Triangle Map Research Articles

Detecting elevated left ventricular end diastolic pressure from simultaneously measured femoral pressure waveform and electrocardiogram

Objective. Instantaneous, non-invasive evaluation of left ventricular end-diastolic pressure (LVEDP) would have significant value in the diagnosis and treatment of heart failure. A new approach called cardiac triangle mapping (CTM) has been recently proposed, which can provide a non-invasive estimate of LVEDP. We hypothesized that a hybrid machine-learning (ML) method based on CTM can instantaneously identify an elevated LVEDP using simultaneously measured femoral pressure waveform and electrocardiogram (ECG). Approach. We studied 46 patients (Age: 39–90 (66.4 ± 9.9), BMI: 20.2–36.8 (27.6 ± 4.1), 12 females) scheduled for clinical left heart catheterizations or coronary angiograms at University of Southern California Keck Medical Center. Exclusion criteria included severe mitral/aortic valve disease; severe carotid stenosis; aortic abnormalities; ventricular paced rhythm; left bundle branch and anterior fascicular blocks; interventricular conduction delay; and atrial fibrillation. Invasive LVEDP and pressure waveforms at the iliac bifurcation were measured using transducer-tipped Millar catheters with simultaneous ECG. LVEDP range was 9.3–40.5 mmHg. LVEDP = 18 mmHg was used as cutoff. Random forest (RF) classifiers were trained using data from 36 patients and blindly tested on 10 patients. Main results. Our proposed ML classifier models accurately predict true LVEDP classes using appropriate physics-based features, where the most accurate demonstrates 100.0% (elevated) and 80.0% (normal) success in predicting true LVEDP classes on blind data. Significance. We demonstrated that physics-based ML models can instantaneously classify LVEDP using information from femoral waveforms and ECGs. Although an invasive validation, the required ML inputs can be potentially obtained non-invasively.

Further results on the concavity of operator means

In this work, we provide some further refinements for the following concavity inequalityAσB+CσD≤(A+C)σ(B+D) for positive invertible bounded linear operators A,B,C,D on a complex Hilbert space and for an operator mean σ. To this end, we use the operator majorization intended for comparing two n+1-tuples of pairs of operators, and prove a Hardy-Littlewood-Pólya-Karamata (HLPK) type theorem for the triangle map induced by σ. Next, we apply a specification of the HLPK Theorem for n=2 in order to obtain the required refinements.

TriClick: Interactive Dermoscopic Image Segmentation with Triangle Map

AbstractLesion segmentation is a fundamental task that has been widely studied in biomedicine. State‐of‐the‐art methods still struggle with the inherent challenges of dermoscopic images such as uncertain boundaries or severe occlusion. In this study, we argue that this task can be better resolved by introducing user interaction and proposing a deep interactive framework for lesion segmentation. Our method is designed to best reflect user expertise to iteratively refine the segmentation results. In each iteration, professional users are expected to click three points on the boundary of the lesion to encourage the network to update the previous round of the segmentation result. To best exploit the clues from the interaction, we explore a novel encoding strategy by producing a triangle map whose vertices are the three clicked points. Owing to the strong guidance within such triangle maps, our method can outperform state‐of‐the‐art methods with baseline segmentation backbones. Extensive experimental results and ablation studies on three commonly used lesion segmentation data sets demonstrated the effectiveness of our method in terms of segmentation accuracy and encoding effectiveness. © 2024 The Authors. IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Generating New Partition Identities via a Generalized Continued Fraction Algorithm

Using the slow triangle map (a type of multi-dimensional continued fraction algorithm), we exhibit a method for generating any number of new identities for subsets of integer partitions.

Records and Occupation Time Statistics for Area-Preserving Maps

A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated with stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for deterministic systems on non-compact phase space. We consider here two examples of area-preserving maps: the Chirikov-Taylor standard map and the Casati-Prosen triangle map, and we investigate transport properties, records statistics, and occupation time statistics. Our results confirm and expand known results for the standard map: when a chaotic sea is present, transport is diffusive, and records statistics and the fraction of occupation time in the positive half-axis reproduce the laws for simple symmetric random walks. In the case of the triangle map, we retrieve the previously observed anomalous transport, and we show that records statistics exhibit similar anomalies. When we investigate occupation time statistics and persistence probabilities, our numerical experiments are compatible with a generalized arcsine law and transient behavior of the dynamics.

On Gauss--Kuzmin statistics and the transfer operator for a multidimensional continued fraction algorithm: the triangle map

On Gauss--Kuzmin statistics and the transfer operator for a multidimensional continued fraction algorithm: the triangle map

Origin of the unusual property contrast in K2Bi8Se13 phase-change material

Phase-change materials are promising foundations for both nonvolatile storage and neuro-inspired computing applications. An attractive phase change material K2Bi8Se13 (KBS) was recently discovered to possess fast structural transition and outstanding property contrast, yet the underlying mechanism remains unclear. We conducted ab initio molecular dynamics simulations to investigate the transition of KBS from a crystalline to amorphous phase. Initiated by the Bi–Se bond breaking at the boundaries of atom blocks, the simulated phase transition proceeds through the conversion between BiSex octahedral and pyramid structures. Remarkable discrepancies in electronic structures and absorption spectra between the two phases are further illustrated by density functional theory simulations, which reproduce the experimental observations. The optical and electrical contrasts between the two phases are found to originate from the band edge states localized at various atom blocks that uniquely appear in the crystalline phase. These states provide pseudo one-dimensional transport channels with resonant bonding that may further intensify the electrical contrast. The distinct phase change properties compared with traditional phase change materials can be attributed to the hierarchical KBS crystal structure comprised of loosely bound atom blocks. The above findings pave an avenue toward the design of phase change materials beyond the traditional scope of the Ge–Sb–Te triangle map.

Sublinear diffusion in the generalized triangle map.

Diffusion of the orbits in a nonchaotic area-preserving map called a generalized triangle map (GTM) is numerically and analytically investigated. We provide accurate empirical evidence that the mean-squared displacement of the momentum for generic perturbation parameter settings increases sublinearly in time, and that the distribution of the momentum obeys a time-fractional diffusion equation. We show that the diffusion properties in the GTM do not follow any of the known stochastic processes generating sublinear diffusion since two seemingly incompatible features, non-Markovian yet stationary, coexist in the dynamics.

Statistical and dynamical properties of the quantum triangle map

We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for spectrum and eigenfunctions to follow the prediction of random matrix theory, even though the underlying classical dynamics is not chaotic. On the other hand, dynamical quantities such as the out-of-time-ordered correlator (OTOC) and the number of harmonics, exhibit a growth rate vanishing in the semiclassical limit, in agreement with the fact that classical dynamics has zero Lyapunov exponent. Our finding show that, while spectral statistics can be used to detect ergodicity, OTOC and number of harmonics are diagnostics of chaos.

Star Identification Based on Radial Triangle Mapping Matrix

In this paper, a novel star image recognition algorithm is proposed based on a voting scheme that utilizes a radial triangle mapping matrix pattern. Inspired by the radial and cyclic algorithm, the radial triangle mapping matrix pattern is rotation-invariant, and does not rely on a location star, which provides a new idea for the construction of rotation-invariant patterns. The algorithm is based on a geometric voting scheme in which the radial triangle group is considered as the basic voting element. The database optimization is used to reduce the memory requirement and improve the query efficiency by extracting the nonzero value of the pattern. During the identification period, the voting scheme can vote for the candidate stars through the radial triangles, which improves the robustness towards the noise. The proposed algorithm exhibits a 98.41% identification rate with 2.0-pixel standard deviation of position noises and 0.3-Mv magnitude noises. The experimental results of the simulation star image and real star image show that the proposed algorithm is quite more robust towards position noise, magnitude noise, and false star noise when compared with other comparing algorithms.

A complementary result to the superadditivity of operator means

In this note, we prove a refinement of the inequality where are positive invertible bounded linear operators on a complex Hilbert space, and, in addition, σ is an operator mean on such operators. To this end we use some commutative operators. We introduce a special preorder on the pairs of operators and show that a related triangle map is nonincreasing with respect to the preorder.

Abstract 14086: A Hybrid Machine Learning Method for Instantaneous Classification of Left Ventricular Filling Pressure Using Femoral Waveforms

Introduction: Non-invasive and instantaneous evaluation of left ventricular end-diastolic pressure (LVEDP) is of high significance in diagnosis and treatment of heart failure patients. We recently proposed the cardiac triangle mapping (CTM), a systems approach that uses information from arterial pressure waveforms and pre-ejection periods to map the global ventricular function (Pahlevan et al. Fluids 4.1 (2019): 16). Here, we propose a hybrid machine learning (ML) method based on CTM theory that uses pressure waveforms at the iliac bifurcation level and ECG to instantaneously classify the level of LVEDP. Methods: We studied 46 patients (Age: 39-90 (66.4±9.9), BMI: 20.2-36.8 (27.6±4.1), 12 females) who were scheduled for clinical left heart catheterization or coronary angiogram at the Keck Medical Center of USC. Exclusion criteria were valvular heart disease, left bundle branch block, or atrial fibrillation. Invasive LVEDP and pressure waveforms at iliac bifurcation were measured using a 3F Millar transducer tipped catheter, with simultaneous 3 channel ECG. The range of patients’ LVEDP was from 9.3 to 40.5 mmHg. LVEDP=18 mmHg was used as the ML classification cut-off. A random forest classifier (of n=30 grown decision trees, ensemble learning method: bootstrap aggregation, 6 inputs) was trained using data from 36 patients. The model was blindly tested on 10 additional patients. Results: Our ML model showed accuracies of 100.0% and 80.0% for predicting the true class of LVEDP on blind test data (i.e., elevated or normal, respectively) (Fig1). The accuracy on all data was higher than 93.4% for all classes. Conclusions: We demonstrated the proof-of-concept that a physics-based ML model can instantaneously classify the LV filling pressure using information extracted from femoral waveform and ECG. Our study is invasive validation; however, all required ML input parameters can be obtained noninvasively and remotely (i.e., using wearable devices or a smartphone).

A note on Clifford bundles and certain Finsler type spaces

We study a relation between certain extensions of the Clifford bundle and Finsler type structures that naturally generalize the standard Clifford relation between (pseudo)-Riemannian metric structures and Dirac matrices. We show for flat metrics that there is a triangle map between Finsler structures constructed from a (pseudo)-Riemannian metric and [Formula: see text]-forms on [Formula: see text], the extension of the Clifford bundle and relevant Dirac type operators.

A slow triangle map with a segment of indifferent fixed points and a complete tree of rational pairs

We study the two-dimensional continued fraction algorithm introduced in Garrity (J Number Theory 88(1):86–103, 2001) and the associated triangle map T, defined on a triangle \(\triangle \subseteq \mathbb {R}^2\). We introduce a slow version of the triangle map, the map S, which is ergodic with respect to the Lebesgue measure and preserves an infinite Lebesgue-absolutely continuous invariant measure. We discuss the properties that the two maps T and S share with the classical Gauss and Farey maps on the interval, including an analogue of the weak law of large numbers and of Khinchin’s weak law for the digits of the triangle sequence, the expansion associated to T. Finally, we confirm the role of the map S as a two-dimensional version of the Farey map by introducing a complete tree of rational pairs, constructed using the inverse branches of S, in the same way as the Farey tree is generated by the Farey map, and then, equivalently, generated by a generalised mediant operation.

Abstract 16334: An Artificial Intelligence Derived Method for Instantaneous Detection of Elevated Left Ventricular End Diastolic Pressure

Introduction: Instantaneous, non-invasive detection of an elevated left ventricular end-diastolic pressure (LVEDP) offers a significant benefit in diagnosis and treatment of heart failure. We recently proposed a systems approach, called cardiac triangle mapping (CTM), that uses intrinsic frequencies (IFs) of the arterial waveform and pre-ejection period (PEP) to map the global ventricular function (Pahlevan et al. Fluids 4.1 (2019): 16). Here, we tested the hypothesis that an elevated LVEDP can be detected using ECG and arterial pressure waveform by applying an artificial neural network (ANN) combined with CTM approach. Methods: This study included 46 patients (12 females, age 39-90 (66.4±9.9), BMI 20.2-36.8 (27.6±4.1)) who were scheduled for a clinical left heart catheterization or coronary angiogram at the Keck Medical Center of USC. Exclusion criteria were valvular heart disease, atrial fibrillation, or left bundle branch block. Invasive LVEDP and aortic pressure waveforms were measured using a 3F Millar transducer tipped catheter with simultaneous 3 channel ECG. The IFs were computed from pressure waveforms. PEPs were calculated as the time difference between the beginning of QRS and the uprising of the pressure waveform. A 3-layer network consisted of 6 input, 6 hidden and one output nodes was developed. LVEDP=18 mmHg was used as the cut-off for a binary outcome. Data from 34 patients were used to design the ANN (27 for training, 7 for validation). The model was tested on 12 additional patients. Results: Our results showed a specificity of 87% and a sensitivity of 96% in detecting an elevated LVEDP (Fig.1). Conclusions: Here, we demonstrated the proof-of-concept that an AI model based on reduced-order parameters (extracted from arterial waveform and ECG) can instantaneously detect an elevated LVEDP. Although our hemodynamic measurements were done invasively, all variables that are required for this AI-LVEDP calculation can be collected noninvasively.

Dual Adaptive Adjustment for Customized Garment Pattern

We present a dual adaptive garment slice adjustment technique for automatic resizing of apparel products with variant body shapes, and this technique can quickly generate clothed characters. Our first contribution is to propose a novel fit evaluation method. When a 2D garment pattern and a 3D draped garment have the same triangle topology connection, we calculate the shape variable of each triangle and output heat map simultaneously. For sewing a pattern to a newly targeted human body, we propose a fully automatic adjustment method that conforms to the body structure and is composed of two stages. In the coarse auto adjustment (CAA) stage, we propose a method of controlling the size of a garment by the length of a bounding box in five parts of the human body. Then, the garment pattern is automatically adjusted using the measured dimension, by stretching or shrinking. In the fine auto adjustment (FAA) stage, boundary vertices control the shape in the adjustment process. For better matching with the body, the vertices of the garment pattern boundary are relocated with the calculated moving distance and moving direction. As demonstrated in the results, our method enables fully automatic adjustment, preserving the original pattern style of garments between characters with vastly body shapes. Compared with the state-of-art 2D editing method, our proposed approach leads to time saving, and it achieves realistic garment effect compared to auto fitting methods.

Cardiac Triangle Mapping: A New Systems Approach for Noninvasive Evaluation of Left Ventricular End Diastolic Pressure

Noninvasive and practical assessment of hemodynamics is a critical unmet need in the treatment of both chronic and acute cardiovascular diseases. Particularly, the ability to monitor left ventricular end-diastolic pressure (LVEDP) noninvasively offers enormous benefit for managing patients with chronic congestive heart failure. Recently, we provided proof of concept that a new cardiac metric, intrinsic frequency (IF), derived from mathematical analysis of non-invasively captured arterial waveforms, can be used to accurately compute cardiovascular hemodynamic measures, such as left ventricle ejection fraction (LVEF), by using a smartphone. In this manuscript, we propose a new systems-based method called cardiac triangle mapping (CTM) for hemodynamics evaluation of the left ventricle. This method is based on intrinsic frequency (IF) and systolic time interval (STI) methods that allows computation of LVEDP from noninvasive measurements. Since the CTM method only requires arterial waveform and electrocardiogram (ECG), it can eventually be adopted as a simple smartphone-based device, an inexpensive hand-held device, or perhaps (with future design modifications) a wearable sensor. Such devices, combined with this method, would allow for remote monitoring of heart failure patients.

Detection of Emotions Induced by Colors in Compare of Two Nonlinear Mapping of Heart Rate Variability Signal: Triangle and Parabolic Phase Space (TPSM, PPSM)

Emotions in the word mean understanding, sensing and recognizing something with one’s senses. Emotions are relatively simple responses that the body presents to external or internal stimuli. As the individual’s mental and emotional state changes, the activity of the various parts of the body also changes and increases. This applies to all cultures. So emotion detection from biological signals especially heart rate variability (HRV) signal is considered in this article. The behavior of HRV in two nonlinear phase space have been evaluated and the extracted features of these two mapping have been used for emotion detection. Triangle and Parabolic Phase Space Mapping (TPSM and PPSM) are recently introduced methods which are able to indicate hidden aspects of HRV in response to different emotions. The Lead II of electrocardiogram signal was recorded from 32 female students while they were stimulated by four main psychology colors (blue, green, red, and yellow) to induce emotions which were labeled by SAM test. The results show that the mentioned colors caused emotions pleasure, joy, anger, and sadness, respectively. After rating the results by Kruskal–Wallis test, k-nearest neighbor classifier was used for emotion classification. The obtained accuracy after 10-fold cross validation was 90.91%. The hypotheses of being a relationship between colors and emotions without awareness of subjects have been proved. Furthermore, by studying the usefulness of TPSM and PPSM as new mapping of HRV, significant results have obtained which indicate the advantages of using them. So it is suggested to use and analyze the usage of these kinds of colors in different psychological situations and for biofeedback tests.

A Generalized Ease Of Separation Index for Selection of Optimal Configuration of Ternary Distillation

The ease of separation index (ESI) that is defined by the ratio of the relative volatility between the light and middle components to that between the middle and heavy components has been adopted in the literature for the selection of optimum distillation configuration for ternary separation. The present work showed that the separation requirements (the products’ purity) have a significant impact on the economic performance of distillation systems. Then we proposed a new index, generalized ease of separation index (GESI), to include the separation requirement into consideration for the selection of the optimum ternary distillation configuration. Simple column sequences with or without heat-integration, side-rectifier, side-stripper column, and dividing wall column (DWC) were evaluated as the candidates. Triangle map of ternary mixture composition was used to show the dependence of the optimal selection on feed compositions. We showed by numerical simulation that, for a given ESI, a profound change of the partition on the triangle map occurred with the change in GESI, and on the other hand, for a given GESI, slight changes of the partition on the map could be found with the change in ESI, showing stronger dependence of the economical behaviours of the ternary distillation configurations on the proposed GESI than on the ESI. Then, the dependence of the map partition on the GESI was investigated, and we found that with the increase in GESI, the area in triangle map where DWC was the optimal configuration shrunk, while the area of direct sequence with backward heat integration (DB) expanded. We concluded that the use of the newly defined index GESI can be conductive to the optimal selection of non-azeotropic ternary distillation configuration.

A cautionary note on elasticity analyses in a ternary plot using randomly generated population matrices

AbstractMatrix population models are one of the most common mathematical models in ecology, which describe the dynamics of stage‐structured populations and provide us many population statistics. One of the statistics, elasticity onto population growth rate, is frequently used and represents the degree of the relative impact of life history parameters to the population growth rate. Due to the utility of elasticities for cross‐taxonomic comparisons, Silvertown and his coauthors have published multiple papers and reported the relationship between elasticities and life forms (or life history) in multiple plant species, using a triangle map (called “ternary plot”). To understand why their elasticities are located in specific regions of the ternary plot, we constructed four archetypes of population matrices, from which we simulated 24,000 randomly generated population matrices and obtained the consequent elasticities. We found a large discrepancy when comparing our results to those in Silvertown et al.'s study (Conserv Biol 10:591–597, 1996): for our simulated matrices where rapid transitions were not allowed (e.g., trees), the elasticity distribution resulted in a line across the ternary plot. We provided the mathematical proof for this result, and found that its slope depends on matrix dimension. We also used 1230 matrices from the COMPADRE Plant Matrix Database and calculated the elasticities. Our simulated results were validated with field data from COMPADRE: two straight lines appeared in the ternary plot. Furthermore, we answered several addressed questions, such as, “Is there any special elasticity distribution in matrices with high population growth rates?” and “Why are the elasticities of natural populations concentrated in the upper half of the ternary plot?”.