Scaling Of Dimensions Research Articles

Extending Species-Area Relationships Into the Realm of Ecoacoustics: The Soundscape-Area Relationship.

The rise in species richness with area is one of the few ironclad ecological relationships. Yet, little is known about the spatial scaling of alternative dimensions of diversity. Here, we provide empirical evidence for a relationship between the richness of acoustic traits emanating from a landscape, or soundscape richness, and island area, which we term the SoundScape-Area Relationship (SSAR). We show a positive relationship between the gamma soundscape richness and island area. This relationship breaks down at the smallest spatial scales, indicating a small-island effect. Moreover, we demonstrate a positive spatial scaling of the plot-scale alpha soundscape richness, but not the beta soundscape turnover, suggesting a direct effect of species on acoustic trait diversity. We conclude that the general scaling of biodiversity can be extended into the realm of ecoacoustics, implying soundscape metrics are sensitive to fundamental ecological patterns and useful in disentangling their complex mechanistic drivers.

The Development of a Comprehensive Dimensions Scale for Assessing Clinical Teachers' Occupational Well-Being.

In Taiwanese clinical and healthcare environments, there is a dearth of appropriate and effective tools to evaluate clinical teachers' occupational well-being. Therefore, this study aimed to develop a culturally adapted scale, a Taiwanese version of the Clinical Teachers' Occupational Well-Being Dimensions Scale (CTOWDS), to accurately measure the occupational well-being of clinical teachers in Taiwan. Following a comprehensive literature review and expert panel discussions, the study developed the CTOWDS and conducted exploratory factor analysis (EFA) with 346 participants using SPSS to identify its underlying dimensional structure and psychometric properties. Confirmatory factor analysis (CFA) was then performed with 255 participants using AMOS to validate the EFA results. The study also assessed internal consistency, convergent and discriminant validities, and goodness-of-fit indexes to ensure that the scale was valid and reliable in the Taiwanese cultural setting. The EFA refined the scale from 51 to 29 items across five dimensions: personal qualities (11 items), academic research and career development pressure (6 items), teaching experience (4 items), learning experience (4 items), and teaching and communication pressure (4 items). These five dimensions explained 65.279% of the total variance. The CFA confirmed the five dimensions and 29 items, with good convergent and discriminant validities, goodness-of-fit indexes, and Cronbach's alpha values exceeding 0.70. The findings affirm the utility of the developed CTOWDS as a reliable and culturally relevant instrument for assessing the occupational well-being of clinical teachers.

Quality of life in acute ischaemic stroke patients treated with recanalisation

<p>Stroke is a serious health problem that has a significant impact on health-related quality of life. Despite the increasing popularity of measuring quality of life among patients, it is not routinely measured in clinical practice, and therefore little is known about how well clinical measures reflect quality of life after stroke. The aim of this study was to investigate the quality of life of patients with acute ischaemic stroke.</p>. <p>For the prospective study, patients diagnosed with acute ischemic stroke at the Neurology Clinic of the Clinical Center of the University of P&eacute;cs were selected through convenience sampling between June 2022 and May 2023. Based on the treatments, patients were divided into three groups: mechanical thrombectomy (MT), intravenous thrombolysis (IVT), and standard care (SC). Modified Rankin Scale (Pre-mRS, Follow-up mRS), NIH Stroke Scale (NIHSS), and European Quality of Life 5 Dimensions Scale (EQ-5D-5L) were used in the research. Descriptive statistics, paired T-tests, Wilcoxon tests, McNemar tests and Pearson correlation analysis were applied for the analysis (SPSS 25.0; p &lt;0.05).</p>. <p>A total of 198 participants (115 males, 83 females) took part in the study (MT: 50, IVT: 69, SC: 79). The Pre-mRS and follow-up mRS values indicate that the majority of patients in all three groups fell into the mild category (Pre-mRS: 176 participants; 88%, follow-up mRS: 158 participants; 80%). There was a significant improvement in NIHSS scores in all three groups (IVT: 4.36 vs. 1.57, p&lt;0.001; MT: 8.98 vs. 4.50, p&lt;0.001; SC: 4.38 vs. 2.84, p&lt;0.001). The EQ-5D-5L value also significantly increased for all groups (IVT: 0.82 vs. 0.88, p&lt;0.001; MT: 0.63 vs. 0.73, p&lt;0.001, SC: 0.76 vs. 0.80, p=0.014). Patients admitted with lower NIHSS values reported better quality of life at the end of our study (r: -0.43451).</p>. <p>At 30 days, significant improvement was observed in MT, IVT and SC groups when measured with EQ-5D-5L, but the extent of improvement was highest in the MT group.</p>.

Post-historicism, Post-territorialism, and the Problem of Scale: A Metacritical Appraisal of the Literary-Theoretical Paradigm of ‘Planetary Time’

Wai Chee Dimock’s literary-theoretical paradigm of ‘planetary time’ neatly fits the epithet ‘post-historicist/post-territorialist’ for its simultaneous repudiation of historicist and nationalist approaches to literary critical practice. Opposed to the absolute jurisdiction of temporal periods and spatial territories as literary analytic units, the ‘post-historicist/post-territorialist’ paradigm seeks to tap into the spatiotemporal entanglements of literary criticism to produce analyses of literature that trace the transtemporal and extraterritorial linkages forged by literary processes and their attendant actors. The article primarily focuses on Wai Chee Dimock’s literary analytic scale of ‘planetary time’, an extended temporal scale that, according to Dimock, is intrinsically coupled to a spatial scale of planetary dimensions. While subjecting Dimock’s literary-theoretical approach to a sustained metacritique, the article also intermittently engages with closely related paradigms that could shed more light on the nuances of literary analytic scales. Two analytic scales appropriated from the field of historiography – Fernand Braudel’s extended longue durée and Carlo Ginzburg’s episodic (micro)history – will not only lend an interdisciplinary perspective to this metacritical study, but also underscore the spatiotemporal implications of scale in literary criticism. These insights could help recalibrate literary critical practice by introducing greater self-reflexivity in its deployment of scale.

Volumetric versus Element-scaling Mass Estimation and Its Application to Permo-Triassic Tetrapods.

Size has an impact on various aspects of an animal's biology, including physiology, biomechanics, and ecology. Accurately and precisely estimating size, in particular body mass, is therefore a core objective of paleobiologists. Two approaches for estimating body mass are common: whole-body volumetric models and individual element-scaling (e.g., bones, teeth). The latter has been argued to be more accurate, while the former more precise. Here, we use minimum convex hulls (MCHs) to generate a predictive volumetric model for estimating body mass across a broad taxonomic and size range (127 g - 2735 kg). We compare our MCH model to stylopodial-scaling, incorporating data from the literature, and find that MCH body mass estimation is both more accurate and more precise than stylopodial estimation. An explanation for the difference between methods is that reptile and mammal stylopod circumference and length dimensions scale differentially (slope 1.179±0.102 vs. 1.038±0.031, respectively), such that reptiles have more robust bones for a given size. Consequently, a mammalian-weighted stylopodial-scaling sample overestimates the body mass of larger reptiles, and this error increases with size. We apply both estimation equations to a sample of 12 Permo-Triassic tetrapods and find that stylopodial-scaling consistently estimates a higher body mass than MCH estimation, due to even more robust bones in extinct species (slope=1.319±0.213). Finally, we take advantage of our MCH models to explore constraints regarding the position of the center of mass (CoM) and find that relative body proportions (i.e., skull:tail ratio) influence CoM position differently in mammals, crocodylians, and Permo-Triassic tetrapods. Further, we find that clade-specific body segment expansion factors do not affect group comparisons but may be important for individual specimens with rather disproportionate bodies (e.g., the small-headed and large-tailed Edaphosaurus). Our findings suggest that the whole-body volumetric approach is better suited for estimating body mass than element-scaling when anatomies are beyond the scope of the sample used to generate the scaling equations and provides added benefits such as the ability to measure inertial properties.

Norms for 718 Persian Words in Emotional Dimensions, Animacy, and Familiarity.

Research frequently uses words as stimuli to assess cognitive and psychological processes. However, various attributes of these words, such as their semantic and emotional aspects, could potentially confound study results if not properly controlled. This study aims to establish a reliable foundation for the semantic and emotional aspects of words for research in Persian. To this end, the present study provided norms for 718 Persian nouns in arousal, valence, familiarity, and animacy dimensions. The words were selected from a previous English dataset (Warriner et al. in Behav Res Methods 45(4):1191-1207, 2013), translated into Persian, and rated by a total of 463 native Persian-speaking participants. The ratings were obtained through an online questionnaire using a 9-point Likert scale for emotional dimensions (i.e., valence and arousal) and a 5-point Likert scale for semantic dimensions (i.e., familiarity and animacy). The reliability of the ratings was measured using the split-half method, and the result indicated a high consistency of ratings in all dimensions. To assess the relationship between the emotional and semantic dimensions, Pearson correlation coefficient was conducted. Gender differences were investigated through the Mann-Whitney U test, and significant differences were observed in all dimensions. These results are compared with findings from previous studies that were conducted in various languages.

Designing Innovative Quick Response Codes-Based Product Authenticity Safeguards: Risk Analysis

This paper examines the potential risks that may occur when designing and implementing innovative products’ authenticity safeguards based on quick response (QR) codes. The study identified ten key risks, which were then analyzed in two dimensions: the probability of their occurrence and the strength of their impact, should they occur. Using the matrix-based method, risks were visualized on an intensity scale in both dimensions and with adequate color notation. Subsequently, the identified risks were grouped thematically. This enabled the identification of four key areas containing the identified risks, namely: competition, external websites, technological integration and risks dependent on internal factors. After aggregating individual risk levels, for each key area the average risk level was calculated. The first three areas were characterized by an average low level of risk, while the area related to risks dependent on internal factors was characterized by an average medium level of risk. The study’s systematic approach to identify and evaluate risks related to the execution of QR code-based authenticity safeguards project can be applied by businesses to similar projects, as it enables scientific-based risk identification and management, and consideration of strategies to mitigate the potential issues, ensuring smoother project execution and more reliable product performance.

Sound absorption uncertainty in small reverberation chambers

Manufacturers in the mobility industry typically measure and specify the sound absorption coefficient of materials using a small reverberation chamber according to SAE J2883. These chambers have a 6 to 25 cubic meter volume, use a 1.0 meter x 1.2 meter sample size and report sound absorption in the one-third octave bands from about 400 Hz to 10,000 Hz. This is in contrast to a full-size chamber built to satisfy the requirements of ASTM C423 or ISO 354, which have about a 200 cubic meter volume, use a 2.4 x 2.7 or 3.2 x 3.2 square meter sample size and report sound absorption in one-third octave bands from 100 to 5,000 Hz. Although the room and sample size dimensions scale, many of the factors that contribute to uncertainty in the measurement do not scale. These include relative humidity, temperature, and other physical measurements and if the same instrumentation is used, microphone calibration and measurement uncertainty in the higher frequency range. This paper examines the potential measurement uncertainty in these chambers over the 400 to 10,000 Hz frequency range and compares this to past uncertainty analyses of full-size chambers over a similar frequency range.

Impact research of pain nursing combined with hospice care on quality of life for patients with advanced lung cancer.

This study aims to evaluate the impact of integrating pain nursing with hospice care on the quality of life among patients with advanced lung cancer. This study involving 60 advanced lung cancer patients admitted from January 2022 to January 2023. Participants were randomly assigned to 2 groups: the observation group received a combination of pain nursing and hospice care, while the control group received standard nursing care. The study assessed changes in the numeric rating scale for pain, self-rating anxiety scale (SAS), self-rating depression scale (SDS), cancer fatigue scale (CFS), death attitude, and various quality of life dimensions as measured by the Quality of Life Questionnaire-Core 30. Post-intervention, both groups exhibited reductions in numeric rating scale, SAS, SDS, and CFS scores compared to baseline, with more significant improvements observed in the observation group (P < .05). Additionally, post-intervention scores for death attitude and Quality of Life Questionnaire-Core 30 domains (physical, cognitive, social, role, and emotional functioning, as well as overall health) increased in both groups, with the observation group showing greater improvements than the control group (P < .05). The combination of pain nursing and hospice care significantly reduces pain, anxiety, and depression, decreases cancer-related fatigue, and improves the quality of life and death attitudes in patients with advanced lung cancer, highlighting the benefits of this integrative approach in palliative care settings.

A Case Report of a Patient with Insomnia Related To Fibromyalgia Treated with Korean Medicine, including Bunshimgi-eum

In this case report, we describe the effects of Korean Medicine therapies, including Bunshimgi-eum, on a patient hospitalized with insomnia due to fibromyalgia in a Korean Medicine Hospital. We treated the patient with Bunshimgi-eum for 21 of 27 hospital days. Post-treatment, we used the Insomnia Severity Index (ISI) to measure the severity of insomnia. To determine the severity of multiple pain, including neck, low back, Lt. shoulder, Lt. elbow, Rt. knee, and hand, we used the Numerical Rating Scale (NRS). For evaluation of generic health status, we used the European Quality of Life-5 Dimensions (EQ-5D) scale. After the treatment, the patient’s clinical symptoms improved, according to the ISI, NRS, and EQ-5D. The results of this case study suggest that Korean Medicine therapies, including Bunshimgi-eum, may have positive effects as a treatment for insomnia related to fibromyalgia.

A Case Report of Complex Korean Medical Treatments, Including Shihogayonggolmoryo-tang, for Sleep Disorders Accompanied by a Herniated Intervertebral Disc

Objectives: We describe the clinical course in a 53-year-old female patient admitted to a Korean Medicine Hospital with insomnia disorder accompanied by a herniated intervertebral disc and managed with Korean medical treatments.Methods: The patient was treated with herbal medicines, including Shihogayonggolmoryo-tang, acupuncture, pharmacopuncture, and Chuna manual therapy for 33 days. The therapeutic effect was evaluated based on the Insomnia Severity Index, Numerical Rating Scale score, Oswestry Disability Index, and European Quality of Life 5 Dimensions Scale.Results: Post-treatment, the Insomnia Severity Index decreased from 21 to 6, the Numerical Rating Scale score decreased from 7 to 3, the Oswestry Disability Index decreased from 60 to 18, and the European Quality of Life 5 Dimensions Scale increased from 0.35 to 0.85.Conclusions: Korean medical treatments improved the symptoms of this patient with insomnia disorder accompanied by a herniated intervertebral disc. Further clinical research on patients with insomnia disorder is needed.

Exploring innovative food in a developing country: Edible insects as a sustainable option

Abstract Today's consumers are becoming more aware of what they eat and the benefits that a healthy diet can provide. Edible insects (EIs) have recently been proposed as a sustainable, protein-rich alternative food source. Consumers' adoption of insects as part of their diet may be influenced by their awareness of this source of food. In this context, the current study investigated the level of knowledge about EI in a developing country, with the goal of understanding how Lebanese people perceive EI as food, as well as whether there are any sociodemographic or socioeconomic differences in their knowledge and motivation to accept EI as food. This was a cross-sectional study conducted using a questionnaire survey of 357 Lebanese participants. Basic descriptive statistics were employed to analyze the data, which were supplemented with statistical tests such as ANOVA for comparisons between three or more groups with post hoc to examine any group differences and Cronbach's alpha to assess internal scale reliability. The search for differences according to sociodemographic and socioeconomic characteristics showed significant differences between age groups and levels of education. Additionally, the results showed that the items used to assess the EI dimensions scale have a very high internal consistency, with the lowest being nutritional aspects (α = 0.669) and the highest being health effects (α = 0.797). This work is relevant because it highlights the EI food dimensions that influence people’s acceptance in Lebanon, which is facing social and economic crises while highlighting many age inequalities and education level differences. Based on the findings, individual EI dimensions were discovered, allowing for strategies deployment to effectively improve knowledge and eventually respond to a Sustainable Development Goal objective even in a nation where this is not a traditional practice.

Prognostic Features of Sarcopenia in Older Hospitalized Patients: A 6-Month Follow-Up Study.

Background: Sarcopenia is associated with adverse health outcomes. Understanding the association between sarcopenia, multidimensional frailty, and prognosis is essential for improving patient care. The aim of this study was to assess the prevalence and prognostic signature of sarcopenia in an acute hospital setting co-led by internists and geriatricians. Methods: Sarcopenia was assessed by applying the European Working Group on Sarcopenia in Older People (EWGSOP2) algorithm, including the SARC-F score, handgrip strength, bioelectrical impedance analysis (BIA), and Timed Up and Go (TUG) test, to 97 older multimorbid inpatients (76.5 ± 6.8 years, 55% women). The patients underwent a Comprehensive Geriatric Assessment (CGA) including an evaluation of Geriatric Syndromes (GSs) and Resources (GR) and prognosis calculation using the CGA-based Multidimensional Prognostic Index (MPI), European Quality of life-5 Dimensions (EQ-5D-5L) scale, Rosenberg Self-Esteem Scale (RSES), and Geriatric Depression Scale (GDS). Information on survival and rehospitalizations was collected 1, 3, and 6 months after discharge. Results: Sarcopenia was present in 63% (95% CI: 54-72%) of patients and categorized as probable (31%), confirmed (13%), and severe sarcopenia (18%). Sarcopenic patients showed significantly higher median MPI-values (p < 0.001), more GSs (p = 0.033), fewer GR (p = 0.003), lower EQ-5D-5L scores (p < 0.001), and lower RSES scores (p = 0.025) than non-sarcopenic patients. Six months after discharge, being sarcopenic at baseline was predictive of falls (p = 0.027) and quality of life (p = 0.043), independent of age, gender, and MPI. Conclusions: Sarcopenia is highly prevalent in older hospitalized multimorbid patients and is associated with poorer prognosis, mood, and quality of life up to 6 months after discharge, independent of age, sex, and MPI as surrogate markers of biological age.

The role of resilience and coping strategies as predictors of well-being in breast cancer patients

PurposeThis study investigated the role of resilience and coping strategies on breast cancer patients' well-being using a structural equation model. To achieve this objective, a model previously developed by Mayordomo's group was partially replicated using a longitudinal study design in an oncological sample. MethodsThe study was a longitudinal observational survey. Patients with breast cancer were recruited (N = 166). Resilience was measured with the Mexican Resilience Measurement Scale, coping strategies with the Forms of Coping and Dimensions Scale and perception of the psychological well-being with a short-form of Ryff's Scales of Psychological Well-Being at the start and end of adjuvant chemotherapy (T1 and T2 respectively). ResultsThe results showed stability in the variables over time and revealed differences with respect to Mayordomo's model. The best predictor of well-being at T2 was well-being at T1. In addition, the model indicated that resilience had a direct impact on well-being through problem-focused coping. Indeed, resilience and problem-focused coping best explained well-being at T2. ConclusionsBoth at the start and end of adjuvant chemotherapy for breast cancer, problem-focused coping positively predicted resilience, which in turn was a positive predictor of well-being. On the other hand, emotion-focused coping showed no association with resilience or well-being. As part of the multidisciplinary cancer team, oncology nurses have a key role to play in promoting resilience and problem-focused coping as an important goal of psychosocial interventions in breast cancer patients.

Universal scaling in real dimension

The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its scaling theory is controlled by a single parameter, the spectral dimension ds, which plays the role of the relevant parameter on complex geometries. The graph under consideration allows us to tune the value of the spectral dimension continuously also to noninteger values and to find the universal exponents as continuous functions of the dimension. By means of extensive numerical simulations, we probe the scaling exponents of a simple instance of O(N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O({{{{{{{\\mathcal{N}}}}}}}})$$\\end{document} symmetric models on the LRDG showing quantitative agreement with the theoretical prediction of universal scaling in real dimensions.

Small skeletons show size-specific scaling: an exploration of allometry in the mammalian lumbar spine.

Studies of vertebrate bone biomechanics often focus on skeletal adaptations at upper extremes of body mass, disregarding the importance of skeletal adaptations at lower extremes. Yet mammals are ancestrally small and most modern species have masses under 5 kg, so the evolution of morphology and function at small size should be prioritized for understanding how mammals subsist. We examined allometric scaling of lumbar vertebrae in the small-bodied Philippine endemic rodents known as cloud rats, which vary in mass across two orders of magnitude (15.5 g-2700 g). External vertebral dimensions scale with isometry or positive allometry, likely relating to body size and nuances in quadrupedal posture. In contrast to most mammalian trabecular bone studies, bone volume fraction and trabecular thickness scale with positive allometry and isometry, respectively. It is physiologically impossible for these trends to continue to the upper extremes of mammalian body size, and we demonstrate a fundamental difference in trabecular bone allometry between large- and small-bodied mammals. These findings have important implications for the biomechanical capabilities of mammalian bone at small body size; for the selective pressures that govern skeletal evolution in small mammals; and for the way we define 'small' and 'large' in the context of vertebrate skeletons.

MONITORING AND ASSESSMENT OF TENURE INSTRUMENTS FOR LAND ADMINISTRATION AND MANAGEMENT

Abstract. The Unified Map and Data Sharing or UMD-Sharing Project are tools and protocols for the preparation of a unified map for the various tenure instrument. It aims to provide NGAs and LGUs with guidelines on how to effectively utilize several tenure data from various NGA and LGU sources. With varying scales of data sources, in both spatial and textual dimensions, the project aims to explore these dimensions to create the Unified Map’s spatial data model. In general, map is regarded as a basic tool in land administration and management (LAM) and a unified map’s solution of harmonizing these disparate tenure instruments could mitigate conflicts. To implement the Unified Map and to show how data sharing is handled among the different organizations, including the LGUs, the project developed a QGIS plugin interface that can utilize a remote database repository.

Personality Traits in Patients with Depression: Association with Symptoms of Depression and Anxiety

Introduction The symptoms of depression and anxiety, which are frequently comorbid, may be significantly impacted by the individual’s personality, even considering the complex etiology of depression. Several studies have shown that while certain personality traits may act as protective factors, others may increase vulnerability to depression and anxiety. Understanding these relationships may be important since personality traits have gained attention as potential determinants of symptom severity and treatment outcomes.ObjectivesTo identify and evaluate the association of personality traits with symptoms of depression and anxiety in patients with depression.Methods The study involved 80 inpatients (≥ 18 years), hospitalised in University psychiatry department with depression diagnosis based on the ICD-10-AM classification. Subjects were asked to fill the Overall Anxiety Severity and Impairment Scale (“OASIS”), the Big Five Personality Dimensions scale and the Patient Health Questionnaire-9 (PHQ-9). Data analysis included descriptive data, Shapiro-Wilk test, Spearman correlation, Kruskal–Wallis test and Chi-Square test, with a significance threshold of p&lt;0.05.Results Severe (26.3%) and very severe (41.3%) depressive symptoms were the most prevalent. Extraversion was associated with minimal (p=0.002), conscientiousness with mild (p&lt;0.001), neuroticism with very severe depressive symptoms (p=0.003). The majority of depressed patients had severe (33,75 %) or very severe (32,5 %) anxiety symptoms. Anxiety symptoms were associated with more severe depressive symptoms (r=0.704, p&lt;0.001). The association of conscientiousness and moderate anxiety symptoms was found (p=0.004). In the presence of expressed neuroticism, most of the respondents showed very severe anxiety symptoms, in the absence of neuroticism – moderate anxiety symptoms (p&lt;0.001).Conclusions The results showed that personality traits were associated with severity of depression and anxiety symptoms in psychiatry inpatient with depression. Therefore, recognition of predominant personality traits in patients with depression may be helpful in selecting treatment and predicting treatment outcomes.Disclosure of InterestNone Declared

Complexity synchronization in emergent intelligence

In this work, we use a simple multi-agent-based-model (MABM) of a social network, implementing selfish algorithm (SA) agents, to create an adaptive environment and show, using a modified diffusion entropy analysis (DEA), that the mutual-adaptive interaction between the parts of such a network manifests complexity synchronization (CS). CS has been shown to exist by processing simultaneously measured time series from among organ-networks (ONs) of the brain (neurophysiology), lungs (respiration), and heart (cardiovascular reactivity) and to be explained theoretically as a synchronization of the multifractal dimension (MFD) scaling parameters characterizing each time series. Herein, we find the same kind of CS in the emergent intelligence of groups formed in a self-organized social interaction without macroscopic control but with biased self-interest between two groups of agents playing an anti-coordination game. This computational result strongly suggests the existence of the same CS in real-world social phenomena and in human–machine interactions as that found empirically in ONs.

Discrete Scaling in Non-integer Dimensions

Discrete Scaling in Non-integer Dimensions