Explicit Values Research Articles

The Explicit Formulae and Evaluations of Ramanujan's Remarkable Product of Theta-functions

On pages 338 and 339 in his first notebook, Ramanujan defined remarkable product of theta-functions $a_{m,n}$ and also recorded eighteen explicit values depending on two parameters $m$ and $n$. All these values have been established by Berndt et al. In this paper, we establish a new general formulae for the explicit evaluations of $a_{3m,3}$ and $a_{m,9}$ by using $P$-$Q$ mixed modular equation and values for certain class invariant of Ramanujan. Using these formulae, we calculate some new explicit values of $a_{3m,3}$ for $m = 2,7,13,17,25,37$ and $a_{m,9}$ for $m = 17,37$.

Treatment for human visceral leishmaniasis: a cost-effectiveness analysis for Brazil.

To estimate the cost-effectiveness of strategies for the treatment of VL in Brazil. Cost-effectiveness study comparing three therapeutic options: meglumine antimoniate (MA), liposomal amphotericin B (LAMB) and a combination of LAMB plus MA (LAMB plus MA), from public health system and societal perspectives. An analytical decision-making model was used to compare strategies for the following outcomes: early therapeutic failure avoided at 30days, days of hospitalisation avoided and VL cure at 180days. The efficacy and safety parameters of the drugs came from a randomised, open-label trial and the cost data came from a cost-of-illness study, both carried out in Brazil. For all outcomes analysed, the LAMB strategy was more effective. The MA strategy was inferior to the LAMB plus MA strategy for the outcomes early therapeutic failure avoided and cure. When only LAMB and MA were compared from a societal perspective, a cost of US$ 278.56 was estimated for each additional early therapeutic failure avoided, a cost of US$ 26.88 for each additional day of hospitalisation avoided and a cost of US$ 89.88 for each additional case of cured VL, for the LAMB strategy vs. MA. In Brazil, the LAMB strategy proved to be cost-effective for treating VL, considering a GDP per capita as the willingness-to-pay threshold, for all of the outcomes analysed in comparison to MA.

Properties of reciprocity formulas for the Rogers–Ramanujan continued fractions

Ramanujan recorded four reciprocity formulas for the Rogers–Ramanujan continued fractions. Two reciprocity formulas each are also associated with the Ramanujan–Gollnitz–Gordon continued fractions and a level-13 analog of the Rogers–Ramanujan continued fractions. We show that all eight reciprocity formulas are related to a pair of quadratic equations. The solution to the first equation generalizes the golden ratio and is used to set the value of a coefficient in the second equation; and the solution to the second equation gives a pair of values for a continued fraction. We relate the coefficients of the quadratic equations to important formulas obtained by Ramanujan, examine a pattern in the relation between a continued fraction and its parameters, and use the reciprocity formulas to obtain close approximations for all values of the continued fractions. We highlight patterns in the expressions for certain explicit values of the Rogers–Ramanujan continued fractions by expressing them in terms of the golden ratio. We extend the analysis to reciprocity formulas for Ramanujan’s cubic continued fraction and the Ramanujan–Selberg continued fraction.

Mean value formulas for Ornstein–Uhlenbeck and Hermite temperatures

We obtain explicit mean value formulas for the solutions of the diffusion equations associated with the Ornstein–Uhlenbeck and Hermite operators. From these, we derive various useful properties, such as maximum principles, uniqueness theorems and Harnack-type inequalities.

Academic Medicine Is Patient-Centered Medicine

The tripartite mission of ‘academic medicine’ is education, research, and patient care. Academic medical centers (AMCs) are carrying out the mission and ultimately aiming to improve the health of people and communities. Globally, AMCs are facing a tremendous financial risk stemming from the changes in health insurance reimbursement plans and a shortage of human resources. Innovative AMCs in the United States are trying to transform their physician-centered, and siloed structure into a patient-centered, and integrated structure. They are also building integrated systems with primary healthcare groups to provide continuous patient care from primary to tertiary levels and making strategic networks based on value-based payment and the patient-centered model. These changes have been proven to improve outcomes of patient care and increase fiscal revenues, which are both crucial in supporting education and research. To address the shortage of human resources, programs are being built to develop newly appointed faculty for the future. AMCs have different approaches to bringing changes into their organizations; however, there is a common emphasis on ‘a patient-centered approach,’ which helps them set more explicit organizational values and make strategic decisions based on their values. Korean AMCs are facing similar challenges to AMCs in the United States in spite of many differences between the countries’ healthcare systems. The innovative efforts of AMCs in the United States to address the challenges will be helpful, well-worked examples for Korean AMCs with similar challenges.

Promoting or Undermining Quality Decision Making? A Qualitative Content Analysis of Patient Decision Aids Comparing Surgical and Medication Abortion.

To understand, describe, and compare the content of patient decision aids on surgical and medication abortion, including 1) attributes used to describe each method, 2) approaches to clarify patients' values, 3) language used to describe each method, and 4) language used to frame women's decision-making role. We analyzed 49 decision aids identified through a previous systematic review and environmental scan. We used summative content analysis for objectives 1 and 2 and directed content analysis for objectives 3 and4. We identified 37 method attributes. Overall, the attributes privileged medical over practical and emotional information. One decision aid included an explicit values clarification approach, and others included implicit approaches, which varied in length, information consistency, and organization. We identified four themes-information consistency, subjective claims, emotive or ambiguous descriptions, and medication abortion as not a real abortion-related to the methods' descriptions. We identified three themes-agency in choice, unclear emphasis on women's preferences, and endorsement of clinic services-related to women's decision-making role. Of the nine tools that listed factors influencing women's decision making, patient preferences was often listed last. Early abortion method decision aids presented a broad range of information and typically framed the method choice as the woman's. However, their emphasis on medical attributes, use of inconsistent information, and, at times, biased presentation of methods may undermine quality decision making. We recommend adapting an existing decision aid or designing a novel tool based on the content and language that women find most acceptable.

Quantum spin probabilities at positive temperature are Hölder Gibbs probabilities

We consider the KMS state associated to the Hamiltonian [Formula: see text] over the quantum spin lattice [Formula: see text] For a fixed observable of the form [Formula: see text] where [Formula: see text] is self-adjoint, and for positive temperature [Formula: see text] one can get a naturally defined stationary probability [Formula: see text] on the Bernoulli space [Formula: see text]. The Jacobian of [Formula: see text] can be expressed via a certain continued fraction expansion. We will show that this probability is a Gibbs probability for a Hölder potential. Therefore, this probability is mixing for the shift map. For such probability [Formula: see text] we will show the explicit deviation function for a certain class of functions. When decreasing temperature we will be able to exhibit the explicit transition value [Formula: see text] where the set of values of the Jacobian of the Gibbs probability [Formula: see text] changes from being a Cantor set to being an interval. We also present some properties for quantum spin probabilities at zero temperature (for instance, the explicit value of the entropy).

Analytic model for transient anomalous diffusion with highly persistent correlations.

In recent decades, many stochastic processes have been proposed as models for real world time series data with anomalous spreading, highly persistent correlations, and transient distributional characteristics. We introduce the higher order fractional tempered stable motion as the stochastic integral of the tempered stable motion with respect to a generalized higher order moving average kernel, which provides an analytic model for stochastic processes possessing these characteristics. This stochastic process provides a mathematical model for anomalous diffusion with a transient distribution resembling higher order fractional stable motion on short timescales and higher order fractional Brownian motion in the long run. The specifics of the crossover dynamics from the Lévy stable anomalous diffusion to the Gaussian anomalous diffusion are controlled by explicit parameter values that correspond to physical attributes of the process. It is well suited to modeling anomalous diffusion of any "type" (sub-, super-, regular, or hyperdiffusion) under appropriate parametrizations due to its power-law scaling of variance with respect to time. It is also a useful model for position-velocity-acceleration triples due to its convenient path differentiability and integrability properties. To highlight the potential physical relevance of this model for real world data, we outline its key statistical properties including its covariance structure, memory, and second order self-similarity. We also give an easy to implement elementary method for sample path generation which may be used as a basis for simulation and Monte Carlo studies.

Quantification of emotional values for attributes from sentiment analysis based on mobile phone reviews

E-commerce online reviews are commonly short in length, lack of contextual semantics, and are mixed with explicit emotions and implicit emotions. The subjects of implicit emotions are not easy to be extracted and be defined. Now product-oriented attributes are used to define implicit and fine-grained emotions with the help of the domain emotion dictionary that is constructed by extracted explicit attribute-emotion pairs through using a variety of part-of-speech rules. And implicit emotion and attribute pairs for product “mobile phone” are mined with the help of explicit attribute-emotion pairs and probability calculation method. At last, explicit and implicit emotion values are calculated by considering degree and negative modifiers. The experimental results show that proposed method is effective and has certain commercial value. And the process method is easy to extend to other product fields.

An Integrative Review of Cytokine/Chemokine Predictors of Neurodevelopment in Preterm Infants.

Preterm infants are at risk of brain injury and poor neurodevelopmental outcomes including impairments in cognition, behavioral functioning, sensory perception, and motor performance. Systemic inflammation has been identified as an important, potentially modifiable precursor of neurologic and neurodevelopmental impairments. Inflammation is typically measured by quantifying circulating cytokines and chemokines. However, it is unclear which specific cytokines/chemokines most consistently predict neurodevelopment in preterm infants. In this integrative review, we evaluated and analyzed the literature (N = 37 publications) to determine the cytokines/chemokines most predictive of neurodevelopment in preterm infants, the optimal timing for these measurements, and the ideal source for collecting cytokines/chemokines. Synthesis of the findings of these studies revealed that interleukin (IL)-6, IL-1β, IL-8, and tumor necrosis factor (TNF)-α collected during the first 3 weeks of life are most predictive of subsequent neurodevelopment. Methodological variation among studies hinders more specific analysis, including the evaluation of cytokine thresholds and meta-analyses, that would allow for the use of cytokines/chemokines to predict neurodevelopment. Future research should focus on identifying explicit cytokine values, specifically for IL-6, IL-1β, IL-8, and TNF-α, that are most predictive for identifying preterm infants most at risk of impairment, keeping in mind that longitudinal measures of cytokines/chemokines may be more predictive of future outcomes than single-time point measures.

Growing through chaos in the Matsuyama map via subcritical flip bifurcation and bistability

Abstract Recent publications revisit the growth model proposed by Matsuyama (”Growing through cycles”, Econometrica 1999), presenting new economic interpretations of the system as well as new results on its dynamics described by a one-dimensional piecewise smooth map (also called M-map). The goal of the present paper is to give the rigorous proof of some results which were remaining open, related to the dynamics of M-map. We prove that an attracting 2-cycle appears via border collision bifurcation, give the explicit flip bifurcation value at which this cycle looses stability, as well as the explicit coordinates of its points at the bifurcation value, proving that the flip bifurcation is always of subcritical type. We show that this leads to the existence of a region of bistability associated with an attracting 2-cycle coexisting with attracting 4-cyclic chaotic intervals. This means that the effects of the destabilization of the 2-cycle, related to a corridor stability, are catastrophic and irreversible. We give also the conditions related to the sharp transition to chaos, proving that the cascade of stable cycles of even periods cannot occur. The parameter region in which repelling cycles of odd period exist is further investigated, namely, we give an explicit boundary of this region and show its relation to the non existence of cycles of period three.

Investing in natural capital and national security: A comparative review of restoration projects in South Africa

Does restoration pay? We seek to answer this question by reviewing the benefits and costs of 37 economic values derived from five groups of actual restoration-related case studies in South Africa at various scales. The mean opportunity costs of not restoring are the following (a negative value implies an economic loss to society): i) local level single species studies concerned with clearing invasive alien plants (mean = -$27.24/ha/yr, sd = +/-22.93; n = 5); ii) local level multiple species studies concerned with clearing invasive alien plants (mean = -$289/ha/yr, sd = +/-550.6; n = 14); iii) national level studies concerned with clearing invasive alien plants (mean = -$40.2/ha/yr, sd = +/-17.2; n = 3); iv) non-clearing related restoration (mean = -$52/ha/yr, sd = +/-154.2; n = 10); and v) agricultural land rehabilitation (mean = -$428.1/ha/yr, sd = +/-352.7; n = 5). When these annual values are capitalised (i.e. discounted into perpetuity) to reflect the temporal impact of the foregone benefits of restoration, the losses amount to between 16 and 50 times greater than the annual values. Capitalisation of these values is an important step towards an asset-based approach in the management, restoration and conservation of natural capital. It is a step towards viewing the investment in restoration not merely as an expenditure item to be minimised, but as a truly worthwhile investment in the future wellbeing of both people and the planet – an investment in the national security of the country. More work, however, is required to transfer this value onto the balance sheets of companies in order to entice the private sector to invest more as well as to convert the implicit societal benefits of restoration to explicit company-wide value enhancement opportunities.

PNS169 SIMILARITIES & DIFFERENCES IN GLOBAL VALUE DOSSIER (GVD) AND ACADEMY OF MANAGED CARE PHARMACY (AMCP) DOSSIER DEVELOPMENT

To support product Market Access, organizations will develop a GVD and an AMCP dossier. Both documents require substantial time and effort to develop. This study determined areas of overlap and possible efficiencies when developing GVDs and AMCP dossiers. AMCP Format guidelines (version 4.0) and GVD content and best practices were reviewed and compared. Internal process maps for constructing each type of dossier were developed and compared to identify areas of overlap and possible efficiencies. Areas of overlap exist regarding dossier content: • Disease Burden: AMCP dossiers require high-level disease descriptions and US-specific burden of disease information. GVDs require the same information, but from a detailed global perspective. • Clinical Evidence: While both dossiers require clinical study summaries, AMCP study summaries include specific elements and are more detail than GVD study summaries. Additionally, AMCP dossiers require extensive evidence tables; GVDs may not include evidence tables. • Economic Value: AMCP modeling sections are based on US-specific models; GVDs generally contains the core model(s). • Other areas of overlap include presentation of relevant treatment guidelines and HTA decisions. Additionally, it is important to consider the overall focus and “theme” of the dossiers. AMCP dossiers are focused on the product’s clinical evidence, organized in a specific format, with limited interpretation of data and no explicit value story. GVDs are built around a specific value story, with flexibility in organization and evidence presentation. While content may overlap, directly transferring text between documents is rarely possible, and content revisions are required to align with the specific type, audience, and messaging/theme of each dossier. While there are several areas of overlap between the dossiers, specific content must be tailored to different audiences and purposes. Developing a clear plan before beginning work can help identify potential efficiencies, allowing for a more streamlined and perhaps less costly development process.

Valued Living Before and After CBT

Whether and to what degree psychotherapy leads to changes in patients’ value-based actions is not well documented. In this study we examined whether cognitive behavioral therapy, without explicit values work, enhanced value-oriented action. We also explored the role of change in valued action for subsequent life satisfaction and continued change after therapy. Additionally, data on the reliability and validity of the Valued Living Questionnaire (VLQ) are reported. We analyzed the pre-, post-, and 6-month-follow-up-data of 3687 patients of a university psychotherapy outpatient clinic, most of which suffered from reliably diagnosed anxiety and mood disorders. Questionnaires included the VLQ (with 10 items each on the “importance” and “consistency” of values), symptom scales (Beck Depression Inventory; Brief Symptom Inventory), and the Satisfaction with Life Scale. Over the course of therapy significant improvements in value-oriented action were found (d = .34), especially in treatment responders (d = .51). Increase of value-oriented action significantly explained satisfaction with life at end of treatment, even after controlling for symptom reduction. Temporally preceding improvement on the VLQ predicted further symptom reduction until follow-up. Data indicate that psychotherapy positively affects valued living, even when it is not explicitly targeted in treatment. Valued living may have a role in the course and maintenance of therapeutic change.

Entanglement production by statistical operators

In the problem of entanglement there exist two different notions. One is the entanglement of a quantum state, characterizing the state structure. The other is entanglement production by quantum operators, describing the action of operators in the given Hilbert space. Entanglement production by statistical operators, or density operators, is an important notion arising in quantum measurements and quantum information processing. The operational meaning of the entangling power of any operator, including statistical operators, is the property of the operators to entangle wave functions of the Hilbert space they are defined on. The measure of entanglement production by statistical operators is described and illustrated by entangled quantum states, equilibrium Gibbs states, as well as by the state of a complex multiparticle spinor system. It is shown that this measure is in intimate relation to other notions of quantum information theory, such as the purity of quantum states, linear entropy, or impurity, inverse participation ratio, quadratic Rényi entropy, the correlation function of composite measurements, and decoherence phenomenon. This measure can be introduced for a set of statistical operators characterizing a system after quantum measurements. The explicit value of the measure depends on the type of the Hilbert space partitioning. For a general multiparticle spinor system, it is possible to accomplish the particle-particle partitioning or spin-spatial partitioning. Conditions are defined showing when entanglement production is maximal and when it is zero. The study on entanglement production by statistical operators is important because, depending on whether such an operator is entangling or not, it generates qualitatively different probability measures, which is principal for quantum measurements and quantum information processing.

Some interactions of spherically symmetric massive scalar field with Brans–Dicke scalar field in Robertson–Walker universe

Here in this work, we investigated the possible cosmological consequences of the interaction of Brans–Dicke scalar field and massive scalar field by considering spherically symmetric Robertson–Walker metric. The present problem can also be treated as an extension work of [K. Priyokumar et al., Interaction of gravitational field and Brans–Dicke field, Res. Astron. Astrophys. 16(4) (2016) 64; K. Priyokumar and M. Dewri, Interaction of electromagnetic field and Brans–Dicke field, Chinease J. Phys. 54 (2016) 845]. The exact solutions of the field equations are obtained with seven different cases. The behavior of the model and their contribution to the process of the evolution are examined in detail from some explicit and reasonable values of free parameter. We also presented the variations of certain physical parameters versus cosmic time graphically to compare our solutions with the present observational findings. When we studied further, it is found that the cosmological term [Formula: see text] takes a great role in the accelerating expansion of our universe when both scalar fields are exponentially increasing functions of time, while the cosmological term will not appear in the case when both the scalar fields are exponentially decreasing functions of time. Also, the scalar field is seen to have a tendency to increase the expansion of the universe, thereby flattening the universe.

Inclusion in the clinical learning environment: Building the conditions for diverse human flourishing

Aim: While diversity, equity, and inclusion are much proclaimed aspirational goals in education programs, the clinical learning environment (CLE) frequently falls short of meaningful incorporation of these concepts in processes, policies, and local culture. In this paper, we explore how inclusion, diversity, and equity can and should be defined and operationalized within medical education.Methods: Three cases, organized around Hafferty’s curricular framework (formal, informal, and hidden), we illustrate lapses and potential best practices in inclusion in the CLE.Results: The essential “best-practice” of programs inclusive of diverse individuals is the design of policies, processes, and behavioral norms co-creatively with all community members. Potential pitfalls to greater inclusion include nostalgic reference to “the past”, a neutrality that is operationalized without the rudder of explicit values and not recognizing that ethical obligations between teachers, learners, and programs are at the heart of the discussion of how inclusive learning and work environments are built.Conclusion: Inclusive CLE’s provide space for co-creation, understand the need to ensure the voices of the vulnerable (i.e. learners) are heard and valued and through this promote the flourishing of diverse human capital, in keeping with a model that views diversity as a key attribute or organizational excellence.

Null Hypothesis Testing ≠ Scientific Inference: A Critique of the Shaky Premise at the Heart of the Science and Values Debate, and a Defense of Value-Neutral Risk Assessment.

Many philosophers and statisticians argue that risk assessors are morally obligated to evaluate the probabilities and consequences of methodological error, and to base their decisions of whether to adopt a given parameter value, model, or hypothesis on those considerations. This argument is couched within the rubric of null hypothesis testing, which I suggest is a poor descriptive and normative model for risk assessment. Risk regulation is not primarily concerned with evaluating the probability of data conditional upon the null hypothesis, but rather with measuring risks, estimating the consequences of available courses of action and inaction, formally characterizing uncertainty, and deciding what to do based upon explicit values and decision criteria. In turn, I defend an ideal of value‐neutrality, whereby the core inferential tasks of risk assessment—such as weighing evidence, estimating parameters, and model selection—should be guided by the aim of correspondence to reality. This is not to say that value judgments be damned, but rather that they should be accounted for within a structured approach to decision analysis, rather than embedded within risk assessment in an informal manner.

Quotients of the mapping class group by power subgroups

We study the quotient of the mapping class group $\operatorname{Mod}_g^n$ of a surface of genus $g$ with $n$ punctures, by the subgroup $\operatorname{Mod}_g^n[p]$ generated by the $p$-th powers of Dehn twists. Our first main result is that $\operatorname{Mod}_g^1 /\operatorname{Mod}_g^1[p]$ contains an infinite normal subgroup of infinite index, and in particular is not commensurable to a higher-rank lattice, for all but finitely many explicit values of $p$. Next, we prove that $\operatorname{Mod}_g^0/ \operatorname{Mod}_g^0[p]$ contains a K\"ahler subgroup of finite index, for every $p\ge 2$ coprime with six. Finally, we observe that the existence of finite-index subgroups of $\operatorname{Mod}_g^0$ with infinite abelianization is equivalent to the analogous problem for $\operatorname{Mod}_g^0/ \operatorname{Mod}_g^0[p]$.

International experience in determining the cost-effectiveness thresholds

The article reviews international methodological guidelines, regulatory documents and existing approaches to the determination of the costeffectiveness threshold (CeT), also known as the willingness-to-pay threshold (WTP), the threshold value of the incremental cost-effectiveness ratio (ICeR), in europe (england and Wales, Scotland, Ireland, France, Belgium, Denmark, the netherlands, Germany, Sweden, Finland, norway, Poland), America (the USA, Canada, Brazil), Asia (Japan, South korea, Taiwan, Thailand), in Australia and new Zealand. The CeT is commonly used to rationalize decision-making in health cost reimbursement. The present review demonstrates that just a few countries (englandandWales,Thailand,Poland,USA) have introduced the explicit value of CeT into their decision making. Some countries (Australia,Canada,new Zealand, thenetherlands,Sweden, andBrazil) use CeT in an implicit manner implying that no specific CeT value is defined by law. In other countries (Finland,Sweden,norway,France,Germany,Denmark,Japan,South korea,Taiwan), the role of the threshold in health reimbursement remains uncertain despite the presence of HTA systems. The CeT is expressed as additional cost per unit of incremental health benefit, which is represented by quality-adjusted life year (QALY) in most counties. However,PolandandBrazilallow using life years gained (LYG) as a measure of additional benefit neglecting the quality of life. In thenetherlandsandengland, different CeT values are applied to the health technology under assessment depending on the severity or rareness of the disease and some other factors.