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An electrophysiological technique for assessment of the development of spatial vision.

An objective visual evoked potential (VEP) technique was developed to evaluate spatial processing in humans over a wide range of ages. The constellation of stimulus conditions and analysis methods constitute a novel tool for the assessment of neural development. The key points that delineate this VEP technique are: (1) A brief, 6-s, swept-parameter stimulus with spatial frequency of square-wave grating patterns varied in octave steps, which facilitates correct accommodation and increases the likelihood of collecting uninterrupted, useable data; (2) data collection synchronous with stimulus presentation, which prevents contamination of the relevant frequency component from other frequency components in the response, thereby increasing the signal-to-noise ratio; (3) noise estimation at the response frequency of interest (second harmonic), based on a multivariate statistic (Tcirc2), which yields a realistic measure of signal-to-noise; (4) estimation of grating acuity from linear interpolation of the signal-to-noise measure; (5) monocular testing followed by multivariate statistical comparison of fellow eye data for each spatial frequency condition, which enables the determination of asymmetries within monocular neural pathways; (6) evaluation of maturation of the visual system based on vector-averaged amplitude and phase measures. Preliminary results indicate that reliable response functions are obtained from infants, children, and adults. Acuity estimates increased as a function of age. Phase values decreased consistently with increases in spatial frequency greater than 4 c/deg. Infants produced larger peak amplitude responses than did older observers, consistent with known developmental changes in cortical synaptic density. Phase data for the 2 c/deg condition provided additional evidence for the lack of maturity in the infant visual system as compared with that of older observers.

Adolescent↗

Metabolites from cerebrospinal fluid in aneurysmal subarachnoid haemorrhage correlate with vasospasm and clinical outcome: a pattern-recognition 1H NMR study.

Following subarachnoid haemorrhage the most significant complication is sustained cerebral vascular contraction (vasospasm), which may result in terminal brain damage from cerebral infarction. Despite this, the biochemical cause of vasospasm remains poorly understood. In this study, the global high-concentration metabolite composition of CSF has been correlated with patient outcome after subarachnoid haemorrhage using multivariate statistics and 1H NMR spectroscopy. In total, 16 patients with aneurysmal subarachnoid haemorrhage (aSAH) were compared with 16 control patients who required a procedure where CSF was obtained but did not have aSAH. Multivariate statistics readily distinguished the aSAH group from the heterogeneous control group, even when only those controls with blood contamination in the CSF were used. Using principal components analysis and orthogonal signal correction, vasospasm was correlated to the concentrations of lactate, glucose and glutamine. These pattern recognition models of the NMR data also predicted Glasgow Coma Score (54% within +/- 1 of the actual score on a scale of 1-15 for the whole patient group), Hunt and Hess SAH severity score (88% within +/- 1 of the actual score on a scale of 1-5 for the aSAH group) and cognitive outcome scores (78% within +/- 3 of the actual score on a 100% scale for the whole patient group). Thus, the approach allowed the prediction of outcome as well as confirming the presence of aSAH.

Adult↗

Agricultural produces: synopsis of employed quality control methods for the authentication of foods and application of chemometrics for the classification of foods according to their variety or geographical origin.

A review of quality control methods and applications of multivariate statistical techniques on the authentication and classification of agricultural products is presented. The products reported within the frame of this article were vegetables, fruits, juices, jams, wines, cereals, bakery products, oils, tea, coffee, honey, sugar-syrups, salad dressings, and gums. The perspective of multivariate statistics as a promising tool to authenticate and classify these food products according to their geographical origin or variety was demonstrated. Several representative figures and informative synoptical tables for agricultural food products were provided both for the quality control methods employed and the multivariate analyses implemented.

Cluster Analysis↗

Treating missing data in a clinical neuropsychological dataset--data imputation.

Missing data frequently reduce the applicability of clinically collected data in research requiring multivariate statistics. In data imputation, missing values are replaced by predicted values obtained from models based on auxiliary information. Our aim was to complete a clinical child neuropsychological data set containing 5.2% of missing observations. This was to be used in research requiring multivariate statistics. We compared four data imputation methods by artificially deleting some data. A real-donor imputation method which preserved the parameter estimates and which predicted the observed values with acceptable accuracy was used to complete the data set. In addressing the lack of studies with regard to treatment of missing data in neuropsychological data sets, this study presents information on the outcomes of applying data imputation methods to such data. The imputation modeling described can be applied to a variety of clinical neuropsychological data sets.

Child↗

A multivariate strategy for prediction of psychoacoustic performance from electroacoustic characteristics of hearing aids.

Sentence length psychoacoustic material was processed through 16 hearing aids and presented to 220 listeners. Twenty-nine indices of electroacoustic performance were abstracted from a testing program under laboratory conditions. Through a multivariate statistical strategy, psychoacoustic achievement was shown to be positively correlated to and could be predicted by a knowledge of white noise gain, bandwidth below and above 1 kHz, frequency response regularity, and transiet distortion (multiple R = 0.77; F = 2.04; df = 5,10). It was concluded that a multivariate statistical tactic, when used with discretion, can be a useful and powerful tool to predict psychoacoustic performance from a knowledge of hearing aid electroacoustic characteristics.

Amplifiers, Electronic↗

Combined survivorship and multivariate analyses of revisions in 799 hip prostheses. A 10- to 20-year review of mechanical loosening.

From 1970 to 1980 cemented metal-on-plastic total hip replacement was performed on 799 hips with primary osteoarthritis using one surgical technique. At the 10- to 20-year follow-up there had been 97 revisions for mechanical loosening. Univariate survivorship analysis showed that an increased risk of revision was associated with male gender, young age at primary THR, the Brunswik and Lubinus snap-fit prostheses with large femoral heads (as compared with the Charnley prosthesis), and varying experience of the surgeon. Multivariate statistical analysis showed a three-fold increased risk of revision for men (p < 0.0001), an increase in relative risk of 1.8 per 10 years younger at surgery (p < 0.0001), a fivefold increase in risk for the Brunswik prosthesis (p < 0.0001) and a twofold increase for the Lubinus prosthesis (p = 0.0067). Inexperience of the surgeon, however, was not validated as a risk factor. The study shows that the true risk factors for revision can be identified accurately by combining univariate survivorship and multivariate statistical analyses.

Aged↗

An exploratory analysis of multiple mutation spectra.

The last decade has witnessed a remarkable increase in the number of mutations identified both in human disease-related genes and mutation reporter genes including those in mammalian cells and transgenic animals. This has led to the curation of a number of computerised databases, which make mutation data freely available for analysis. A primary interest of both the clinical researcher and the genetic toxicologist is determination of location and types of mutation within a gene of interest. Collections of mutation data observed for a disease-related gene or, for a gene exposed to a particular chemical, permits discovery of regions of sequence along the gene prone to mutagenesis and may provide clues to the origin of a mutation. The principal tool for visualising the distribution pattern of mutant data along a gene is the mutation spectrum: the distribution and frequency of mutations along a nucleotide sequence. In genetic toxicology, the current wealth of mutation data available allows us to construct many mutation spectra of interest to investigate the mutagenic mechanisms and mutational sites for one or a group of mutagens. Using the multivariate statistical methods principal components analysis (PCA) and cluster analysis (CA) we have tested the ability of these methods to establish the underlying patterns within and between 60 UV-induced, mitomycin C-induced and spontaneous mutations in the supF gene. The spectra were derived from human, monkey and mouse cells including both repair efficient and repair deficient cell lines. We demonstrate and support the successful application of multivariate statistical methods for exploring large sets of mutation spectra to reveal underlying patterns, groupings and similarities. The methods clearly demonstrate how different patterns of spontaneous and UV-induced supF mutation spectra can result from variation in plasmid, culture medium, species origin of cell line and whether mutations arose in vivo or in vitro.

Animals↗

Crossover design in pharmacy research.

OBJECTIVE: Reports of pharmacy research using crossover designs were reviewed to determine if the studies adequately consider interaction effects and use appropriate statistical analyses. DATA SOURCES: All crossover studies published in DICP, The Annals of Pharmacotherapy during 1988 and 1989 were analyzed. STUDY SELECTION: Reports of crossover studies were included only if at least two treatments were applied in a different order to two or more groups of subjects. DATA EXTRACTION: The principal characteristics of crossover studies and the critical design variables were listed and each study analyzed according to these variables. The critical design variables included consideration of period, sequence, and carryover effects as well as the presentation of data by groups and the use of multivariate statistical analysis. The analysis was conducted independently by each author and conflicts were discussed until consensus was obtained. RESULTS: A total of 11 crossover studies were identified: 6 were bioavailability trials, 3 were treatment comparisons, and 2 had multiple objectives. The possibility of period, sequence, or carryover effects was less with bioavailability studies than with treatment comparisons. Only 1 study presented data by group and only 4 studies used multivariate analysis. CONCLUSIONS: The crossover design appears more appropriate for bioavailability trials than for treatment trials in pharmacy research. Analysis of data from crossover designs could be improved by presenting the data for each treatment group and using multivariate statistical analysis.

Analysis of Variance↗

[Principles and methods of geometric morphometrics].

The basic concepts, notions and methods of geometric morphometrics (GM) are considered. This approach implies multivariate analysis of landmark coordinates located following certain rules on the surface of a morphological object. The aim of GM is to reveal differences between morphological objects by their shapes as such, the "size factor" being excluded. The GM is based on the concept of Kendall's space (KS) defined as a hypersphere with points distributed on its surface. These points are the shapes defined as aligned landmark configurations. KS is a non-Euclidian space, its metrics called Procrustes is defined by landmark configuration of a reference shape relative to which other shapes are aligned and compared. The differences among shapes are measured as Procrustes distances between respective points. For the linear methods of multivariate statistics to be applied to comparison of shapes, the respective points are projected onto the tangent plane (tangent space), the tangent point being defined by the reference. There are two principal methods of shape comparisons in GM: the Procrustes superimposition (a version of the least squares analysis) and thin-plate spline analysis. In the first case, Procrustes residuals are the outcome shape variables which remain after isometric alignment of the shapes being compared. Their summation over all landmarks yields Procrustes distances among these shapes. The Procrustes distances can be used in multivariate analyses just as the Euclidian distances. In the second case, the shapes are fitted to the references by stretching/compressing and shearing until complete identity of their landmark configurations. Eigenvectors of resulting bending energy matrix are defined as new shape variables, principal warps which yield another shape space with the origin defined by the reference. Projections of the shapes being compared onto principal warps yield partial warps, and their covariance matrix decomposition into eigenvectors yields relative warps which are similar to principal components (in particular, they are mutually orthogonal). Both partial and relative warps can be used in many multivariate statistic analyses as quantitative shape variables. Results of thin-plate spline analysis can be represented graphically by transformation grid which displays type, amount and localization of the shape differences. Basis rules of sample composition and landmark positioning to be used in GM are considered. At present, rigid (with minimal degrees of freedom) 2D morphological objects are most suitable for GM applications. It is important to recognize three type of real landmarks, and additionally semi-landmarks and "virtual" landmarks. Some procedures of thin-plate spline analysis are considered exemplified by some study cases, as well as applications of some standard multivariate methods to GM results. They make it possible to evaluate correlation between different shapes, as well as between a shape and some non-shape variables (linear measurements etc); to evaluate the differences among organisms by shape of a morphological structure; to identify landmarks which most accounted for both correlation and differences between the shapes. An annotated list of most popular softwares for GM is provided.

Animals↗

Comparison of statistical methods for identification of Streptococcus thermophilus, Enterococcus faecalis, and Enterococcus faecium from randomly amplified polymorphic DNA patterns.

Thermophilic streptococci play an important role in the manufacture of many European cheeses, and a rapid and reliable method for their identification is needed. Randomly amplified polymorphic DNA (RAPD) PCR (RAPD-PCR) with two different primers coupled to hierarchical cluster analysis has proven to be a powerful tool for the classification and typing of Streptococcus thermophilus, Enterococcus faecium, and Enterococcus faecalis (G. Moschetti, G. Blaiotta, M. Aponte, P. Catzeddu, F. Villani, P. Deiana, and S. Coppola, J. Appl. Microbiol. 85:25-36, 1998). In order to develop a fast and inexpensive method for the identification of thermophilic streptococci, RAPD-PCR patterns were generated with a single primer (XD9), and the results were analyzed using artificial neural networks (Multilayer Perceptron, Radial Basis Function network, and Bayesian network) and multivariate statistical techniques (cluster analysis, linear discriminant analysis, and classification trees). Cluster analysis allowed the identification of S. thermophilus but not of enterococci. A Bayesian network proved to be more effective than a Multilayer Perceptron or a Radial Basis Function network for the identification of S. thermophilus, E. faecium, and E. faecalis using simplified RAPD-PCR patterns (obtained by summing the bands in selected areas of the patterns). The Bayesian network also significantly outperformed two multivariate statistical techniques (linear discriminant analysis and classification trees) and proved to be less sensitive to the size of the training set and more robust in the response to patterns belonging to unknown species.

Bayes Theorem↗

Immunodetection and clinico-pathological correlates of two tumour growth regulators in laryngeal carcinoma.

Activation of telomerase, present in the vast majority of all human cancers, is associated with elongation of chromosomal telomeres and consequent cell immortalization. Telomere length homeostasis is a dynamic process governed by the negative feedback mechanism of the telomeric repeat binding factor 1 (TRF1) which inhibits the action of telomerase in telomerase-positive cells. In an attempt to investigate markers of tumour growth as possible prognostic indicators in laryngeal cancer, we studied the expression of TRF1 and of the proliferation marker Ki67 on 96 invasive squamous carcinomas of the larynx. A standard three step immunoperoxidase staining method was applied on paraffin sections incubated with appropriate polyclonal antibodies. The percentages of Ki67- and TRF1-immunopositive cancerous cells were calculated by image analysis. Univariate and multivariate statistical analysis of the staining results were performed in order to detect any association of the examined immunomarkers with the tumours' classical clinicopathological variables including nuclear morphometric features as well as with patients' disease-free survival. Ki67 immunostaining was positively linked with advanced patients' age, nodal involvement as well as presence of early recurrence. No relation was found between proliferative fraction and TRF1 immunoexpression. TRF1 was expressed in 55.2% of all cases and was positively linked only to tumour size. Multivariate statistical analysis revealed the presence of lymph nodal metastasis and Ki67 immunopositivity index > or = 20% as significant predictors of relapse. Increased Ki67 immunostaining appears to be a promising marker of tumour aggressiveness in laryngeal cancer. After one point at the tumour's natural history, the maintenance of tumour growth does not seem to depend on cell proliferation but on TRF1 immunoexpression. Whether the latter can be used for the identification of immortalized cells in every-day practice is worth investigating.

Adolescent↗

Oligodendroglioma. An analysis of the value of radiation therapy.

The role of radiation therapy in the treatment of supratentorial oligodendrogliomas is controversial. To evaluate the role of radiation therapy, the Duke University Medical Center series was retrospectively analyzed. Clinical history, radiation dosages, and pathologic materials were reviewed. Seventy-one patients were identified as having histologically proven oligodendroglioma. Analysis of the patient population demonstrated it to be similar in all major parameters to other populations previously reported in the literature. Multivariate statistical analysis of the demographic, clinical and radiographic variables of these patients showed that a poorer prognosis was associated with persons of increased age (P = 0.052) and black persons (P = 0.014), and in those with papilledema (P = 0.07), hemiparesis (P = 0.001), intellectual deficits (P = 0.0002), and necrosis (P = 0.041). All patients had a surgical procedure as first treatment while 18 and three patients, respectively, underwent a second and third surgical procedure. Thirty-seven patients had a subsequent course of radiotherapy. Univariate and multivariate statistical analysis comparing the patients treated with surgery alone those treated with surgery plus radiotherapy revealed no significant population or prognostic differences between the groups. The median times until clinical deterioration were 39 versus 27 months, the median times until documented tumor recurrence were 27 versus 28 months and the median survival times were 4.5 versus 5.2 years, for nonirradiated versus irradiated patients. These data, from a large and rigidly evaluated population, demonstrated no statistically significant difference in the symptom-free interval, time until tumor recurrence, or survival between the groups nor did radiation appear beneficial to any subgroup evaluated. The results suggest the need for a prospective clinical trial to evaluate the true role of radiation therapy in the treatment of this tumor.

Adolescent↗

Surgery of epilepsy associated with focal lesions in childhood.

OBJECT: Surgery in children with epilepsy is a new, evolving field. The important practical issues have been to define strategies for choosing the most suitable candidates and the type and optimal timing of epilepsy surgery. This study was undertaken to elucidate these points. METHODS: To identify the factors that correlated with outcome, the authors analyzed a series of 200 children (aged 1-15 years (mean 8.7 years) who underwent surgery between 1981 and 1996 at the Hôpital Necker-Enfants Malades. In 171 cases (85.5%) the epilepsy was medically refractory and was associated with focal cortical lesions. Surgery consisted of resection of the lesion without specifically attempting to identify and remove the "epileptogenic area. "In the group of children whose seizures were medically refractory, the mean follow-up period was 5.8 years. According to Engel's classification, 71.3% of these children became seizure free (Class 1a,) whereas 82% were in Class I. A multivariate statistical analysis revealed that among all the factors studied, the success of surgery in a patient in whom there was a good clinical/electroencephalogram/imaging correlation depended on the patient's having undergone a minimally traumatic operation, a complete resection of the lesion, and a short preoperative seizure duration. After the surgical control of epilepsy, behavior disorders were more improved (31% of all patients) than cognitive function (25%). The patient age at onset, duration and frequency of seizures, intractability of the disease to therapy, and seizure characteristics were correlated with cognitive, behavioral, and academic performance pre- and postoperatively. Multivariate statistical analysis revealed that cognitive dysfunction correlated highly with the duration of epilepsy prior to surgery, whereas behavioral disorders correlated more with seizure frequency. CONCLUSIONS: These data must be taken into account when selecting patients for surgical treatment and when deciding the timing of surgery. Early surgical intervention allows for optimum brain development.

Adolescent↗

Introduction of a neuronal network as a tool for diagnostic analysis and classification based on experimental pathologic data.

A neuronal network, as well as uni- and multivariate statistics and a discriminant analysis were applied to a morphometric database of 58 cases with thyroid neoplasms and normal thyroid tissue. The ability to classify cases correctly according to their diagnosis was compared between the neuronal network and discriminant analysis. For all pairwise comparisons, classification by neuronal network was as least as good as classification by discriminant analysis. For some comparisons, the neuronal network provided more correct diagnoses than discriminant analysis. On the contrary, in a comparison between tumors which are not significantly different according to multivariate statistics, the network reclassifies only half of the cases correctly, whereas discriminant analysis falsely suggests the possibility of classifying cases with either diagnosis. Our results confirm a higher sensitivity of the neuronal network to the diagnostic information contained in the present morphometric database, and we will therefore use this concept for analysis and diagnostic classification in further morphometric studies.

Diagnosis, Computer-Assisted↗

Multivariate analysis of fears in dental phobic patients according to a reduced FSS-II scale.

This study analyzed and assessed dimensions of a questionnaire developed to measure general fears and phobias. A previous factor analysis among 109 dental phobics had revealed a five-factor structure with 22 items and an explained total variance of 54%. The present study analyzed the same material using a multivariate statistical procedure (LISREL) to reveal structural latent variables. The LISREL analysis, based on the correlation matrix, yielded a chi-square of 216.6 with 195 degrees of freedom (P = 0.138) and showed a model with seven latent variables. One was a general fear factor correlated to all 22 items. The other six factors concerned "Illness & Death" (5 items), "Failures & Embarrassment" (5 items), "Social situations" (5 items), "Physical injuries" (4 items), "Animals & Natural phenomena" (4 items). One item (opposite sex) was included in both "Failures & Embarrassment" and "Social situations". The last factor, "Social interaction", combined all the items in "Failures & Embarrassment" and "Social situations" (9 items). In conclusion, this multivariate statistical analysis (LISREL) revealed and confirmed a factor structure similar to our previous study, but added two important dimensions not shown with a traditional factor analysis. This reduced FSS-II version measures general fears and phobias and may be used on a routine clinical basis as well as in dental phobia research.

Adult↗

Analysis of blood chemistry and hearing levels in a sample of older persons.

OBJECTIVE: As part of an ongoing study of presbyacusis, the relationship between blood chemistry levels and hearing levels was investigated. Previous reports often used small sets of blood chemistry measures, and results were inconclusive. This experiment examined hearing levels and 27 measures of blood chemistry using various univariate and multivariate statistical procedures. DESIGN: Blood from 89 female and 128 male human subjects was collected. Subjects' ages ranged from 60 to 82 yr, and hearing levels ranged from normal to moderate/severe. Subjects with a history of middle ear disease were excluded. Electrolyte panel (Na, K, Cl, CO2, Ca, urea nitrogen, glucose, creatinine, and Mg), hematology panel (WBC, RBC, Hgb, hematocrit, platelet, etc.), serum lipids (total cholesterol, low-density lipoprotein [LDL], and high-density lipoprotein [HDL]), immunoglobulins (IgG, IgA, IgM, and IgE), and thyroxine were analyzed using univariate and multivariate statistical procedures. RESULTS: Blood chemistry levels of most subjects were within normal ranges as defined by our laboratory. Correlation between blood chemistry measures and pure-tone averages (PTAs) ranged from minimal to low. Results of factor analysis, discriminant analysis, and canonical analysis showed that combining blood chemistry measures from the same panel still could not predict PTA effectively. One exception to this was a gender-specific effect of cholesterol. Hearing levels of women with high LDL/HDL ratios were 5 dB better than those of women with low LDL/HDL ratios. The comparable difference in men was only 1 dB. CONCLUSION: Results suggest that blood chemistry measures that are primarily within the normal range have very little value in predicting pure-tone thresholds in older subjects.

Age Factors↗

Computer interpretation of pediatric orthogonal electrocardiograms: statistical and deterministic classification methods.

Statistical multivariate and conventional deterministic methods of computerized interpretation of the electrocardiogram (ECG) were compared in the analysis of 1711 pediatric orthogonal ECGs validated by nonelectrocardiographic criteria on the basis of clinical and anatomic diagnoses. Among 642 children catheterized for the evaluation of congenital heart disease, there were 140 patients with left ventricular hypertrophy, 299 with right ventricular hypertrophy, and 203 with biventricular hypertrophy. A group of 1069 obviously healthy school children was studied as a control. The overall accuracy of multigroup ECG diagnosis was 85% and 79% for the statistical and deterministic methods, respectively. The diagnostic performances of both methods expressed in terms of sensitivity and predictive value were the highest for normal children and those with right ventricular hypertrophy and lowest for children with biventricular hypertrophy. The statistical method was more sensitive in the diagnosis of left ventricular hypertrophy (74% vs 64%), right ventricular hypertrophy (86% vs 83%), and biventricular hypertrophy (62% vs 50%). Mutual agreement for a correct diagnosis by the two methods was 83% for normal children and 82% for those with right ventricular hypertrophy but only 61% for children with left ventricular hypertrophy and 39% for those with biventricular hypertrophy. In conclusion, better classification results are obtained with statistical multivariate techniques as compared with conventional deterministic analysis, but both methods of ECG interpretation are complementary and their combination in the same electrocardiographic computer program can improve diagnostic accuracy.

Adolescent↗

[Prospective study of the therapeutic usefulness and safety of a new disposable intraurethral occlusive device (Uriabsorber) for female stress urinary incontinence].

OBJECTIVES: To determine the therapeutic usefulness and side effects of a new disposable intraurethral device (Uriabsorber) for female stress urinary incontinence. METHODS: A prospective study was performed in a cohort of 48 women (mean age 42.7 yr.) consulting because of urinary incontinence with coughing. Lack of manual ability or difficulty to understand, pregnancy, puerperium, vaginitis, urinary tract infection and current administration of active treatment for urinary incontinence were all exclusion criteria. Patients were instructed about the use of the device. Two visits were performed: one after two weeks and the other at the end of the month. Clinical results were collected and urine analysis was performed. A multivariate statistical analysis was performed to determine what variables influenced the final result. RESULTS: Treatment withdrawal rate was 42% after one month, being most withdrawals before 14 days (19 cases, 40%). The causes of withdrawal were local discomfort (11 cases, 23%) and difficult insertion (3 cases, 6%). There were only five cases (10%) of urinary tract infection, and two cases (4%) of macroscopic hematuria. The presence of cystocele was associated with higher frequency of complications (80%). 79% of the patients completing the month of treatment had positive results (50% resolution of incontinence and 29% improvement). Multivariate statistical analysis showed that variables independently influencing the results were: incontinence intensity (the lower the intensity, the better the results), presence of urinary tract symptoms (the lower the intensity of the symptoms, the better the results), and absence of past history of pathology. CONCLUSIONS: The intraurethral disposable device significantly reduces the rate of urinary tract infections. Tolerance depends on the ability and motivation of the patients. It is indicated in the control of non intense urinary incontinence in motivated patients, without evident cystocele.

Adult↗