subspace go to infinity, then the proportion of derangements goes to one. Similar results are proved for elements in finite classical groups in cosets of the simple group. The results in this paper have applications to probabilistic generation of finite simple groups and maps between varieties over finite fields. [ABSTRACT FROM AUTHOR]

A derangement is a permutation that has no fixed points. In this paper, we are interested in the proportion of derangements of the finite affine general linear groups. We prove a remarkably simple and explicit formula for this proportion. We also give a formula for the proportion of derangements of prime power order. Both formulae rely on a result of independent interest on partitions: we determine the generating function for the partitions with m parts and with the kth largest part not k, for every $$k\in \mathbb {N}$$ . [ABSTRACT FROM AUTHOR]

We study the derangement number on a Ferrers board B = (n × n) - λ with respect to an initial permutation M, that is, the number of permutations on B that share no common points with M. We prove that the derangement number is independent of M if and only if λ is of rectangular shape. We characterize the initial permutations that give the minimal and maximal derangement numbers for a general Ferrers board, and present enumerative results when λ is a rectangle. [ABSTRACT FROM AUTHOR]

The coefficients of the local h-polynomial of the barycentric subdivision of the simplex with n vertices are known to count derangements in the symmetric group 핾n by the number of excedances. A generalization of this interpretation is given for the local h-polynomial of the rth edgewise subdivision of the barycentric subdivision of the simplex. This polynomial is shown to be γ-nonnegative and a combinatorial interpretation to the corresponding γ-coefficients is provided. The new combinatorial interpretations involve the notions of flag excedance and descent in the wreath product ℤr l 핾n, A related result on the derangement polynomial for ℤr l 핾n, studied by Chow and Mansour, is also derived from results of Linusson, Shareshian, and Wachs on the homology of Rees products of posets. [ABSTRACT FROM AUTHOR]

STUDY DESIGN: Randomized controlled trial. OBJECTIVES: To examine the efficacy of exercise intervention in patients with knee osteoarthritis (OA), as directed by Mechanical Diagnosis and Therapy (MDT) assessment, and, secondarily, to explore outcomes between MDT assessment-defined subgroups within the exercise group. BACKGROUND: Due to the high physical and economic burden of knee OA, the effectiveness of conservative interventions and determining those patients who will respond to them should be investigated. METHODS: Patients with knee OA (n = 180) were randomized to an exercise intervention group or a control group. The intervention group, in which patients classified as having knee derangements (MDT derangement) received MDT directional exercises and patients classified as nonresponders (MDT nonresponders) received evidence-based exercises, was compared to a control group that received no exercise intervention. Pain and function were assessed at baseline, 2 weeks, and 3 months, using the P4 pain scale and Knee injury and Osteoarthritis Outcome Score (KOOS) pain and function subscales. Two-way analysis of covariance was used to examine treatment and time effects. Multiple comparisons were examined, and mean differences with 95% confidence intervals (CIs) were reported. RESULTS: The exercise intervention group had significantly improved P4 scores (mean difference, -6; 95% CI: -8, -3), KOOS pain scores (mean difference, 9; 95% CI: 5, 13), and KOOS function scores (mean difference, 11; 95% CI: 7, 15) compared to those of the control group at 2 weeks. At 3 months, the exercise intervention group had significantly improved KOOS pain scores (mean difference, 7; 95% CI: 3, 11) and KOOS function scores (mean difference, 5; 95% CI: 1, 9) compared to controls. CONCLUSION: Patients with knee OA who were prescribed exercises based on an MDT assessment had superior outcomes compared to those of wait-list controls. The MDT subgroup of knee derangement may warrant further investigation in patients with knee OA. [ABSTRACT FROM AUTHOR]

Copyright of Rehabilitation & Physical Medicine / Rehabilitace a Fyzikální Lékařství is the property of Czech Medical Association of JE Purkyne and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Solitary paraspinal masses in the pediatric age group commonly occur secondary to spinal dysraphism, chronic inflammatory conditions, and tumors. We describe the unusual case of a 10-year-old boy with a nondysraphic, paraspinal mass that had occurred secondary to congenital spinal epidural lipomatosis (SEL) in the setting of poorly controlled maternal type-I diabetes mellitus. The mass was picked up along with a ventricular septal defect (VSD) on an antenatal ultrasonogram. This is the first report in literature of SEL presenting as a solitary paraspinal mass at birth, and in the unusual setting of an antenatal mesodermal derangement that simultaneously engendered a VSD. [ABSTRACT FROM AUTHOR]

Belief in and rejection of a relationship of occlusion and temporomandibular joint ( TMJ) condyle-fossa position with normal and abnormal function are still contentious issues. Clinical opinions can be strong, but support in most published data (mostly univariate) is problematic. Distribution overlap, low sensitivity and specificity are a common basis to reject any useful prediction value. Notwithstanding, a relationship of form with function is a basic tenet of biology. These are multifactor problems, but the questions mostly have not been analysed as such. This review moves the question forward by focusing on TM joint anatomic organisation as the multifactor system it is expected to be in a closed system like a synovial joint. Multifactor analysis allows the data to speak for itself and reduces bias. Classification tree analysis revealed useful prediction values and usable clinical models which are illustrated, backed up by stepwise logistic regression. Explained variance, R2, predicting normals from pooled TMJ patients was 32·6%, sensitivity 67·9%, specificity 85·7%; 37% versus disc displacement with reduction; and 28·8% versus disc displacement without reduction. Significant osseous organisational differences between TM joints with clicking and locking suggest that this is not necessarily a single disease continuum. However, a subset of joints with clicking contained characteristics of joints with locking that might contribute to symptom progression versus resistance. Moderately strong models confirm there is a relationship between TMJ osseous organisation and function, but it should not be overstated. More than one model of normals and of TM derangement organisation is revealed. The implications to clinical decision-making are discussed. [ABSTRACT FROM AUTHOR]

The temporomandibular disorders are complex and multifactorial. Temporomandibular disorders (TMDs) are essentially characterized by the appearance of pain, joint sounds and alterations in mandibular movement. They are primarily found in young and middle-aged adults and are nearly twice as prevalent in women. The successful management of temporomandibular disorders is dependent on identifying and controlling the contributing factors. This article describes the classiication, diagnosis of various temporomandibular disorders and their management. [ABSTRACT FROM AUTHOR]

Copyright of Rehabilitation & Physical Medicine / Rehabilitace a Fyzikální Lékařství is the property of Czech Medical Association of JE Purkyne and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We construct and analyze an explicit basis for the homology of the boolean complex of a finite simple graph. This provides a combinatorial description of the spheres in the wedge sum representing the homotopy type of the complex. We assign a set of derangements to any finite simple graph. For each derangement, we construct a corresponding element in the homology of the complex, and the collection of these elements forms a basis for the homology of the boolean complex. In this manner, the spheres in the wedge sum describing the homotopy type of the complex can be represented by a set of derangements. We give an explicit, closed-form description of the derangements that can be obtained from any finite simple graph, and compute this set for several families of graphs. In the cases of complete graphs and Ferrers graphs, these calculations give bijective proofs of previously obtained enumerative results. [ABSTRACT FROM AUTHOR]

J Oral Pathol Med (2011) 40: 587–592 Lubricin is a chondroprotective, mucinous glycoprotein which contribute to joint lubrication, especially to boundary lubrication and maintains joint integrity. The present investigation aimed to study the immunolocalization of lubricin in TMJ discs from patients affected by anterior disc displacement with reduction (ADDwR) ADDwoR. Eighteen TMJ displaced disc affected by ADDwoR were processed immunohistochemically, with a polyclonal anti‐lubricin antibody, used at 1:50 working dilution. The percentage of lubricin immunopositive cells (extent score = ES) and the extent of lubricin staining of the disc extracellular matrix (ECM), were evaluated. Each sample was scored for histopathological changes. Percentage of immunostained surface disc cells was the same (ES = 4) in both control and ADDwOR cells, being this data not statistically significant (P < 0.05). In pathological specimens the percentages of lubricin‐stained cells was very high with an ES of 4 respect to control specimen, and this difference was statistically significant different (P > 0.05). The extracellular matrix (ECM) of discs at the disc surfaces of both pathological and normal specimens was very heavily stained (++++). Both the ES and ECM staining were not statistically correlated to the TMJ degeneration score according to the Spearman's rank correlation coefficient. According to our findings, a longstanding TMJ disc injury, affects lubricin expression in the TMJ disc tissue and not its surfaces, moreover, lubricin immunostaining is not correlated to TMJ disc histopathological changes. [ABSTRACT FROM AUTHOR]

In this note we obtain and discuss formulae for the number of partial one-one transformations (of an n-element set) of height (equivalently, width) r and having exactly k fixed points. Moreover, we consider a generalization of the 'Hat Problem' or 'Probleme des Rencontres'. [ABSTRACT FROM AUTHOR]