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PubMed2005

An empiric approach to level of care determinations: the importance of executive measures.

BACKGROUND: The ability to predict the level of care received by elderly retirees was compared in a discriminant model and using a classification tree derived from cognitive and noncognitive variables. Methods. Participants were 193 residents (mean age, 79.1+/-5.1 years) of a single, 1,500-bed, continuing care retirement community. They were given a battery of cognitive measures that included tests of general cognition, memory, and executive control function. A multivariate discriminant model of level of care was compared with a classification tree. RESULTS: Residents in congregate high-rises (n=115) differed significantly from those in apartment settings (n=78) with respect to age, Executive Interview (EXIT 25), and the Executive Clock-Drawing Task (CLOX). Only age and executive control function measures (CLOX1, EXIT 25, and Trail Making Test Part B [Trails B]) contributed independently to a discriminant model of level of care (Wilke's lambda=0.92; F [df 4,170]=3.48; p <.01). Sixty-three percent of participants were correctly classified. A classification tree derived from the same variable set was more accurate (75% correctly classified). Age, CLOX1, and EXIT 25 made the most important contributions to the model. The EXIT 25 and CLOX1 thresholds empirically derived from this model coincide with the fifth percentiles for these instruments in a young adult sample. CONCLUSIONS: Executive control function appears to be most responsible for the effect of cognition on level of care. Young adult norms may be most relevant when the effects of cognitive impairment on functional status are assessed.

Activities of Daily Living↗

PubMed1990

Computer simulation of Rocky Mountain spotted fever transmission by the American dog tick (Acari: Ixodidae).

A computer model was developed for simulation of the transmission of Rickettsia rickettsii, the causative agent of Rocky Mountain spotted fever (RMSF), by the American dog tick, Dermacentor variabilis (Say). The model of RMSF was combined with a model for population dynamics of the American dog tick and included simulation of infection and transmission of rickettsiae between ticks and host mammals and transmission of RMSF to humans. The model simulated the effects of biotic and environmental variables such as weather, host density, habitat, transovarial transmission, fecundity of infected ticks, and infectivity level of ticks and mammals. Some parameters in the model were fitted by iterative simulations to produce realistic rates of R. rickettsii infection in adult ticks and small and medium-sized mammal hosts. Parameters also were fitted to yield the historical average number of RMSF cases for Virginia. Comparisons of the simulated and actual number of cases for nine other states indicated a reasonable level of validity for the model. A theoretical tick density threshold of 252 unfed adult ticks/ha for transmission of RMSF was determined from a relationship between rate of transmission to humans and density of ticks. The transmission threshold can be used for additional modeling efforts to study the effects of management technologies on tick densities and RMSF human cases. The model can serve as a framework for modeling other tick-borne diseases such as Lyme disease, babesiosis, and heartwater.

Animals↗

PubMed2004

Population response to climate change: linear vs. non-linear modeling approaches.

BACKGROUND: Research on the ecological consequences of global climate change has elicited a growing interest in the use of time series analysis to investigate population dynamics in a changing climate. Here, we compare linear and non-linear models describing the contribution of climate to the density fluctuations of the population of wolves on Isle Royale, Michigan from 1959 to 1999. RESULTS: The non-linear self excitatory threshold autoregressive (SETAR) model revealed that, due to differences in the strength and nature of density dependence, relatively small and large populations may be differentially affected by future changes in climate. Both linear and non-linear models predict a decrease in the population of wolves with predicted changes in climate. CONCLUSIONS: Because specific predictions differed between linear and non-linear models, our study highlights the importance of using non-linear methods that allow the detection of non-linearity in the strength and nature of density dependence. Failure to adopt a non-linear approach to modelling population response to climate change, either exclusively or in addition to linear approaches, may compromise efforts to quantify ecological consequences of future warming.

Age Factors↗

PubMed1981

Genetic heterogeneity in affective disorders. Implications for psychobiological research.

The extent of genetic heterogeneity in major affective illness was estimated via three paradigms of single-major-locus inheritance. In the first paradigm bipolar and unipolar disorders were represented at different liability thresholds on a genetic-environmental continuum. The second paradigm incorporated sex-related thresholds into the model, thereby testing the hypothesis that affective illness is a transmitted trait whose phenotypic expression is a function of the individual's sex. The third paradigm included both clinical polarity and sex effect as threshold phenomena. All three paradigms predicted considerable genetic heterogeneity in affective disorders. Bipolar homozygotes were far more common than unipolar homozygotes, although the majority of ill individuals in the first two paradigms were heterozygotes. According to the third paradigm bipolar males had the highest proportion of homozygotes amongst the affected population. Significant increases in homozygosity occurred using the dual mating sampling method. Depending on the model paradigm and parameters these increases were 140-25,000% over the random sample method. The implications for biologic and genetic research in affective disorders were discussed.

Affective Disorders, Psychotic↗

PubMed1992

Computer simulation of Babesia bovis (Babes) and B. bigemina (Smith & Kilborne) transmission by Boophilus cattle ticks (Acari: Ixodidae).

A computer model was developed to simulate the processes involved in transmission of the cattle fever parasites Babesia bovis (Babes) and Babesia bigemina (Smith & Kilborne) between cattle and Boophilus ticks. The model of Babesia transmission was combined with a dynamic life history model for population dynamics of the tick vectors, Boophilus microplus (Canestrini) and B. annulatus (Say). Epidemiological parameters and relationships in the model include the reduction in fecundity of infected ticks, rate of transovarial transmission, effect of cattle type and inoculation rate on infectivity of cattle, variation of infected cattle recovery rate with age of infection, inoculation rate, and species of parasite. Some parameters in the model were fitted by iterative simulations to produce realistic rates of Babesia infection in larval ticks. Comparisons of simulated and reported epidemiological data from one location in Australia indicated a reasonable level of validity for the model. Theoretical tick density thresholds for maintenance of Babesia in cattle and for inoculation of greater than or equal to 99.5% calves were determined by iterative simulations at 10 locations with B. microplus and six locations with B. annulatus. The model and transmission thresholds can serve as the basis for further simulation studies on strategies for control or eradication of babesiosis.

Animals↗

PubMed1990

Radiation-related posterior lenticular opacities in Hiroshima and Nagasaki atomic bomb survivors based on the DS86 dosimetry system.

This paper investigates the quantitative relationship of ionizing radiation to the occurrence of posterior lenticular opacities among the survivors of the atomic bombings of Hiroshima and Nagasaki suggested by the DS86 dosimetry system. DS86 doses are available for 1983 (93.4%) of the 2124 atomic bomb survivors analyzed in 1982. The DS86 kerma neutron component for Hiroshima survivors is much smaller than its comparable T65DR component, but still 4.2-fold higher (0.38 Gy at 6 Gy) than that in Nagasaki (0.09 Gy at 6 Gy). Thus, if the eye is especially sensitive to neutrons, there may yet be some useful information on their effects, particularly in Hiroshima. The dose-response relationship has been evaluated as a function of the separately estimated gamma-ray and neutron doses. Among several different dose-response models without and with two thresholds, we have selected as the best model the one with the smallest x2 or the largest log likelihood value associated with the goodness of fit. The best fit is a linear gamma-linear neutron relationship which assumes different thresholds for the two types of radiation. Both gamma and neutron regression coefficients for the best fitting model are positive and highly significant for the estimated DS86 eye organ dose.

Cataract↗

PubMed2000

Transmission thresholds for dengue in terms of Aedes aegypti pupae per person with discussion of their utility in source reduction efforts.

The expense and ineffectiveness of drift-based insecticide aerosols to control dengue epidemics has led to suppression strategies based on eliminating larval breeding sites. With the notable but short-lived exceptions of Cuba and Singapore, these source reduction efforts have met with little documented success; failure has chiefly been attributed to inadequate participation of the communities involved. The present work attempts to estimate transmission thresholds for dengue based on an easily-derived statistic, the standing crop of Aedes aegypti pupae per person in the environment. We have developed these thresholds for use in the assessment of risk of transmission and to provide targets for the actual degree of suppression required to prevent or eliminate transmission in source reduction programs. The notion of thresholds is based on 2 concepts: the mass action principal-the course of an epidemic is dependent on the rate of contact between susceptible hosts and infectious vectors, and threshold theory-the introduction of a few infectious individuals into a community of susceptible individuals will not give rise to an outbreak unless the density of vectors exceeds a certain critical level. We use validated transmission models to estimate thresholds as a function of levels of pre-existing antibody levels in human populations, ambient air temperatures, and size and frequency of viral introduction. Threshold levels were estimated to range between about 0.5 and 1.5 Ae. aegypti pupae per person for ambient air temperatures of 28 degrees C and initial seroprevalences ranging between 0% to 67%. Surprisingly, the size of the viral introduction used in these studies, ranging between 1 and 12 infectious individuals per year, was not seen to significantly influence the magnitude of the threshold. From a control perspective, these results are not particularly encouraging. The ratio of Ae. aegypti pupae to human density has been observed in limited field studies to range between 0.3 and >60 in 25 sites in dengue-endemic or dengue-susceptible areas in the Caribbean, Central America, and Southeast Asia. If, for purposes of illustration, we assume an initial seroprevalence of 33%, the degree of suppression required to essentially eliminate the possibility of summertime transmission in Puerto Rico, Honduras, and Bangkok, Thailand was estimated to range between 10% and 83%; however in Mexico and Trinidad, reductions of >90% would be required. A clearer picture of the actual magnitude of the reductions required to eliminate the threat of transmission is provided by the ratio of the observed standing crop of Ae. aegypti pupae per person and the threshold. For example, in a site in Mayaguez, Puerto Rico, the ratio of observed and threshold was 1.7, meaning roughly that about 7 of every 17 breeding containers would have to be eliminated. For Reynosa, Mexico, with a ratio of approximately 10, 9 of every 10 containers would have to be eliminated. For sites in Trinidad with ratios averaging approximately 25, the elimination of 24 of every 25 would be required. With the exceptions of Cuba and Singapore, no published reports of sustained source reduction efforts have achieved anything near these levels of reductions in breeding containers. Practical advice on the use of thresholds is provided for operational control projects.

Aedes↗

PubMed2001

Informational masking in profile analysis: comparing ideal and human observers.

Predictions from an ideal observer model are compared with human thresholds for two profile analysis tasks. Past work has shown that ideal observer models reasonably account for human thresholds when the profile components are fixed in frequency and amplitude. Randomly varying the frequencies of the tones making up the profile leads to higher thresholds. Owing in part to large interobserver variation, the ideal observer model is not successful in accounting for the pattern of psychophysical thresholds associated with increases in frequency uncertainty. The ideal observer also fails to account for the results of a recent profile analysis experiment in which amplitude randomization was studied [Lentz JJ, Richards VM: J. Acoust. Soc. Am. 102: 535-541, 1998]. Overall, the ideal observer predicts smaller effects of uncertainty on thresholds than are observed in psychophysical experiments.

Auditory Perception↗

PubMed1985

Postadaptation orientation discrimination.

An orientational difference of only 0.3-0.5 deg can be discriminated between two gratings or two lines, although psychophysical channels and cortical cells both have comparatively broad orientation bandwidths of 10-25 deg. One proposed explanation for the fineness of orientation discrimination is that, while detection is determined by the most excited orientation-tuned neural elements, superthreshold orientation discrimination is determined by difference signals between these elements [Westheimer et al., J. Opt. Soc. Am. 66, 332 (1976)]. This implies that, if stimulus orientation is changed slightly, the most important elements for discriminating this change will be those whose relative activity changes most, even though the excitation of these elements may be comparatively weak. In accord with this prediction, we found that adapting to a high-contrast grating degraded discrimination for test gratings inclined at about 10-20 deg to the adapting grating while having little effect on the detection of these inclined gratings. For test gratings parallel to the adapting grating, discrimination was improved, but detection was degraded. Either an opponent-process or a line-element model can account for these effects of adaptation. An opponent model can also explain our findings that subjects do not confound orientation change with contrast change and that suprathreshold orientation discrimination is almost independent of contrast, varying by only +/- 10% from about 3 to about 25 times contrast threshold. A discrimination model must incorporate reliable storage of spatial frequency, because discrimination was not affected by increasing the interval between grating presentations from 1 to 10 sec.(ABSTRACT TRUNCATED AT 250 WORDS)

Adaptation, Ocular↗

PubMed1994

Determination of the compartment pressure threshold of muscle ischemia in a canine model.

A canine model was used to test the hypothesis that critical intracompartmental pressure leading to ischemic muscle necrosis is linked to diastolic blood pressure. Twenty adult dogs were subjected to an infusion of autologous plasma into the anterolateral muscle compartment of the left hindlimb to create an elevation in compartment pressure. There were four experimental groups of five dogs each. In group I, the compartment pressure (CP) was maintained at the animals' diastolic blood pressure (DBP); in group II, at 10 mm Hg less than the DBP; in group III, at 20 mm Hg less than the DBP; and in group IV, at 30 mm Hg. The pressure was measured continuously in the proximal, central, and distal segments of the compartment during an 8-hour period. Immediately postoperatively, and, on the first, fourth, seventh, and fourteenth days one animal from each group was killed. The tibialis cranialis muscle was then removed and analyzed using light and electron microscopy. The critical pressure threshold for ischemic muscle necrosis was found to be 20 mm Hg less than the diastolic blood pressure.

Analysis of Variance↗

PubMedDate not supplied

Determination of threshold conditions for a non-linear stochastic partnership model for heterosexually transmitted diseases with stages.

When comparing the performance of a stochastic model of an epidemic at two points in a parameter space, a threshold is said to have been crossed when at one point an epidemic develops with positive probability; while at the other there is a tendency for an epidemic to become extinct. The approach used to find thresholds in this paper was to embed a system of ordinary non-linear differential equations in a stochastic process, accommodating the formation and dissolution of marital partnerships in a heterosexual population, extra-marital sexual contacts, and diseases such as HIV/AIDS with stages. A symbolic representation of the Jacobian matrix of this system was derived. To determine whether this matrix was stable or non-stable at a particular parameter point, the Jacobian was evaluated at a disease-free equilibrium and its eigenvalues were computed. The stability or non-stability of the matrix was then determined by checking if all real parts of the eigenvalues were negative. By writing software to repeat this process for a selected set of points in the parameter space, it was possible to develop search engines for finding points in the parameter space where thresholds were crossed. The results of a set of Monte Carlo simulation experiments were reported which suggest that, by combining the stochastic and deterministic paradigms within a single formulation, it was possible to obtain more informative interpretations of simulation experiments than if attention were confined solely to either paradigm.

Acquired Immunodeficiency Syndrome↗

PubMed2001

The outcome of retinopathy of prematurity: screening for retinopathy of prematurity using an outcome predictive program.

PURPOSE: The purpose of this study was to compare the calculated risk of progression to threshold retinopathy of prematurity (ROP) and risk of an unfavorable structural outcome using the computer program, RM-ROP, with the observed incidence for infants born at Jackson Memorial Hospital (JMH) and to determine how many children would have been treated unnecessarily if the threshold criteria for treatment were lowered on the basis of the clinical findings and RM-ROP risk calculations. DESIGN: Noncomparative interventional case series. PARTICIPANTS: All 292 surviving premature infants weighing 1250 g or less at birth and born at JMH between January 1, 1997, and December 31, 1998, were included in the study. METHODS: Baseline demographic factors and data from sequential ophthalmic examinations were entered into the RM-ROP program for risk calculation. Infants reaching threshold disease received diode laser indirect photocoagulation of the avascular retina. Three-month follow-up was obtained for infants receiving laser treatment. MAIN OUTCOME MEASURES: The development of threshold ROP and an unfavorable structural outcome, defined as a posterior retinal fold or posterior retinal detachment occurring within 3 months of threshold disease. RESULTS: Thirty-eight eyes were diagnosed with threshold ROP, with 18 of 20 subjects having bilateral disease. Three-month posttreatment follow-up was obtained on all 20 children, with 19 having good structural outcomes. Thirty-two percent of eyes (12 of 38) reaching threshold never had a risk estimate greater than 0.10. However, only 6% of eyes (35 of 546) that did not reach threshold ever had a model predicted risk greater than 0.15. All right eyes with zone 1 prethreshold disease, 60% of those with zone 2 stage 2+ disease, and 23% with zone 2 stage 3 disease progressed to threshold ROP. CONCLUSIONS: The similarity between the risk distributions for the Miami and the Multicenter Trial of Cryotherapy for Retinopathy of Prematurity study indicates the similarity in the populations with respect to risk factors identified as important by the model. The Miami data validated the model, with eyes reaching threshold having higher risks than eyes that did not. Actual risk estimates for eyes reaching threshold can be small. Changing the threshold criteria for treatment on the basis of various clinical and computer-generated prethreshold risk levels in our population would have resulted in the unnecessary treatment of many infants who never progressed to threshold disease. In the Miami population, if the model were used to manage an individual subject, close attention would have to be paid to small differences in risk. Although the RM-ROP software program may be a useful tool for following premature infants with ROP, the clinical examination remains the "gold standard."

Disease Progression↗

PubMed2001

Pharmacokinetic and pharmacodynamic modeling of NN703, a growth hormone secretagogue, after a single po dose to human volunteers.

The objective of this study was to describe the pharmacokinetics and pharmacodynamics of NN703, a growth hormone (GH)-releasing secretagogue, after po administration to healthy human male subjects. The study was designed as a randomized, placebo-controlled, double-blind, dose-escalating, single-dose trial of NN703 covering eight dose levels. Each of the dose levels had 6 subjects on active treatment and 2 subjects on placebo. NN703 was administered po as a solution. Blood samples for serum concentrations of NN703 and GH were collected before dosing and up to 24 hours after dosing. Serum concentrations of NN703 were determined using a validated analytical method, based on solid-phase extraction and LC/MS/MS detection. A two-compartmental model with zero-order input was used to describe the pharmacokinetics of NN703. The parameters of the elimination phase were fitted simultaneously, whereas the parameters describing the absorption phase were allowed to vary between the dose levels. The pharmacodynamics of NN703 was described by use of an indirect-response model containing both a threshold value and a modulator for the development of tolerance. It was concluded that the absorption of NN703 after po administration was nonlinear; the bioavailability increased with the dose. The serum concentration of NN703 required for half-maximal stimulation of GH was determined to be 485 ng/ml. The proposed indirect-response model requiring a threshold concentration and development of tolerance provided a useful mean of quantifying the effects of NN703. Furthermore, the development of tolerance shown based on pharmacokinetic/pharmacodynamic modeling of single-dose data presented here has been confirmed following multiple dosing in healthy male subjects.

Administration, Oral↗

PubMed2003

Cyclooxygenase-1 in the spinal cord plays an important role in postoperative pain.

Cyclooxygenase-2 (COX-2) activity in the spinal cord plays a key role in sensitization to sensory stimuli during acute inflammation. In contrast, intrathecal administration of COX-2 specific inhibitors has minimal analgesic effects in an incisional model of postoperative pain. We investigated the role of COX isoforms in this model by examining the expression of COX-1 and the effect of intrathecal COX inhibitors. A 1cm longitudinal incision was made through skin, fascia and muscles of the plantar aspect of the left paw in male rats, and withdrawal threshold to von Frey filaments measured. Rats were perfused at 1, 2, 3, 5, and 7 days after incision, and COX-1 immunohistochemistry was performed on L3 to S2 spinal cord and gracile nucleus sections. Other rats received intrathecally the COX-1 preferring inhibitor, ketorolac, the specific COX-1 inhibitor, SC-560, the COX-2 inhibitor, NS-398 or vehicle 1 day after surgery. Withdrawal threshold was measured at intervals up to 5 days later. COX-1 immunoreactivity increased in glia in the ipsilateral L4-L6 spinal dorsal horn and ipsilateral gracile nucleus after incision. Mechanical allodynia peaked on postoperative day 1, and COX-1 immunoreactivity increased on day 1, peaked on day 2, and declined thereafter. Ketorolac and SC-560 dose-dependently increased withdrawal threshold in this model, but NS-398 had no effect. These results suggest that COX-1 plays an important role in spinal cord pain processing and sensitization after surgery. Increased COX-1 activity could precede the up-regulation of COX-1 protein, and spinally administered specific COX-1 inhibitors may be useful to treat postoperative pain.

Animals↗

PubMed1981

A cybernetical model of the internal cellular clock.

A model of a cell-labeling mechanism for the development tree of a multicellular organism is suggested. The cell-labeling information is assumed to originate because the DNA strands are complementary, rather than identical, so a pair of replicated DNA can carry different information content to newly created pairs of chromosomes. This mechanism can serve as an internal cellular clock and as one of the factors involved in the control of cell differentiation. Some possible structures were analyzed by means of the mathematical theory of reliability and compared with the results of Hayflick's experiments on limited cells'lifetime. The external destruction of the clock mechanism can remove limitations on cell's reproductions and is considered as a cause of carcinogenesis; the model exhibits cumulative and threshold effects. The cell-labeling mechanism of the model is able to provide sometimes equivalent labeling for the initial zygote division as a necessary condition for the appearance of monozygote twins; it is most likely that this may occur only for pairs of monozygote twins with the probability equal to an integer power of 1/2.

Animals↗

PubMed1989

A computational model for rate-level functions from cat auditory-nerve fibers.

A computationally tractable form of the rate-level model proposed by Sachs and Abbas (1974) is presented. The first stage of the model is a compressive nonlinearity whose input-output function is chosen to reflect current data on basilar-membrane displacement. The output of this nonlinearity is converted to driven discharge rate by the saturating nonlinearity originally used by Sachs and Abbas (1974). In fitting the model to data four model parameters are chosen to minimize the mean squared error between rate functions generated by the model and the data. With parameters chosen in this way, the model provides good fits to the range of rate-level shapes from flat saturations to sloping saturations. One important parameter in the model is the 'threshold for compression'. For low- and medium-spontaneous rate fibers with similar best frequencies (BFs), the minimum mean squared error compression threshold is roughly constant at about 30 dB above the thresholds of the most sensitive (high-spontaneous rate) fibers at that BF.

Animals↗

PubMed1998

Threshold analysis of Helicobacter pylori therapy.

OBJECTIVE: Conflicting recommendations have been made on whom to treat with antibacterials to eradicate Helicobacter pylori. The present analysis aims to explain the basis of such discrepancies. DESIGN AND SETTING: The decision in favour of or against antibacterial therapy in patients with upper gastrointestinal symptoms is modelled as a threshold analysis. The threshold is the lowest probability for a given diagnosis at which the decision in favour of antibacterial therapy yields a higher expected outcome than the decision against it. A strong indication for antibacterial therapy is shown by a low threshold value. MAIN OUTCOME MEASURES AND RESULTS: In patients with suspected peptic ulcer disease, both the high success rate of antibacterial therapy and its low cost make it the most favourable treatment option, its threshold being less than 35%. In ulcer patients receiving nonsteroidal anti-inflammatory drugs, the threshold is 73% if based on success rates of different treatment modalities, but only 7% if treatment costs are considered. The relatively poor success rate of antibacterial therapy in non-ulcer dyspepsia raises the diagnostic threshold for antibacterial therapy to 76% if based on therapeutic success rates. The small marginal cost of antibacterial therapy lowers the diagnostic threshold to 16%. CONCLUSION: If therapeutic success is the primary concern, patients with vague abdominal symptoms should not be given antibacterial therapy, unless H. pylori has been established as a probable cause of their symptoms. If healthcare costs are the driving force for choosing one type of therapy over another, a trial of antibacterials appears indicated irrespective of any firm validation of H. pylori playing a role in the patient's disease.

Anti-Bacterial Agents↗

PubMed1998

Topics in dose-response modeling.

Great uncertainty exists in conducting dose-response assessment for microbial pathogens. The data to support quantitative modeling of dose-response relationships are meager. Our philosophy in developing methodology to conduct microbial risk assessments has been to rely on data analysis and formal inferencing from the available data in constructing dose-response and exposure models. The probability of illness is a complex function of factors associated with the disease triangle: the host, the pathogen, and the environment including the food vehicle and indigenous microbial competitors. The epidemiological triangle and interactions between the components of the triangle are used to illustrate key issues in dose-response modeling that impact the estimation of risk and attendant uncertainty. Distinguishing between uncertainty (what is unknown) and variability (heterogeneity) is crucial in risk assessment. Uncertainty includes components that are associated with (i) parameter estimation for a given assumed model, and (ii) the unknown "true" model form among many plausible alternatives such as the exponential, Beta-Poisson, probit, logistic, and Gompertz. Uncertainty may be grossly understated if plausible alternative models are not tested in the analysis. Examples are presented of the impact of variability and uncertainty on species, strain, or serotype of microbial pathogens; variability in human response to administered doses of pathogens; and effects of threshold and nonthreshold models. Some discussion of the usefulness and limitations of epidemiological data is presented. Criteria for development of surrogate dose-response models are proposed for pathogens for which human data are lacking. Alternative dose-response models which consider biological plausibility are presented for predicting the probability of illness.

Adult↗