Non-solved Problem Research Articles

Energy Efficient Resource Allocation for Multinumerology Enabled Hybrid Services in B5G Wireless Mobile Networks

Multi-numerology (MN) providing a flexible transmission frame structure has attracted a considerable attention for supporting abundant services for beyond fifth-generation (B5G) networks. However, mobility induces severe performance degradation under different numerologies including temporal and spectral fluctuation, which is not well-investigated in existing literature. We have conceived an MN-enabled energy efficiency (EE) problem aiming for alleviating mobility- and MN-induced interferences through moderate power and sub-carrier assignment, while considering quality-of-service (QoS) and latency requirements for different services. We propose a multi-numerology based power and resource block allocation (MNPRA) scheme considering time-/frequency-division (TD/MD) based MN leveraging temporal and spectral features among numerologies. The original non-solvable problem is theoretically transformed into a convex one by employing Dinkelbach process, Taylor approximation and difference of two concave functions (D.C.). Convergence of proposed MNPRA scheme is analyzed and verified by simulations. In simulation results, we have evaluated MNPRA under different service demands, user velocities and MN types. Our proposed scheme outperforms the conventional single-numerology framing and existing methods in open literature, which results in performances of higher EE as well as of lower throughput/delay outage probability.

A microphysiological system combining electrospun fibers and electrical stimulation for the maturation of highly anisotropic cardiac tissue

The creation of cardiac tissue models for preclinical testing is still a non-solved problem in drug discovery, due to the limitations related to the in vitro replication of cardiac tissue complexity. Among these limitations, the difficulty of mimicking the functional properties of the myocardium due to the immaturity of the used cells hampers the obtention of reliable results that could be translated into human patients. In vivo models are the current gold standard to test new treatments, although it is widely acknowledged that the used animals are unable to fully recapitulate human physiology, which often leads to failures during clinical trials. In the present work, we present a microfluidic platform that aims to provide a range of signaling cues to immature cardiac cells to drive them towards an adult phenotype. The device combines topographical electrospun nanofibers with electrical stimulation in a microfabricated system. We validated our platform using a co-culture of neonatal mouse cardiomyocytes and cardiac fibroblasts, showing that it allows us to control the degree of anisotropy of the cardiac tissue inside the microdevice in a cost-effective way. Moreover, a 3D computational model of the electrical field was created and validated to demonstrate that our platform is able to closely match the distribution obtained with the gold standard (planar electrode technology) using inexpensive rod-shaped biocompatible stainless-steel electrodes. The functionality of the electrical stimulation was shown to induce a higher expression of the tight junction protein Cx-43, as well as the upregulation of several key genes involved in conductive and structural cardiac properties. These results validate our platform as a powerful tool for the tissue engineering community due to its low cost, high imaging compatibility, versatility, and high-throughput configuration capabilities.

Closed-form solutions for the Schrödinger wave equation with non-solvable potentials: A perturbation approach

Abstract To obtain closed-form solutions for the radial Schrödinger wave equation with non-solvable potential models, we use a simple, easy, and fast perturbation technique within the framework of the asymptotic iteration method (PAIM). We will show how the PAIM can be applied directly to find the analytical coefficients in the perturbation series, without using the base eigenfunctions of the unperturbed problem. As an example, the vector Coulomb ( ∼ 1 / r ) \left( \sim 1\hspace{0.1em}\text{/}\hspace{0.1em}r) and the harmonic oscillator ( ∼ r 2 ) \left( \sim {r}^{2}) plus linear ( ∼ r ) \left( \sim r) scalar potential parts implemented with their counterpart spin-dependent terms are chosen to investigate the meson sectors including charm and beauty quarks. This approach is applicable in the same form to both the ground state and the excited bound states and can be easily applied to other strongly non-solvable potential problems. The procedure of this method and its results will provide a valuable hint for investigating tetraquark configuration.

Following up of Surgical Treated Human Liver Cystic Echinococcosis: A Proteomics Approach.

Background:Cystic echinococcosis (CE) is one of the most important parasitic zoonosis in the world. Post-surgery follow up in CE patients is an important non-solved problem up to now. Therefore, the investigations on this problematic issue would be very applicable in the view of CE clinical treatment.Methods:A total of 24 confirmed liver CE patients sera including eight sera before surgery (BS), eight sera three months post-surgery (3MPS), and eight sera six months post-surgery (6MPS) were used in the present study. Proteomics methods including 2DE and LC-MS/MS were performed on the specimens followed by bioinformatics analysis such as Gene Ontology (GO) and Protein-Protein Interaction (PPI) network analysis.Results:A total of 235 proteins were detected of which 12 differentially expressed proteins (DEP) were identified by LC-MS/MS in all sera. The proteins were presented in BS and suppressed after surgery as follows: HPX, SERPINA1, SERPINC1, CP, HBD, and HBA2. Comparisons of the protein expression in sera of patients BS, 3MPS, and 6MPS revealed that GC, IGJ, AHSG, CD5L, FGG, and APOC3 have been overexpressed in 3MPS and 6MPS. PPI network analysis demonstrated that SERPINC1 and AHSG with more connection in the network could be considered as hub proteins and potential prognostic biomarkers in response to surgical treatment of liver CE.Conclusion:Application of proteomics methods on patient’s sera could be used as a novel biomarker tool for following-up liver CE patients. In this regards, proteomics and, application of bioinformatics analysis including GO and PPI showed that SERPINC1, AHSG and HPX are of more value as a potential follow up biomarkers in response to surgical treatment.

Systematic modeling of discrete‐continuous optimization models through generalized disjunctive programming

Discrete‐continuous optimization problems are commonly modeled in algebraic form as mixed‐integer linear or nonlinear programming models. Since these models can be formulated in different ways, leading either to solvable or nonsolvable problems, there is a need for a systematic modeling framework that provides a fundamental understanding on the nature of these models. This work presents a modeling framework, generalized disjunctive programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions. An overview is provided of major research results that have emerged in this area. Basic concepts are emphasized as well as the major classes of formulations that can be derived. These are illustrated with a number of examples in the area of process systems engineering. As will be shown, GDP provides a structured way for systematically deriving mixed‐integer optimization models that exhibit strong continuous relaxations, which often translates into shorter computational times. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3276–3295, 2013

Influence of extraction methods on proteins and carbohydrates analysis from MBR activated sludge flocs in view of improving EPS determination

One of the main operational problems in membrane bioreactors (MBRs) is membrane fouling. It can be stated that extracellular polymeric substances (EPSs) analysis is of paramount importance for membrane fouling prediction and subsequently to enhance the performance of the MBR process. In this way, the standardization of EPS separation and their analytical procedures is a non-solved problem that plays an important role in order to be able of comparing data of pilot and full-scale bioreactors. Prior to unveil this fact, it is necessary to assure the accuracy of the analyzed data. In this paper, the Standard Addition Method (SAM) is applied with the aim of studying eventual interferences by other mixed liquor substances or by reagents used in the extraction procedures on the analytical methods for determining proteins and carbohydrates and as a consequence, to improve the data accuracy and reliability. For that, several extraction protocols were applied and compared in order to obtain the EPS from the activated sludge. Moreover, DNA was measured and viability tests were carried out to evaluate cell lysis extent. BCA and Lowry methods were used to quantify proteins, meanwhile Dubois and Anthrone were applied for carbohydrates.Results showed that Triton X-100 achieved the highest extraction values in terms of proteins (81.64±12.9mg BSA/g VSS) and carbohydrates (10.3±1.4mg Glucose/g VSS) concentrations linked to lower DNA values (4.9±0.8mg DNA/g VSS). In addition, epifluorescence microscope images showed the high extent of the extraction achieved. For this protocol, BCA and Dubois analytical methods were chosen since SAM found out interferences with Anthrone and Lowry, and consequently, they were recommended for data comparison in MBR plants, and for fouling prediction.

On the computability of quasi-transitive binary social choice rules in an infinite society and the halting problem

This paper investigates the computability problem of the existence of a vetoer and an oligarchy for quasi-transitive binary social choice rules (Mas-Colell and Sonnenschein in Rev Econ Stud 39:185–192, 1972) in a society with an infinite number of individuals (infinite society) according to the computable calculus (or computable analysis) by Aberth (Computable analysis, McGraw-Hill, New York, 1980; Computable calculus, Academic Press, Dublin, 2001). We will show the following results. The problem whether a quasi-transitive binary social choice rule which satisfies Pareto principle and independence of irrelevant alternatives (IIA) has a vetoer or has no vetoer in an infinite society is a nonsolvable problem, that is, there exists no ideal computer program for a quasi-transitive binary social choice rule which satisfies Pareto principle and IIA that decides whether it has a vetoer or has no vetoer. And it is equivalent to nonsolvability of the halting problem. We also show that if for any quasi-transitive binary social choice rule there exists an oligarchy in an infinite society, whether it is finite or infinite is a nonsolvable problem. A vetoer is an individual such that if he strictly prefers an alternative to another alternative, then the society prefers the former to the latter or is indifferent between them regardless of the preferences of other individuals, and an oligarchy is the minimal set of individuals which has dictatorial power and its each member is a vetoer. It will be shown that an oligarchy is a set of vetoers if it exists.

On the computability of binary social choice rules in an infinite society and the halting problem

This paper investigates the computability problem of the Arrow impossibility theorem [K.J. Arrow, Social Choice and Individual Values, second ed., Yale University Press, 1963] of social choice theory in a society with an infinite number of individuals (infinite society) according to the computable calculus (or computable analysis) by Aberth [O. Aberth, Computable Analysis, McGraw-Hill, 1980, O. Aberth, Computable Calculus, Academic Press, 2001]. We will show the following results. The problem whether a transitive binary social choice rule satisfying Pareto principle and independence of irrelevant alternatives (IIA) has a dictator or has no dictator in an infinite society is a nonsolvable problem, that is, there exists no ideal computer program for a transitive binary social choice rule satisfying Pareto principle and IIA that decides whether the binary social choice rule has a dictator or has no dictator. And it is equivalent to nonsolvability of the halting problem. A binary social choice rule is a function from profiles of individual preferences to social preferences, and a dictator is an individual such that if he strictly prefers an alternative to another alternative, then the society must also strictly prefer the former to the latter.

Efeito do ultra-som na prevenção da hérnia incisional mediana em ratos

OBJETIVO: Investigar se o ultra-som é capaz de evitar o aparecimento da hérnia incisional (HI), uma vez que o seu tratamento ainda é um problema não resolvido. MÉTODO: Induziu-se a HI, por secção da linha alba, em 20 ratos Wistar, distribuídos em dois grupos: um recebeu a aplicação do ultra-som, na área operada, por 14 dias e o outro por 28 dias, cada qual com seu subgrupo controle (não tratado). Utilizou-se aparelho com cabeçote reduzido, modo pulsado (1:5), freqüência de 3,0MHz e intensidade de 0,5W/cm², durante 5min/dia, iniciando-se as aplicações no primeiro dia pós-operatório. Ao final, mediu-se o diâmetro transverso do anel herniário ou da largura da cicatriz na linha alba, definindo-se a HI quando esses valores ultrapassassem 2mm. A densidade de vasos sangüíneos, de fibroblastos e de fibras colágenas, nessas estruturas, foi estudada à microscopia óptica. As médias e o erro padrão foram submetidos à análise de variância (ANOVA) e ao teste de comparação múltipla de Tukey-Kramer. RESULTADOS: Dos animais tratados com o ultra-som, 60% não desenvolveram HI e, nos restantes, o anel herniário foi menor do que os não tratados (p<0,0001). A densidade de vasos sangüíneos (p=0,0031), de fibroblastos (p<0,0001) e de fibras colágenas (p=0,0015) também foi maior, em relação aos controles. Não houve diferença significante nesses parâmetros, comparando-se os dois períodos de tratamento. CONCLUSÃO: O ultra-som evitou o aparecimento da HI ou reduziu o seu tamanho, quando aplicado por 14 dias pós-operatórios, nas condições deste experimento.

Precise numerical methods using C++

Introduction. Various Arithmetics. Solvable Problems and Nonsolvable Problems. Computing Derivatives and Integrals. Finding Zeros of Real Functions. Finding Zeros of Polynomials and Other Analytic Functions. Problems of LinearAlgebra. Optimization Problems. Numerical Solution of Ordinary Differential Equations. The C++ System for Precise Computation. Subject Index.

Algebraic nonsolvability of the problem of existence of holomorphic first integrals

We prove that the existence of a holomorphic first integral of an analytic differential equation is an algebraically nonsolvable problem. Moreover, we prove a perturbation lemma showing that a nilpotent singularity of a differential equation in the plane cannont have a holomorphic first integral independently of the prolongation of anynth-order jet. We give an application to the case of nilpotent centers.

Exact and approximate solutions to the Schrödinger equation for the harmonic oscillator with a singular perturbation

I obtain exact solutions for the quantum-mechanical harmonic oscillator with a perturbation potential which belongs to a class of polynomial functions of 1 r . I show that some of the eigenfunctions enable the calculation of expectation values in closed form and are therefore suitable trial functions for the application of the variational method to related nonsolvable problems.

Constructively presented projective planes

An attempt to define a finite presentation for projective planes by analogy to finitely presented groups has been made in [9]. In this article we suggest another definition for a presentation of projective planes: constructively presented planes. A few simple results about such planes and an example of constructively presented planes with nonsolvable word problem are given.