Improved upper bound on superbridge index from 5b-3 to 3b-1.
problem Improving bounds on superbridge index for knots.
method Improved upper bound formula for superbridge index.
result Upper bound on superbridge index reduced from 5b-3 to 3b-1.
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48 results for “superbridge indices”
New superbridge index calculations for knots with odd edges.
problem Computing superbridge index of knots.
method Polygonal realizations with odd edges and linear programming.
result Exact superbridge index of many new knots, including 9- and 12-crossing knots.
An upper bound of the superbridge index of the connected sum of two knots is given in terms of the braid index of the summands. Using this upper bound and minimal polygonal presentations, we give an upper bound in terms of the superbridge index and the bridge index of the summands when they are torus knots. In contrast…
The paper finds petal numbers of torus knots using superbridge indices.
problem Determining petal numbers of torus knots.
method Using superbridge indices, the paper establishes relations between superbridge indices and petal numbers of torus knots.
result The petal number of is found to be when and . The upper bound is $2s - 2\Big\lfloor \frac{s}{r} \Big
floor +1$.
New upper bounds on superbridge index for 49 knots, increasing known results to 49.
problem Determining superbridge index for knots not covered by stick number.
method New upper bounds not derived from stick number.
result Superbridge index of 4 for 49 knots, increasing known results to 49.
Although there are infinitely many knots with superbridge index n for every even integer n>2, there are only finitely many knots with superbridge index 3.
The study proves all prime knots up to 10 crossings have superbridge index ≤ 5.
problem Determining the maximum superbridge index for prime knots up to 10 crossings.
method New upper bounds on stick numbers and equilateral stick numbers for specific knots, leading to conclusions about superbridge index.
result All prime knots through 10 crossings have a superbridge index ≤ 5.
The spiral index of knotsmath.GT
Two new invariants that are closely related to Milnor's curvature-torsion invariant are introduced. The first, the spiral index of a knot, captures the minimum number of maxima among all knot projections that are free of inflection points. This invariant is closely related to both the bridge and braid index of the knot…
The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of s…
Composite development indicators used in policy making often subjectively aggregate a restricted set of indicators. We show, using dimensionality reduction techniques, including Principal Component Analysis (PCA) and for the first time information filtering and hierarchical clustering, that these composite indicators m…
Optimal text-based indices track VIX and inflation.
problem Maximizing contemporaneous relation or predictive performance with target variables.
method Optimizing text-based indices focusing on VIX and inflation expectations.
result Superior performance compared to existing indices.
Indices of vector fields and 1-forms studied for singular varieties and actions.
problem Understanding indices of vector fields and 1-forms in various contexts.
method Generalization to singular varieties and actions of finite groups.
result New insights into indices of vector fields and 1-forms.
We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest ei…
This study examined how the correlation and network structure of 30 global indices and 145 local Korean indices belonging to the KOSPI 200 have changed during the 13-year period, 2000-2012. The correlations among the indices were calculated. The results showed that although the average correlations of the global indice…
Financial market created for wellbeing indices to mitigate socioeconomic risks.
problem Risk mitigation in financial indices of socioeconomic wellbeing.
method Developed new quantitative measure, created financial market, and implemented insurance instruments.
result Optimal portfolio weights and efficient frontiers for wellbeing indices.
We study the dynamic interactions and structural changes in global financial indices in the years 1998-2012. We apply a principal component analysis (PCA) to cross-correlation coefficients of the stock indices. We calculate the correlations between principal components (PCs) and each asset, known as PC coefficients. A …
To lag or not to lag? How to compare indices of stock markets that operate at different timesq-fin.GN
Financial markets worldwide do not have the same working hours. As a consequence, the study of correlation or causality between financial market indices becomes dependent on wether we should consider in computations of correlation matrices all indices in the same day or lagged indices. The answer this article proposes …
The paper shows how reducible complexes affect local indicability.
problem The local indicability of subcomplexes in reducible complexes.
method Characterization of diagrammatic reducibility and application to local indicability.
result Injective labeled oriented trees are locally indicable if reducible of degree 2.
New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.
problem Estimating first-and total-orders Sobol' indices accurately.
method Comparing two Monte Carlo estimators for Sobol' indices.
result New method outperforms current approach in accuracy.
Invariants for virtual and twisted links using affine indices.
problem Computing invariants for virtual and twisted links.
method Using affine indices to define invariants for virtual and twisted links.
result Invariants for virtual and twisted links computed using affine indices.
Investigates local indicability of groups with circle homology presentations.
problem Conditions for local indicability in groups with circle homology presentations.
method Generalizes results for two-relator presentations to circle homology presentations.
result Extends results on local indicability to LOT groups and non-cycle-free Adian presentations.
We apply RMT, Network and MF-DFA methods to investigate correlation, network and multifractal properties of 20 global financial indices. We compare results before and during the financial crisis of 2008 respectively. We find that the network method gives more useful information about the formation of clusters as compar…
Novel approach detects early warning indicators in complex systems.
problem Detecting abrupt transitions in complex systems.
method Directed anisotropic diffusion map and latent stochastic dynamical systems.
result Early warning indicators can detect tipping points in state transitions.
A non-parametric method for ranking stock indices according to their mutual causal influences is presented. Under the assumption that indices reflect the underlying economy of a country, such a ranking indicates which countries exert the most economic influence in an examined subset of the global economy. The proposed …
In unsupervised machine learning, agreement between partitions is commonly assessed with so-called external validity indices. Researchers tend to use and report indices that quantify agreement between two partitions for all clusters simultaneously. Commonly used examples are the Rand index and the adjusted Rand index. …
New algorithm forecasts health indicators for better equipment lifespan prediction.
problem Improving equipment lifespan prediction through health indicator forecasting.
method Generative + scenario matching approach using Gaussian Process.
result Superior performance compared to existing methods.
New indices for determining cluster compactness and separability.
problem Challenges in identifying true clusters in data sets.
method Developed absolute cluster indices to measure compactness and separability.
result Demonstrated improved performance compared to existing indices.
Study fragility in global financial indices using network analysis.
problem Monitor fragility in global financial indices.
method Network-based approach to analyze daily closing prices of global financial indices.
result Network-centric measures reveal fragility in global financial indices.
Secondary analytic indicesmath.DG
We define analytic indices which involve the eta form and the analytic torsion form. We show that these indices are independent of the geometric choices made in their definitions, and hence are topological in nature.
Study shows HFT improves market liquidity indicators.
problem Impact of high-frequency trading on market liquidity.
method Agent-based simulations comparing HFT and non-HFT markets.
result All liquidity indicators improved in markets with HFTs.
This research simplifies computation of feature attribution methods under certain conditions.
problem Computational complexity of feature attribution methods, especially power indices.
method Identifying conditions for polynomial computation and introducing new indices.
result Conditions for efficient computation of feature attribution methods are identified.
The paper introduces a new financial market for environmental indices to attract investors.
problem Inherent risks and sustainability concerns in environmental investments.
method Quantitative measures, econometric analysis, dynamic asset pricing tools, and financial options.
result Monetization and construction of country-specific environmental indices as dollar-denominated assets.
This research finds three meta-indicators for university rankings.
problem Complexity in university ranking systems.
method Interpretable machine learning approach.
result Identified three meta-indicators: time, space, and relationships.
In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …
The study analyzes performance indices for class-imbalanced data and identifies conditions they must meet.
problem Distortions in performance indices under class imbalance.
method Identified two conditions for performance indices and analyzed four binary and five multi-class indices.
result Recommended appropriate indices for evaluating classifiers in class-imbalanced scenarios.
We propose a new indicator for technical analysis. The indicator emphasizes maximums and minimums in price series with inherent smoothing and has a potential to be useful in both mechanical trading rules and chart pattern analysis.
We give a formula to calculate the indices of special (non-totally geodesic) minimal orbits of Hermann actions. Also, we give examples of such minimal orbits of Hermann actions and calculate their indices by using the formula.
New parities defined on virtual knots linked to crossing indices.
problem Defining parities on virtual knots.
method Connecting parities to invariant cycles on arcs and quasi-indices on crossings.
result New series of parities on virtual knots defined.
Improved MACD trading strategies with other indicators for better performance.
problem Evaluating the effectiveness of MACD-based trading strategies in the US stock market.
method Backtested various MACD-based trading strategies on US stock indices using Python.
result Win-rate of MACD strategies improved with other momentum indicators, leading to a new VPVMA indicator.
Generalizes Collins' theorem to products of locally indicable groups.
problem Intersection of conjugates of Magnus subgroups in one-relator groups.
method Generalization to one-relator products of locally indicable groups.
result Result holds for a broader class of groups.
Study finds traditional technical indicators underperform in high-frequency trading, suggesting risk management over prediction.
problem Inadequately explored effectiveness of technical indicators in high-frequency trading, particularly at minute-level frequency.
method Evaluation of random forest models with traditional technical indicators on minute-level SPY data.
result In-sample performance is superior to out-of-sample, with risk-adjusted metrics not outperforming a simple buy-and-hold strategy.
Dynamic Assessment Indicesmath.PR
This paper provides a unified framework, which allows, in particular, to study the structure of dynamic monetary risk measures and dynamic acceptability indices. The main mathematical tool, which we use here, and which allows us to significantly generalize existing results is the theory of -modules. In the first p…
Gittins indices provide an optimal solution to the classical multi-armed bandit problem. An obstacle to their use has been the common perception that their computation is very difficult. This paper demonstrates an accessible general methodology for the calculating Gittins indices for the multi-armed bandit with a detai…
Study shows diverse data sources improve cryptocurrency forecasting models.
problem Improving cryptocurrency market forecasting accuracy.
method Integrating various data types, including on-chain metrics, traditional indices, and macroeconomic indicators.
result Data source diversity significantly enhances forecasting model performance.
Invariant detects sliceness of virtual knots with specific chord indices.
problem Detecting sliceness in virtual knots with chord indices.
method Constructs an invariant using sliceness obstruction and sensitivity to Δ-move.
result Invariant detects sliceness and is sensitive to chord indices.
Study uses Hawkes processes to analyze stock market contagion in China.
problem Understanding contagion in Chinese stock market.
method Fitting Hawkes processes to daily returns and sector indices.
result Identifies long-term dependencies and trending patterns in sector indices.
The purpose of this research is to apply technical analysis of Sutte Indicator in stock trading which will assist in the investment decision making process i.e. buying or selling shares. This research takes data of "A" on the Indonesia Stock Exchange(IDX or BEI) 29 November 2006 until 20 September 2016 period. To see t…
This paper reviews and proposes a new approach for evaluating internal cluster validation indices.
problem Selecting the best-performing unsupervised classification algorithm without external information.
method Examines and proposes a new evaluation approach for internal validation indices.
result Suggests a new evaluation approach for internal validation indices.