Marginal Problem Research Articles

Moments of Random Quantum Marginals via Weingarten Calculus

Abstract The randomized quantum marginal problem asks about the joint distribution of the partial traces (“marginals”) of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this problem based on studying the mixed moments of the entries of the marginals. For randomized quantum marginal problems that describe systems of distinguishable particles, bosons, or fermions, we prove formulae for these mixed moments, which determine the joint distribution of the marginals completely. Our main tool is Weingarten calculus, which provides a method for computing integrals of polynomial functions with respect to Haar measure on the unitary group. As an application, in the case of two distinguishable particles, we prove some results on the asymptotic behavior of the marginals as the dimension of one or both Hilbert spaces goes to infinity.

Projections of orbital measures and quantum marginal problems

This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn’s problem, the randomized Schur’s problem, and the orbital corners process. In this general setting, we prove integral formulae for the probability densities, establish some properties of the densities, and discuss connections to multiplicity problems in representation theory as well as to known results in the symplectic geometry literature. As applications, we show a number of results on marginal problems in quantum information theory and also prove an integral formula for restriction multiplicities.

Price timing and financing strategies for a capital-constrained supply chain with price-dependent stochastic demand

We investigate the pricing timing strategy in the context of trade credit (TC), under which the capital-constrained retailer applies for deferred payments from its supplier. Based on the wholesale price offered by the supplier, the retailer determines the order volume before observing the random demand and the selling price after observing it (a.k.a., price postponement). We formulate the Stackelberg game to show how their equilibrium decisions and profits are affected by: the pricing timing, financing mode, the demand structure. In a multiplicative demand framework, the analytical and numerical results indicate that TC alleviates double marginalization problem, depending on price timing and demand structure. With the traditional bank finance (BF) as a benchmark, the supplier is reluctant to provide TC to the retailer without postponement when the market is extremely sensitive to price. Postponement not only benefits both members, but also enhances retailer’s repayment ability and thus participants’ preference for TC. They can reach an agreement on utilizing price postponement and trade credit as long as the supplier choose a suboptimal wholesale decision for deferred payment that is slightly lower the optimal one. We further extend our results to consider the additive demand structure.

Methods of compiling "Problem Nodes" as a toolkit for analyzing and monitoring the condition of neighborhoods (micro-districts) of the outdated housing stock

Housing and communal services are one of the largest industries in the economic complex of Ukraine. At the same time, 61% of residential buildings in the country were built before 1970, that is, they are morally and physically outdated. This fact is a significant problem that threatens the stable functioning of our cities. It is for this reason that it is extremely important to develop methods of monitoring, strategic planning and anti-crisis management in architectural urbanism. In this article, as such a tool, the methods of compiling "Nodes of problems" are proposed, which are a component of a new paradigm - "Anti-crisis management in architectural urbanism", which is a component of such scientific and practical directions "Architectural urbanism" and "Urban management". "Node of problems" is a grapho-analytical method of outputting data obtained with the help of the "Software complex for modeling the city as a dynamic system", which is currently being developed at XNUUE named after O.M. Beketov.
 The new scientific direction "Anti-crisis management in architectural urbanism" is an actual response to the problem that has arisen in the field of complex reconstruction of quarters (microdistricts) of the outdated housing stock. Urban planning is the science of the city of extensive type of development. No urban planning regulations and rules indicate what to do with urban voids on the sites of abandoned factories, what to do with the problem of marginalization of "working quarters", how to implement road maps for optimizing the city's housing stock in conditions of almost complete disregard by the population of legislative requirements, and most importantly - how to achieve positive changes in the problem of housing reconstruction in conditions of limited access to resources.
 The essence of the method is to reflect the set of contradictions between the principles of functioning of the elements of the city system. The contradiction is the result of centrifugal and centripetal efforts arising in the processes of meeting the vital needs of the social component of the city. The city itself is considered as a collection of artifacts belonging to the social, man-made or natural subsystem. Dynamic processes of city functioning occur as a result of the interaction of these subsystems.

Computation of the phase and gain margins of MIMO control systems

This paper solves the problem of exact computation of the phase and gain margins of multivariable control systems. These stability margins are studied using the concept of the Davis–Wielandt shell of complex matrices. Calculation of the phase and gain margins requires solving a quadratically constrained quadratic program (QCQP) and a parametrized quadratically constrained problem, respectively, which are known to be difficult in general. The semidefinite relaxation (SDR) technique is often used as a computationally efficient approximation technique to solve QCQPs. It turns out that the QCQPs formulated from the phase and gain margin problems in this paper fall under the class of quadratic optimization problem, for which the SDR is exact. This is so in the sense that optimal values of the QCQP and its SDR are equal, and an optimal solution for the original QCQP problem can be obtained from an optimal solution of its SDR. Thus, we are able to propose computationally efficient algorithms to compute the phase and gain margins with an arbitrarily high precision. Numerical examples are given to illustrate the effectiveness of the proposed algorithms.

Derivation of geographical marginalization index of Bosnia and Herzegovina using GIS multicriteria decision analysis

Across Europe marginalization has been highlighted as an object of important political concern. In the area of Central Europe and the Balkans, the problem of marginalization has not been sufficiently researched. This particularly applies to the Bosnia and Herzegovina (BiH). Using the GIS multicriteria decision analysis a composite index of geographical marginalization (GMAR) was created. Marginalization is analyzed as a multidimensional concept using the 4 groups with a total of 40 criteria. Spatial patterns were detected from extremely marginalized to extremely non-marginalized regions. The GMAR indicates the existence of regional disparities in BiH. The high degree of marginalization, especially those in the border sector, alerts the implementation of the demarginalization measures.

An optimal freshness-keeping effort model for fresh produce with constraints of special funds

<p style='text-indent:20px;'>The quality deterioration in the post-production process of fresh products is very serious, and the life-cycle freshness-keeping technology investment is an effective way to reduce the deterioration. Because the investment cost is high in practice, enterprises need to allocate special funds for each stage to maximize their marginal revenue. In this paper, we use freshness to characterize the quality level of fresh products and investigate a maximize marginal revenue problem where a firm assigns special funds for the freshness-keeping effort with each post-production process. An optimal freshness-keeping model with the constraints of special funds is discussed. The investigation shows that both the optimal freshness-keeping effort and the closed-form optimal solutions of enterprises exist uniquely. A reasonable freshness-keeping investment in different post-production processes can improve the performance of enterprises with limited fund constraints. We then simulate the effect rules of funds constraint on these solutions based on numerical analysis and give some management insights.</p>

Obrazovanje i kultura u dnevnoj štampi - između afirmacije i marginalizacije

Starting from the attitude that education and culture play a key role in the progress of every society, this paper deals with the affirmation of these activities through media. Media play an important role in the creation of public awareness and can contribute to the development of public interest and support towards education and culture, but also to their marginalization. The subject of this paper is therefore the presence of education and culture in the front pages of the daily press in Serbia. The goal of the paper is to investigate how much education and culture are present in the discourse of Serbian print media, based on the recording and classification of front page news. The research was conducted from November the 1st 2021 till October the 31st 2022, on daily basis. The analysis covered 10 daily newspapers: Politika, Danas and Dnevnik as quality newspaper, Večernje novosti, Blic and Nova as semi-tabloids and Informer, Kurir, Srpski telegraf and Alo! as tabloids. The results were presented in relation to time, newspapers and title tonality. A combination of qualitative (content analysis) and quantitative methods (descriptive statistical analysis of news frequency) was used. During the observed period, 405 titles were published - 274 about education and 131 about culture. The results of the dynamics and structure of reporting indicate insufficient affirmation of education and culture through print media, as well as the imbalance between neutral and polarized news and reduced level of regular reporting due to acute socio-political events. In order to remove the problem of marginalization of education and culture in social consciousness, systematic efforts in popularization of these topics and a more responsible media policy are needed, in which the professionalism, social responsibility and the enlightening role of the media would be set as priorities.

Research on the Innovation of Labor Education Based on the Integration of “Five Educations” in Colleges and Universities

The integration of five educations is the means and way to implement quality education in colleges and universities. Labor education, as one of the five educations, still exists in the education system of colleges and universities with certain problems of marginalization of status, proceduralization of form and utilitarianization of value. The integration of five educations in colleges and universities is an important means and way to implement quality education. Based on the current situation and problems of labor education in the integration of five educations in colleges and universities, the article proposes innovative and efficient labor education system in terms of establishing the objectives of labor education, refining the content of labor education, organization and implementation of labor education and evaluation body of labor education.

Dynamic game analysis in multiple marginalization problems

Dynamic game analysis in multiple marginalization problems

Auroral kilometric radiation—The electron cyclotron maser paradigm

Auroral kilometric radiation (AKR) is the paradigm of intense radio emission from planetary magnetospheres. Being close to the electron gyro frequency and/or its lower harmonics, its observation indicates the non-thermal state of the source plasma. Emission is produced when the plasma enters a state of energetic excitation which results in deformation of the electron distribution function. Under certain conditions this leads to “quasi-coherent” emission. It is believed that the weakly-relativistic electron-cyclotron-maser instability is responsible for this kind of radiation. Since energetically radio radiation normally is not of primary importance in the large-scale magnetospheric phenomena, AKR as such has, for the purposes of large-scale magnetospheric physics, become considered a marginal problem. Here this notion is questioned. AKR while applying to the auroral region mainly during magnetospherically disturbed times carries just a fraction of the total substorm energy. It is, however, of diagnostic power in the physics of the upper auroral ionosphere and Space Weather research. As a fundamental physical problem of generation of radiation in non-thermal plasmas it remains not resolved yet. Many questions have been left open even when dealing only with the electron-cyclotron-maser. These can advantageously be studied in the magnetosphere proper both by observation and theory, the only continuously accessible place in space. The most important are listet here with hint on how they should be attacked. Its value is to be sought in the role it should play in application to the other magnetized planets, extra-solar planets, and to strongly magnetized astronomical objects as an important tool to diagnose the matter state responsible for radiation in the radio frequency range beyond thermal, shock or synchrotron radiation.

A deep learning solution to the marginal stability problems of acoustic feedback systems for hearing aids

For hearing aids, it is critical to reduce the acoustic coupling between the receiver and microphone to ensure that prescribed gains are below the maximum stable gain, thus preventing acoustic feedback. Methods for doing this include fixed and adaptive feedback cancellation, phase modulation, and gain reduction. However, the behavior of hearing aids in situations where the prescribed gain is only just below the maximum stable gain, called here "marginally stable gain," is not well understood. This paper analyzed marginally stable systems and identified three problems, including increased gain at frequencies with the smallest gain margin, short whistles caused by the limited rate of decay of the output when the input drops, and coloration effects. A deep learning framework, called deep marginal feedback cancellation (DeepMFC), was developed to suppress short whistles, and reduce coloration effects, as well as to limit excess amplification at certain frequencies. To implement DeepMFC, many receiver signals in closed-loop systems and corresponding open-loop systems were simulated, and the receiver signals of the closed-loop and open-loop systems were paired together to obtain parallel signals for training. DeepMFC achieved much better performance than existing feedback control methods using objective and subjective measures.

Dynamics of structural change in agriculture, transaction cost theory and market efficiency: The case of cultivation contracts between agricultural enterprises and the food industry

In developed economies, the increasing openness of markets, the ease of trade and the speed of information lead to territorial imbalance and marginalization phenomena of small agricultural activities that cannot compete with the new models of agri-food systems. In this research, starting from this situation, we analyze through the Transaction Cost Theory what can be practised too recover competitiveness margins for small farms. From the study, it emerges that cultivation contracts represent a valid tool for the solution of various marginalization problems of many agricultural enterprises. In particular, from the experience gained over the past few years in Sicily, the cultivation contract brings benefits to both the food and agricultural enterprise. The validity of the food supply chain vertical integration model is based on this aspect. • Coordination between companies is a strategy to increase competitiveness. • Transaction cost theory shows that coordination between firms increases market efficiency. • Cultivation contracts are a form of vertical coordination between companies in the agri-food chain. • Cultivation contracts improve the allocative efficiency of resources.

Immigrant Organizations and Labor Market Integration: The Case of Sweden

In line with recent trends in sociology of migration, the paper presents major research findings on Swedish immigrant organizations (SIOs) and their labor market integration activities. Analyses of engagement in these activities are particularly important as Sweden wrestles with significant problems of labor market marginalization, particularly among non-European migrants. Drawing on official data and interviews, we find surprisingly low incidence in direct labor market support but quite active indirect support. Our regression model shows significant correlation between region of origin and labor market activities, and further analyses using regional typologies indicate that SIOs’ activities are partly driven by members’ different modes of incorporation and relative integration, where Middle-Eastern SIOs stand out as particularly active. Our findings further indicate potential for scale-up of SIO-assistance in the Swedish Government’s efforts towards increased immigrant labor market integration.

The Condition of the Underprivileged People in Puthumaippithan's Short Stories

It is the writer Puthumaippithan who, through his writings, displayed the various kinds of tribulations in the world, the real-life messages of man, etc. In his works, Puthumaippithan highlighted social miseries, hunger, misery, small amounts of happiness, the pain of the real man, the love of the poor, economic difficulties, the oppression of the oppressed, the economic inequalities faced by the middle class, the poverty of the socially marginalized, etc. It was the writer Puthumaippithan who innovated in the field of short stories and outlined the complexities of human life and material difficulties in his works. From the reader's point of view, it appears that he has recorded the characteristics of poverty in great depth through his writings from various angles. Murugadoss struggling to spend a day, Maruthi who is oppressed in the grip of poverty and caste, Vellachi who yearns to learn writing, Brahmanayagam Pillai, a poor worker who wants to save his wife, etc., are some of the storytellers who have brought out the problems of economic marginalization and the lives of the downtrodden through his works. This study has been conducted based on some of the works of the author.

Quantum earth mover’s distance, a no-go quantum Kantorovich–Rubinstein theorem, and quantum marginal problem

The quantum coupling of two given quantum states denotes the set of bipartite states whose marginal states are these given two states. In this paper, we provide tight inequalities to describe the structure of quantum coupling. These inequalities directly imply that the trace distance between two quantum states cannot be determined by the quantum analog of the earth mover’s distance, thus ruling out the equality version of the quantum Kantorovich–Rubinstein theorem for trace distance even in the finite-dimensional case. In addition, we provide an inequality that can be regarded as a quantum generalization of the Kantorovich–Rubinstein theorem. Then, we generalize our inequalities and apply them to the three tripartite quantum marginal problems. Numerical tests with a three-qubit system show that our criteria are much stronger than the known criteria: the strong subadditivity of entropy and the monogamy of entanglement.

The Bright Side of Inequity Aversion

Modern consumers are concerned about not only their material payoff, but also the fairness of the transaction when making purchasing decisions. In this paper, we investigate how consumers’ inequity aversion affects a manufacturer who sources inputs from upstream suppliers. We find that, when the manufacturer sources from a single supplier or when consumers observe the manufacturer’s cost, inequity aversion hurts both the supplier’s and manufacturer’s profits. However, when the manufacturer sources from multiple suppliers and consumers do not observe the manufacturer’s cost, inequity aversion reduces both the suppliers’ and manufacturer’s margins, which significantly alleviates the double marginalization problem, increases consumer demand, and improves channel efficiency. As a result, inequity aversion benefits the suppliers, manufacturer, and consumers alike, leading to a “win–win–win” outcome. By comparing cases in which consumers observe and do not observe the manufacturer’s cost, we also find that, when faced with inequity-averse consumers, a manufacturer may find it optimal to withhold its cost information to help secure lower procurement costs from upstream suppliers. This paper was accepted by Dmitri Kuksov, marketing. Funding: This work was supported by the Hong Kong Research Grants Council [Grant 21500920].

Participation Styles, Turn-Taking Strategies, and Marginalization in Intercultural Decision-Making Discourse

Marginalization in decision-making discourse results in disempowerment of the marginalized and detracts from the efficacy of participatory decision making. In ESL contexts, it is usually associated with English proficiency. But this view ignores the influence of preferences for different participation styles, an understanding of which is essential for the development of effective pedagogical remedies to the problem of marginalization. The present study addresses this gap by investigating discourse participation and marginalization from a participation styles perspective. Findings reveal that marginalization resulted from a failure to adopt turn-taking strategies associated with dominant participation styles. Implications for pedagogy are discussed.

Information algebras in the theory of imprecise probabilities, an extension

In recent works, we have shown how to construct an information algebra of coherent sets of gambles, considering firstly a particular model to represent questions, called the multivariate model, and then generalizing it. Here we further extend the construction made to the highest level of generality, setting up an associated information algebra of coherent lower previsions, analyzing the connection of both the information algebras constructed with an instance of set algebras and, finally, establishing and inspecting a version of the marginal problem in this framework.Set algebras are particularly important information algebras since they are their prototypical structures. They also represent the algebraic counterparts of classical propositional logic. As a consequence, this paper details as well how propositional logic is naturally embedded into the theory of imprecise probabilities.

Effect of Social Influence on a Two-Party Election: A Markovian Multiagent Model

In digital social networks, the filtering algorithms employed by the platform management to sieve the contents shared among the users can alter the social influence intensity. In this article, a Markov multiagent model of opinion dynamics is used to analyze possible opinion manipulation under apparently neutral interventions on the influence intensity. We consider a two-party election, whose voters, modeled as heterogeneous agents, are connected in a social network with an arbitrary topology. The equations describing the variance of the vote share, both in transient and steady state, are derived. The key is the solution of the second-order marginalization problem under the form of a numerically tractable characterization of pairwise joint probabilities of the voters’ opinions. In particular, these probabilities are computed by means of a Lyapunov-like matrix differential equation driven by first-order moments. This result is used to answer some important questions, like the possible nonmonotonic effect of the influence intensity on the vote volatility and the interplay of topology and individuals’ stubbornness to determine the electoral balance between two parties.