Partial Decompositions Research Articles

The Common Basis Complex and the Partial Decomposition Poset

Abstract For a finite-dimensional vector space $V$, the common basis complex of $V$ is the simplicial complex whose vertices are the proper non-zero subspaces of $V$, and $\sigma $ is a simplex if and only if there exists a basis $B$ of $V$ that contains a basis of $S$ for all $S\in \sigma $. This complex was introduced by Rognes in 1992 in connection with stable buildings. In this article, we prove that the common basis complex is homotopy equivalent to the proper part of the poset of partial direct sum decompositions of $V$. Moreover, we establish this result in a more general combinatorial context, including the case of free groups, matroids, vector spaces with non-degenerate sesquilinear forms, and free modules over commutative Hermite rings, such as local rings or Dedekind domains.

Non-Negative Decomposition of Multivariate Information: From Minimum to Blackwell-Specific Information.

Partial information decompositions (PIDs) aim to categorize how a set of source variables provides information about a target variable redundantly, uniquely, or synergetically. The original proposal for such an analysis used a lattice-based approach and gained significant attention. However, finding a suitable underlying decomposition measure is still an open research question at an arbitrary number of discrete random variables. This work proposes a solution with a non-negative PID that satisfies an inclusion-exclusion relation for any f-information measure. The decomposition is constructed from a pointwise perspective of the target variable to take advantage of the equivalence between the Blackwell and zonogon order in this setting. Zonogons are the Neyman-Pearson region for an indicator variable of each target state, and f-information is the expected value of quantifying its boundary. We prove that the proposed decomposition satisfies the desired axioms and guarantees non-negative partial information results. Moreover, we demonstrate how the obtained decomposition can be transformed between different decomposition lattices and that it directly provides a non-negative decomposition of Rényi-information at a transformed inclusion-exclusion relation. Finally, we highlight that the decomposition behaves differently depending on the information measure used and how it can be used for tracing partial information flows through Markov chains.

Exploring the asymmetric effect of remittance inflows on gold import demand: Evidence from a large gold-consuming and remittance-receiving country

The focus of this research is to look at how remittance inflows affect gold imports in India for the period from 1980 to 2020. The study uses both the linear (symmetric) autoregressive distributed lag (ARDL) model of Pesaran et al. (2001) and the non-linear (asymmetric) autoregressive distributed lag (NARDL) model of Shin et al. (2014) to assess the symmetric and asymmetric impact of remittance inflows on gold imports. The key advantage of the NARDL model relies on its ability to simultaneously capture the short run and long run asymmetries through the positive and negative partial sum decompositions of changes in the independent variable(s). The results of linear ARDL model reveal that remittance inflows positively and significantly affect the gold imports in the long run, although negatively and significantly in the short run. The findings of NARDL model, on the other hand, show that there is significant asymmetric impact of remittance inflows upon the gold imports over the study period. The results confirm that whereas an increase in remittance inflows leads to a considerable increase in gold imports, a reduction in remittance inflows has no substantial impact in the long run. Another notable outcome is that, while a decline in gold prices boosts gold imports in the short run, both an increase and a decrease in gold prices enhance gold imports in the long run. Concerning the results of our study, it is suggested that more efficient channelization of remittance revenues and adoption of non-price measures may be deemed effective to curb the gold imports, which can contribute to reduce unfavourable trade balance.

Trigonometric Sums and Riemann Zeta Function

ABSTRACTSeveral trigonometric sums are examined by means of partial fraction decompositions. Their generating functions will be evaluated in closed forms and the related asymptotic formulae in terms of Riemann zeta function will be established.

The Symmetric and Asymmetric Effect of Remittances on Financial Development: Evidence from South Africa

Investigating the remittance-financial development relationship is an ongoing endeavor among economists and policy makers. Building and improving on the existing work, this study considers the possibility that the relation between remittances and financial development is potentially asymmetric. This study applies the linear ARDL and captures the possibility of an asymmetrical relationship by applying the non-linear Autoregressive Model (NARDL). Using NARDL, an attempt is made to estimate the short-run and long-run asymmetric responses of financial development through positive and negative partial sum decompositions of changes in remittances. To assess the robustness of the ARDL and NARDL estimates, a battery of long-run robustness tests were employed, including the linear and nonlinear versions of the fully modified ordinary least squares (FMOLS). Annual data series from 1980 to 2017, derived from the World Development Indicators, Fred Economic data and Penn World Tables were used for this study. The ARDL results reveal a positive and significant impact of remittances on financial development, whereas NARDL estimations suggest a both positive and negative shock of remittances on financial development in the long run: a percentage (%) increase in the remittances brings about 0.121568 percent increase in financial development, whereas a one-percent decrease in remittances produces a 0.33363 percent decrease in financial development.

Combined ab initio and experimental screening of phase stabilities in the Ce-Fe-Ti- X system ( X=3d and 4d metals)

One of the main challenges for the synthesis and application of the promising hard-magnetic compound $\mathrm{Ce}{\mathrm{Fe}}_{11}\mathrm{Ti}$ is the formation of Laves phases that are detrimental for their thermodynamic stability and magnetic properties. In this paper, we present an ab initio based approach to modify the stability of these phases in the Ce-Fe-Ti system by additions of $3d$ and $4d$ elements. We combine highly accurate free-energy calculations with an efficient screening technique to determine the critical annealing temperature for the formation of $\mathrm{Ce(Fe,X)}{}_{11}\mathrm{Ti}$. The central findings are the dominant role of the formation enthalpy at $T=0$ K on chemical trends and the major relevance of partial chemical decompositions. Based on these insights, promising transition metals to promote the stability of the hard-magnetic phase, such as Zn and Tc, were predicted. The comparison with suction casting and reactive crucible melting experiments for Ce-Fe-Ti-X (X = Cu, Ga, Co, and Cr) highlights the relevance of additional phases and quaternary elements.

The asymmetric effect of COVID-19 on investor sentiment: evidence from NARDL model

PurposeThis study aims to investigate the asymmetric impact of daily announcements regarding COVID-19 on investor sentiment in the stock market.Design/methodology/approachThis study uses a Non-Linear Autoregressive Distribution Lag (NARDL) model that relies on positive and negative partial sum decompositions of the Coronavirus indicators. Five investor sentiments had been used and the analysis is conducted on the full sample period from 24th February 2020 to 25th March 2021.FindingsThe results show that new cases have a greater impact on investor sentiment compared to daily announcements of new deaths related to COVID-19. In addition to revealing a significant impact of new COVID-19 new cases and new death announcements on a daily basis on investor sentiment over the short- and long-term, this paper also highlights the nonlinearity and asymmetry of this relationship in the short and long run. Investors' sentiments are more affected by negative news regarding Covid 19 than positive news.Originality/valueFinancial markets have been severely affected by COVID-19 pandemic. This study is the first to measure the extent of reaction of investors to positive and negative announcements of COVID-19. Interestingly, this study examines the asymmetric effect of daily announcements on new cases and new deaths by COVID-19 on investor sentiments and derive many implications for portfolio managers.

On the asymmetric effects of trade openness on CO2 emissions in SADC with a nonlinear ARDL approach

In this study, the expected asymmetric relationship between trade openness and CO2 emissions is investigated for the Southern African Development Community (SADC). We make use of a nonlinear autoregressive distributed lag (NARDL) framework proposed to capture the short- and long-run asymmetries for increases and decreases in trade openness and its impact on CO2 emissions over the period 1960–2020. We proxy trade openness using an innovative approach that considers both a country’s trade share to GDP and its size of trade relative to world trade. Both short- and long-run nonlinearity are tested by deriving the positive and negative partial sum decompositions of the trade openness variable. The results show mixed evidence of asymmetric behaviour between trade openness and CO2 emissions. Long-run asymmetry is found for Botswana, Madagascar, Mozambique and Tanzania, while in Comoros, Namibia and South Africa, there is evidence of both short- and long-run asymmetry. The remaining cases (Angola, Democratic Republic of Congo (DRC), Lesotho, Malawi, Mauritius, Seychelles, Zambia and Zimbabwe) show ample evidence of symmetric behaviour and linear long-run relationships between trade openness and CO2 emissions. The policy implication is that the SADC member countries should amend and reinforce environmental policies that can promote production and trade of environmentally friendly goods. For instance, a “tax or subsidy” policy, which taxes the trading of environmentally damaging goods, while subsidizing the trading of eco-friendly goods, can be implemented.Graphical

SHORTER PROOF OF THE RIESZ INTERPOLATION FORMULA FOR TRIGONOMETRIC POLYNOMIALS

By means of partial fraction decompositions, a shorter proof is presented for the important interpolation formula of trigonometric polynomials discovered by Riesz (1914).

Signed and unsigned partial information decompositions of continuous network interactions

Abstract We investigate the partial information decomposition (PID) framework as a tool for edge nomination. We consider both the $I_{\cap}^{\text{min}}$ and $I_{\cap}^{\text{PM}}$ PIDs, from Williams & Beer (2010, Nonnegative decomposition of multivariate information, CoRR, arXiv:2106.12393) and Finn & Lizier (2018, Entropy, 20, 297), respectively, and we both numerically and analytically investigate the utility of these frameworks for discovering significant edge interactions. In the course of our work, we extend both the $I_{\cap}^{\text{min}}$ and $I_{\cap}^{\text{PM}}$ PIDs to a general class of continuous trivariate systems. Moreover, we examine how each PID apportions information into redundant, synergistic and unique information atoms within the source-bivariate PID framework. Both our simulation experiments and analytic inquiry indicate that the atoms of the $I_{\cap}^{\text{PM}}$ PID have a non-specific sensitivity to high predictor-target mutual information, regardless of whether or not the predictors are truly interacting. By contrast, the $I_{\cap}^{\text{min}}$ PID is quite specific, although simulations suggest that it lacks sensitivity.

Partial wave analysis for the in-hadron condensate

In-hadron condensates, defined as the scalar form factors at zero-momentum transfer, are investigated for flavor-symmetric mesons in pseudoscalar and vector channels under the rainbow-ladder (RL) truncation within the Dyson-Schwinger equations framework. We confirm the efficiency of the in-hadron condensates in describing the effects of dynamical chiral symmetry breaking from both global and structural perspectives by comparing the meson masses, the dimensionless in-hadron condensates, and the partial wave decompositions of in-hadron condensates as functions of current-quark mass. From partial wave analysis, $\ensuremath{\pi}(1300)$ is inferred as a radial excitation dominated by $s$ waves, while $\ensuremath{\rho}(1450)$ needs further studies beyond the RL truncation. This work provides a new insight into the studies of hadron properties with partial wave analysis for the in-hadron condensates.

A Comparison of Partial Information Decompositions Using Data from Real and Simulated Layer 5b Pyramidal Cells.

Partial information decomposition allows the joint mutual information between an output and a set of inputs to be divided into components that are synergistic or shared or unique to each input. We consider five different decompositions and compare their results using data from layer 5b pyramidal cells in two different studies. The first study was on the amplification of somatic action potential output by apical dendritic input and its regulation by dendritic inhibition. We find that two of the decompositions produce much larger estimates of synergy and shared information than the others, as well as large levels of unique misinformation. When within-neuron differences in the components are examined, the five methods produce more similar results for all but the shared information component, for which two methods produce a different statistical conclusion from the others. There are some differences in the expression of unique information asymmetry among the methods. It is significantly larger, on average, under dendritic inhibition. Three of the methods support a previous conclusion that apical amplification is reduced by dendritic inhibition. The second study used a detailed compartmental model to produce action potentials for many combinations of the numbers of basal and apical synaptic inputs. Decompositions of the entire data set produce similar differences to those in the first study. Two analyses of decompositions are conducted on subsets of the data. In the first, the decompositions reveal a bifurcation in unique information asymmetry. For three of the methods, this suggests that apical drive switches to basal drive as the strength of the basal input increases, while the other two show changing mixtures of information and misinformation. Decompositions produced using the second set of subsets show that all five decompositions provide support for properties of cooperative context-sensitivity—to varying extents.

Evidence from the nonlinear autoregressive distributed lag model on the asymmetric influence of the first wave of the COVID-19 pandemic on energy markets

The COVID-19 pandemic remained a global risk factor and integrated into various means in the functioning of companies, economies and financial markets. Therefore, this paper investigates how COVID-19 influences the energy market in the main financial markets (China, France, Germany, Italy, Spain and the United States), using time series from February 28, 2020, to November 3, 2020. The goal of this research is to investigate the asymmetric impact of COVID-19 from leading financial markets on energy commodities. In this regard, the non-linear auto-regressive distributed lag (NARDL) framework is employed to capture the long-run asymmetric reactions. The econometric design allows to explore the long-term asymmetric reactions of dependent variables through positive and negative partial sum decompositions of changes in the explanatory variables. The quantitative results show a significant long-run asymmetric interdependence between the number of new SARS-CoV-2 incidence and mortality and the daily percent change in close price of future contracts pertaining to Brent oil, crude oil WTI, carbon emissions, gasoline RBOB, heating oil, Chukyo kerosene, and natural gas. Furthermore, no asymmetry is found in the case of ethanol and fuel oil futures. The novelty of this article is the study of the impact of COVID-19 on the energy sector during the first two waves of COVID-19 by applying the NARDL model that allows to capture long-term asymmetric reactions. Certainly, further research on this topic is necessary due to the permanent shifts in the pandemic, as well as the availability of longer data periods on COVID-19.

Nexus between Governance Indicators & Sustainable Stock Market Development in Pakistan: Evidences from Symmetric and Asymmetric Analysis

The hidden non-linear association between governance indicators & stock market development (SMD) of Pakistan has been scrutinized in this study by using two comparative co-integrating techniques known as ARDL (Auto-regressive Distributed Lag) & NARDL (Non-linear ARDL). Empirical evidence suggests that misrepresented inferences arise by ignoring hidden non-linearity nexus between the variables. The ARDL results indicate that political stability & absence of violence/terrorism does not impact directly the SMD of Pakistan. Voice & accountability positively and significantly impact SMD, but rule of law does not impact SMD of Pakistan directly. The regulatory quality is highly significant and negatively impacts SMD. Contrarily, the NARDL frame indicates significant differences amid coefficients of components of governance index, denoting asymmetric links between variables. The Positive & Negative sums of partial decompositions of Rule of Law, Regulatory Quality, Political Stability & Absence of Violence/Terrorism (PS&AVT), and Voice & Accountability (V&A) significantly impact SMD. The impact of partial Negative multipliers of Regulatory Quality, and PS&AVT has a highly significant and negative impact, while V&A has a significant and positive impact on SMD. The impact of Positive partial multipliers of all variables is positive and significant except V&A. The comparative diagnostics extricate precariousness in policy moratorium. This study will add credence to the predictive power of governance indicators towards SMD of Pakistan by incorporating Positive and Negative decomposed multipliers.

Insurance and geopolitical risk: Fresh empirical evidence

Researchers continue to debate on how geopolitical events affect financial development. We contribute to this debate by questioning the possibility of asymmetric linkages between the geopolitical risk index and insurance premium for 14 countries over the annual period of 2000−2019. Using the most up-to-date non-linear autoregressive distributed lag framework, we simultaneously examine short- and long-run asymmetric responses of insurance premiums through positive and negative partial sum decompositions of changes in the geopolitical risk index. Our findings point out that the geopolitical risk affects insurance premiums in an asymmetric and nonlinear manner, except for India, but the transmission mechanism is not the same. In addition, for most emerging countries, we show that the impact is considerably greater in the long- run than in the short-run. Finally, the results support the demand following hypothesis for some of the countries included in our sample. The study recommends the insurers and policymakers to consider the asymmetric dynamics of insurance premium to minimize risk related to long – run negative global and domestic geopolitical uncertainty.

MultivariateApart: Generalized partial fractions

We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied to terms of a sum separately. The package is designed to work in Mathematica, but also provides interfaces to the Form and Singular computer algebra systems. Program summaryProgram title:MultivariateApartCPC Library link to program files:https://doi.org/10.17632/zbt9tfpkgv.1Developer's repository link:https://gitlab.msu.edu/vmante/multivariateapartLicensing provisions: GPLv3Programming language: Mathematica (Wolfram Language)Nature of problem: Partial fraction decomposition is widely used in particle physics to bring rational functions into a unique form. Treating the multivariate case by applying the univariate method iteratively risks the introduction of spurious singularities. Here, we formulate an algorithm that handles non-linear multivariate denominators, avoids the introduction of spurious denominators, and aims at providing good performance for typical applications in particle physics. It can be used to obtain unique results also when decomposing individual terms of a sum separately, independent of the details of the input form. A variant of the approach allows to reach a Leĭnartas' decomposition as the output form.Solution method: We reformulate the problem of calculating a partial fraction decomposition into the problem of reducing a polynomial with respect to a specific ideal. The polynomial reduction is based on a Gröbner basis calculation and guarantees a unique result for the partial fraction decomposition. We provide a complete implementation as a Mathematica package. Optionally, the included interfaces to Form and Singular can be used to speed up the computation.Additional comments including restrictions and unusual features: Our algorithm does not introduce new singularities that were not presented in the input. If, however, the input contains spurious singularities, our package can be used in such a way that the cancellation of these singularities is not guaranteed. By default, the main MultivariateApart function of our package avoids this problem by first putting terms in a sum over a common denominator, and canceling factors in the result.

Exploring the asymmetric effect of oil price on exchange rate: Evidence from the top six African net oil importers

The paper investigates the oil price fluctuation on exchange rates for main African net oil importing countries, namely South Africa, Morocco, Côte d’Ivoire, Kenya, Ghana and Senegal that cover for the period from 1983Q2 to 2018Q4. In order to thoroughly examine the subject matter, this study takes a specific account of the symmetric and asymmetric effects of oil price changes in modelling process by utilizing innovative linear autoregressive distributed lag (ARDL) technique and asymmetric nonlinear autoregressive distributed lag (NARDL) technique, which accommodate the short-run and long-run asymmetries via positive (increase) and negative (decrease) partial sum decompositions of oil price shocks. The result suggests that the variables are cointegrated, signifying the evidence of long and short run relationships of each country. Evidence of long and short run asymmetries is also confirmed in Côte d’Ivoire, Ghana and Senegal, suggesting that rising and declining oil price have different effect on exchange rate, while symmetric effect is observed in South Africa and Morocco. Rising oil price has positive effect on exchange rate in South Africa and Senegal leading to depreciation of exchange rate, while falling oil price leads to exchange rate appreciation of South Africa rand, Ghanaian cedi and Senegal francs but exchange rate depreciation of Moroccan dirham and Cote d’Ivoire francs. The result further suggests that negative decrease in oil price has a larger impact on exchange rate than the positive increase that varies in sign and size across countries. This suggests that oil price changes play a significance role that influence the behaviour of exchange rate and hence leading to contribute to the development of national economic progress.

Meta partial benders decomposition for the logistics service network design problem

Supply chain transportation operations often account for a large proportion of product total cost to market. Such operations can be optimized by solving the Logistics Service Network Design Problem (LSNDP), wherein a logistics service provider seeks to cost-effectively source and fulfill customer demands of products within a multi-echelon distribution network. However, many industrial settings yield instances of the LSNDP that are too large to be solved in reasonable run-times by off-the-shelf optimization solvers. We introduce an exact Benders decomposition algorithm based on partial decompositions that strengthens the master problem with information derived from aggregated subproblem data. More specifically, the proposed Meta Partial Benders Decomposition intelligently switches from one master problem to another by changing both the amount of subproblem information to include in the master as well as how it is aggregated. Through an extensive computational study, we show that the approach outperforms existing benchmark methods and demonstrate the benefits of dynamically refining the master problem in the course of a partial Benders decomposition-based scheme.

An asymmetric examination of the environmental effect of tourism in China

This article employs the non-linear autoregressive distributed lag model in analysing the environmental impact of tourism in China from 2002Q1 to 2018Q4, while controlling for non-renewable energy consumption, trade openness, urbanisation, per capita GDP and its quadratic form. The approach permits the simultaneous testing of non-linearities in the short and long run. This is achieved through negative and positive partial sum decompositions of the regressor of interest. Findings from the article indicate the following: (i) long-run co-movements exist between tourism activities and environmental performance in China, (ii) tourism activities considerably damage the environment in China, (iii) the environment responds to tourism in an asymmetric manner, such that the damage caused by increasing tourism is smaller than the positive environmental effect of decline in tourism. Thus, less tourism protects the environment faster than more tourism damages it. A supplementary non-parametric test for non-linear causality was also performed. The result further provides strong evidence of a non-linear feedback causality between tourism activities and environmental performance in China in the first moment (mean) and second moment (variance). Tourism (environmental performance) is thus a significant predictor of China’s environmental performance (tourism).

A novel proof of two partial fraction decompositions

In this paper, by constructing contour integral and using Cauchy’s residue theorem, we provide a novel proof of Chu’s two partial fraction decompositions.