Weinberg Model Research Articles

Two pseudo-Goldstone bosons in the Gildener–Weinberg model

In a dimensionless multi-scalar extension of the Standard Model, Gildener and Weinberg assumed that along a flat direction, there is only one classically massless scalar, known as the scalon, which acquires mass through radiative corrections à la Coleman–Weinberg, while all other scalars remain heavy. In this paper, by introducing a toy model with four scalar degrees of freedom we demonstrate the existence of two scalons along a specific flat direction that we construct. We present the effective potential for the model and provide the masses of the heavy scalars and two radiatively light pseudo-Goldstone bosons.

An Effective GNSS/PDR Fusion Positioning Algorithm on Smartphones for Challenging Scenarios.

The location-based smartphone service brings new development opportunities for seamless indoor/outdoor positioning. However, in complex scenarios such as cities, tunnels, overpasses, forests, etc., using only GNSS on smartphones cannot provide stable and reliable positioning results. Usually, additional sensors are needed to assist GNSS. This paper investigates the GNSS positioning algorithm assisted by pedestrian dead reckoning (PDR) in complex scenarios. First, we introduce a step detection algorithm based on the peak-valley of acceleration modulus, and the Weinberg model and the Mahony algorithm in PDR are used to estimate step length and heading. On this basis, we evaluated the performance of GNSS/PDR fusion positioning in an open scenario, a semiopen scenario, and a blocked scenario, respectively. Finally, we develop a GNSS/PDR real-time positioning software, called China University of Mining and Technology-POSitioning (CUMT-POS) version 1.0, on the Android 10 platform. By comparing GNSS solutions, PDR solutions, GNSS/PDR solutions, and real-time kinematic (RTK) solutions, we verify the potential auxiliary ability of PDR for GNSS positioning in complex environments, proving that multisource sensor fusion positioning significantly improves reliability and stability. Our research can help the realization of urban informatization and smart cities.

ЕКОНОМІКО-СТАТИСТИЧНЕ МОДЕЛЮВАННЯ В АНАЛІТИЦІ І ПРОГНОЗУВАННІ БЮДЖЕТУ МАРКЕТИНГОВИХ КОМУНІКАЦІЙ: МЕТОДИЧНИЙ АСПЕКТ

In the conditions of global challenges, the problem of justified management decision-making, information and analytical support for forecasting marketing results is becoming increasingly relevant for enterprises operating in the conditions of a market economy. The purpose of the article is the methodical justification of building a model that allows forecasting the costs of marketing communication appeals of an enterprise to achieve the desired market share based on data on the market share of the totality of enterprises in the industry, activity costs and the specific weight of the costs of communication appeals in the total amount of expenses. According to the well-known Weinberg model in the theory of marketing analysis and forecasting, as a factor characteristic that should determine the size of the marketing communications budget, an indicator reflecting the ratio of the share of marketing communications costs in the total amount of costs of the investigated company and the company of the competitor, which is the leader in terms of market share, was chosen. The company's share on the market was chosen as an effective indicator. The presented model building and forecasting algorithm was developed on the basis of the application of a formalized method and regression analysis, which made it possible to analytically describe the statistical correlation dependence between the variation of the resulting and factor characteristics and to evaluate the adequacy of the obtained linear pair model on the basis of variance analysis. Regression analysis was carried out using the available toolkit of the Excel spreadsheet analysis package. The approach to building the Weinberg model substantiated in the article can be easily implemented in practice to analyze the results of the company's marketing activities and develop and forecast the marketing communications budget to achieve the desired market share. The practical significance of using the proposed model in practice is to ensure an increase in the efficiency of costs directed to communication activities in marketing in order to achieve the desired marketing results and strengthen the company's position on the market.

The Higgs Boson and its physics: an overview

The Higgs boson plays a central role in the Standard Model, as well as in theories which go beyond it. This article is therefore divided into two parts. The first takes s historical approach and shows how the mass problem entered weak interaction theory from the beginning and how it was solved by invoking the Higgs boson. This is followed by a construction of the Glashow–Salam–Weinberg model, again stressing the role played by the Higgs doublet. This part culminates in the Higgs boson discovery of 2012. The second part first discusses the shortcomings of the Standard Model and then touches upon the major theories which try to improve upon it, mostly with profound consequences on the Higgs sector. This is followed up by short descriptions of a number of popular extensions of the Higgs sector, and culminates in a brief introduction to effective field theory approaches to studying the Higgs sector.

An improved pedestrian dead reckoning algorithm based on smartphone built-in MEMS sensors

With the advantages of low cost, small size and lightweight, the smartphone has played a more and more important role in pedestrian indoor positioning. In particular, the application of Pedestrian Dead Reckoning (PDR) in the smartphone built-in MEMS sensors makes the application of smartphone more extensive. However, the zero-bias instability of the smartphone built-in MEMS sensors leads to the rapid accumulation of pedestrian trajectory calculation error. To solve this problem, we used the bias drift model and Kalman filter (KF) to denoise the original MEMS data. The dual-feature step detection model of peak domain and time domain was established to provide accurate step information for step length estimation and heading correction. Based on the Weinberg model, the three-steps constraint step length estimation (TCSLE) model was proposed to estimate step length accurately. Then, based on the improved heuristic drift elimination (iHDE), the adaptive drift elimination (ADE) model was proposed to identify different walking states. The correction models under different walking states were established to correct the heading angle accurately. Finally, the pedestrian trajectory was reconstructed using accurate step length and heading information. To verify the performance of the PDR algorithm based on the above model, three experimenters with different heights and genders were recruited, and three mobile phones with different sensor performance were selected. The experimenters moved smoothly and steadily with hand-held mobile phone, and 18 sets of experiments were carried out along two paths. The experiment results shown that the step length deviation was less than 1.4871 %, the horizontal positioning error was less than 1.6070 m, and the relative positioning error was less than 1.1816 %D. The proposed PDR algorithm has strong adaptability and robustness, and meets the needs of pedestrian indoor positioning.

A Step Length Estimation Model of Coefficient Self-Determined Based on Peak-Valley Detection

Without any preinstalled infrastructure, pedestrian dead reckoning (PDR) is a promising indoor positioning technology for pedestrians carrying portable devices to navigate. Step detection and step length estimation (SLE) are two essential components for the pedestrian navigation based on PDR. To solve the overcounting problem, this study proposes a peak-valley detection method, which can remove the abnormal values effectively. The current step length models mostly depend on individual parameters that need to be predetermined for different users. Based on fuzzy logic (FL), we establish a rule base that can adjust the coefficient in the Weinberg model adaptively for every detected step of various human shapes walking. Specifically, to determine the FL rule base, we collect user acceleration data from 10 volunteers walking under the combination of diverse step length and stride frequency, and each one walks 49 times at all. The experimental results demonstrate that our proposed method adapts to different kinds of persons walking at various step velocities. Peak-valley detection can achieve an average accuracy of 99.77% during 500 steps of free walking. Besides, the average errors of 5 testers are all less than 4 m per 100 m and the smallest one is 1.74 m per 100 m using our coefficient self-determined step length estimation model.

Parity and CP operations for Majorana neutrinos

The parity transformation law of the fermion field $\psi(x)$ is usually defined by the "$\gamma^{0}$-parity" $\psi^{p}(t,-\vec{x}) = \gamma^{0}\psi(t,-\vec{x})$ with eigenvalues $\pm 1$, while the "$i\gamma^{0}$-parity" $\psi^{p}(t,-\vec{x})=i\gamma^{0}\psi(t,-\vec{x})$ is required for the Majorana fermion. The compatibility issues of these two parity laws arise in generic fermion number violating theories where a general class of Majorana fermions appear. In the case of Majorana neutrinos constructed from chiral neutrinos in an extension of the Standard Model, the Majorana neutrinos can be characterized by CP symmetry although C and P are separately broken. It is then shown that either choice of the parity operation, $\gamma^{0}$ or $i\gamma^{0}$, in the level of the starting fermions gives rise to the consistent and physically equivalent descriptions of emergent Majorana neutrinos both for Weinberg's model of neutrinos and for a general class of seesaw models. The mechanism of this equivalence is that the Majorana neutrino constructed from a chiral neutrino, which satisfies the classical Majorana condition $\psi(x)=C\overline{\psi(x)}^{T}$, allows the phase freedom $\psi(x)=e^{i\alpha}\nu_{L}(x) + e^{-i\alpha}C\overline{\nu_{L}(x)}^{T}$ with $\alpha=0\ {\rm or}\ \pi/4$ that accounts for the phase coming from the different definitions of parity for $\nu_{L}(x)$ and ensures the consistent definitions of CP symmetry $({\cal CP})\psi(x)({\cal CP})^{\dagger}= \pm i\gamma^{0}\psi(t,-\vec{x})$.

Boundedness from below in theU(1)×U(1)three-Higgs-doublet model

Establishing if multi-Higgs potentials are bounded from below (BFB) can be rather challenging, and it may impede efficient investigation of all phenomenological consequences of such models. In this paper, we find the necessary and sufficient BFB conditions for the Three-Higgs-Doublet model (3HDM) with the global symmetry group $U(1)\times U(1)$. We observed an important role played by charge-breaking directions in the Higgs space, even for situations when a good-looking neutral minimum exists. This remark is not limited to the particular model we consider but represents a rather general feature of elaborate multi-Higgs potentials which must be carefully dealt with. Also, applying this method to Weinberg's model (the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetric 3HDM) turned out to be more challenging than was believed in the literature. In particular, we have found that the approach taken in a paper from 2009 does not lead to the necessary and sufficient BFB conditions for this case.

Population genetics of immune-related multilocus copy number variation in Native Americans.

While multiallelic copy number variation (mCNV) loci are a major component of genomic variation, quantifying the individual copy number of a locus and defining genotypes is challenging. Few methods exist to study how mCNV genetic diversity is apportioned within and between populations (i.e. to define the population genetic structure of mCNV). These inferences are critical in populations with a small effective size, such as Amerindians, that may not fit the Hardy-Weinberg model due to inbreeding, assortative mating, population subdivision, natural selection or a combination of these evolutionary factors. We propose a likelihood-based method that simultaneously infers mCNV allele frequencies and the population structure parameter f, which quantifies the departure of homozygosity from the Hardy-Weinberg expectation. This method is implemented in the freely available software CNVice, which also infers individual genotypes using information from both the population and from trios, if available. We studied the population genetics of five immune-related mCNV loci associated with complex diseases (beta-defensins, CCL3L1/CCL4L1, FCGR3A, FCGR3B and FCGR2C) in 12 traditional Native American populations and found that the population structure parameters inferred for these mCNVs are comparable to but lower than those for single nucleotide polymorphisms studied in the same populations.

Effects of Goldstone bosons on gamma-ray bursts

Gamma-ray bursts (GRBs) are the most energetic explosion events in the universe. An amount of gravitational energy of the order of the rest-mass energy of the Sun is released from a small region within a short time. This should lead to the formation of a fireball of temperature in the MeV range, consisting of electrons/positrons, photons, and a small fraction of baryons. We exploit the potential of GRB fireballs for being a laboratory for testing particle physics beyond the Standard Model, where we find that Weinberg's Higgs portal model serves as a good candidate for this purpose. Due to the resonance effects, the Goldstone bosons can be rapidly produced by electron-positron annihilation process in the initial fireballs of the gamma-ray bursts. On the other hand, the mean free path of the Goldstone bosons is larger than the size of the GRB initial fireballs, so they are not coupled to the GRB's relativistic flow and can lead to significant energy loss. Using generic values for the GRB initial fireball energy, temperature, radius, expansion rate, and baryon number density, we find that the GRB bounds on the parameters of Weinberg's Higgs portal model are indeed competitive to current laboratory constraints.

Weinberg’s Higgs portal confronting recent LUX and LHC results together with upper limits onB+andK+decay into invisibles

We discuss a number of experimental constraints on Weinberg's Higgs portal model. In this framework, the standard model (SM) particle spectrum is extended to include one complex scalar field $S$ and one Dirac fermion $\ensuremath{\psi}$. These new fields are singlets under the SM gauge group and are charged under a global $U(1)$ symmetry. Breaking of this $U(1)$ symmetry results in a massless Goldstone boson $\ensuremath{\alpha}$ and a massive $CP$-even scalar $r$ and splits the Dirac fermion into two new mass-eigenstates ${\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}$, corresponding to Majorana fermions. The interest on such a minimal SM extension is twofold. On the one hand, if the Goldstone bosons are in thermal equilibrium with SM particles until the era of muon annihilation, their contribution to the effective number of neutrino species can explain the hints from cosmological observations of extra relativistic degrees of freedom at the epoch of last scattering. On the other hand, the lightest Majorana fermion ${\ensuremath{\psi}}_{\ensuremath{-}}$ provides a plausible dark matter candidate. Mixing of $r$ with the Higgs doublet $\ensuremath{\phi}$ is characterized by the mass of hidden scalar ${m}_{h}$ and the mixing angle $\ensuremath{\theta}$. We constrain this parameter space using a variety of experimental data, including heavy meson decays with missing energy, the invisible Higgs width, and direct dark matter searches. We show that different experimental results compress the allowed parameter space in complementary ways, covering a large range of ${\ensuremath{\psi}}_{\ensuremath{-}}$ masses ($5\ensuremath{\lesssim}{m}_{\ensuremath{-}}\ensuremath{\lesssim}100\text{ }\text{ }\mathrm{GeV}$). Though current results narrow the parameter space significantly (for the mass range of interest, $\ensuremath{\theta}\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$ to ${10}^{\ensuremath{-}4}$), there is still room for discovery ($\ensuremath{\alpha}$ decoupling at the muon annihilation era requires $\ensuremath{\theta}\ensuremath{\gtrsim}{10}^{\ensuremath{-}5}$ to ${10}^{\ensuremath{-}4}$). In the near future, measurements from ATLAS, CMS, LHCb, NA62, XENON1T, LUX, and CDMSlite will probe nearly the full parameter space.

Tricritical point in quantum phase transitions of the Coleman–Weinberg model at Higgs mass

The tricritical point, which separates first and second order phase transitions in three-dimensional superconductors, is studied in the four-dimensional Coleman–Weinberg model, and the similarities as well as the differences with respect to the three-dimensional result are exhibited. The position of the tricritical point in the Coleman–Weinberg model is derived and found to be in agreement with the Thomas–Fermi approximation in the three-dimensional Ginzburg–Landau theory. From this we deduce a special role of the tricritical point for the Standard Model Higgs sector in the scope of the latest experimental results, which suggests the unexpected relevance of tricritical behavior in the electroweak interactions. • The predictions for the tricritical point in the Ginzburg–Landau theory and the Coleman–Weinberg model are compared. • We prove the tricritical point in the Coleman–Weinberg is in agreement with the Thomas–Fermi approximation. • The recent discovery of the Higgs boson suggests the presence of tricritical behavior in the electroweak interactions.

Anthropic likelihood for the cosmological constant and the primordial density perturbation amplitude

Weinberg et al. calculated the anthropic likelihood of the cosmological constant using a model assuming that the number of observers is proportional to the total mass of gravitationally collapsed objects, with mass greater than a certain threshold, at t \rightarrow \infty. We argue that Weinberg's model is biased toward small \Lambda, and to try to avoid this bias we modify his model in a way that the number of observers is proportional to the number of collapsed objects, with mass and time equal to certain preferred mass and time scales. Compared to Weinberg's model, this model gives a lower anthropic likelihood of \Lambda_0 (T_+(\Lambda_0) ~ 5%). On the other hand, the anthropic likelihood of the primordial density perturbation amplitude from this model is high, while the likelihood from Weinberg's model is low. Furthermore, observers will be affected by the history of the collapsed object, and we introduce a method to calculate the anthropic likelihoods of \Lambda and Q from the mass history using the extended Press-Schechter formalism. The anthropic likelihoods for $\Lambda$ and Q from this method are similar to those from our single mass constraint model, but, unlike models using the single mass constraint which always have degeneracies between \Lambda and Q, the results from models using the mass history are robust even if we allow both \Lambda and Q to vary. In the case of Weinberg's flat prior distribution of \Lambda (pocket based multiverse measure), our mass history model gives T_+(\Lambda_0) ~ 10%, while the scale factor cutoff measure and the causal patch measure give T_+(\Lambda_0) \geq 30%.

Decomposition of Kullback–Leibler risk and unbiasedness for parameter-free estimators

The bias and variance of traditional parameter estimators are parameter-dependent quantities. The maximum likelihood estimate (MLE) can be defined directly on a family of distributions P and so is parameter-free. The parameter-invariance property of the MLE can be described by the fact that the MLE for the original parameter and the MLE for any reparametrization name the same distribution. We define parameter-free estimators to be P-valued random variables rather than parameter-valued random variables. The Kullback–Leibler (KL) risk is decomposed into two parameter-free quantities that describe the variance and squared bias of the estimator. We show that for exponential families the P-valued MLE is unbiased. We define the KL mean K of a P-valued random variable and show how K describes the long-run properties of this random distribution. For most families P, the KL mean of any P-valued random variable will not lie in P so that we define another mean M, called the distribution mean that is related to K and is an element of P. By allowing the distribution estimator to take values outside of P, the KL mean can be made to lie in P. We compare the MLE to non-P-valued estimators that have been suggested for the Hardy–Weinberg model. Results for the dual KL risk are also given.

The Tangled Bank: an introduction to evolution

The Tangled Bank: an introduction to evolution

Transforming growth factor-beta receptor type 1 (TGFBR1) is not associated with non-syndromic cleft lip with or without cleft palate in patients of Central European descent

Objective Transforming growth factor-beta (TGF-β) type 1 receptor (also known as activin receptor-like kinase 5, ALK5) is expressed in palatal tissue during embryogenesis. Experimental studies in transgenic mice with a genetic deletion of Alk5 showed that TGF-β type 1 receptor is required for upper lip and midline fusion of the hard and soft palate. In humans, association of TGF-β type 1 receptor gene ( TGFBR1) and the development of non-syndromic cleft lip with or without cleft palate (NSCL/P) had been observed in a multiethnic sample of Chinese, Philippine, Indian and Turkish families. In order to re-evaluate the relevance of these findings, we carried out a family-based association study among 218 NSCL/P families of Central European descent. Methods Genomic DNA was obtained from peripheral blood of 218 complete parent–offspring triads with NSCL/P. The sample comprised 14 patients with cleft lip only (CLO) and 204 patients with cleft lip and palate (CLP). Genotyping and transmission disequilibrium test (TDT) were performed on all 218 triads with a total of 17 tagging single-nucleotide polymorphisms (SNPs). We also performed testing for extended haplotypes and a log-linear model by Weinberg was used to screen parent-of-origin effects. Furthermore the use of estimates for the relative risks (RR) of Weinberg's model was obtained. Results TDT analysis revealed no significant transmission distortion, neither at the level of individual markers nor at the level of haplotypes. Similarly negative results were obtained when we restricted our analysis to the subgroup of patients with CLP ( n = 204). Relative risk calculations (RR) of the children's and mothers’ genotypes obtained negative results, after correction of p-values for multiple testing. Likewise application of Weinberg's log-linear model did not find any evidence for parent-of-origin effects in our sample. Conclusion Despite the ample evidence supporting the role of TGF-β type 1 receptor as a critically important and widespread morphogenetic regulator of craniofacial development in murine models, our results do not support TGFBR1 as major risk factor for NSCL/P in patients of Central European descent.

Mytilus species under rope culture in Scotland: implications for management

Mussel (Mytilus spp.) production is one of the most economically important aspects of global aquaculture and, in Scotland, production has increased from 262 t in 1986 to 4,219 t in 2006. Until recently, mussel production in Scotland was considered to be based exclusively on the blue mussel Mytilus edulis, the native species. In Europe, production is known to consist of M. edulis and M. galloprovincialis, while a third less profitable species M. trossulus occurs in the Baltic Sea, where it is unexploited. In Scotland, the sympatric occurrence of M. edulis, M. trossulus, M. galloprovincialis and their hybrids in cultivation in Loch Etive has recently been reported, with significant losses in production attributed to the presence of M. trossulus. Samples of mussels were taken at three depths from 10 rope-farm sites in Loch Etive. The distribution of the Mytilus species and their hybrids in Loch Etive was investigated using the Me 15/16 nuclear DNA locus for species and hybrid identification. All three species and their hybrids were detected and the data were in agreement with the Hardy–Weinberg model suggesting panmixia. Frequencies of M. galloprovincialis and its hybrids were very low. Overall, M. trossulus (37%) was found to be more common than M. edulis (30%) and 23% of the sampled mussels were M. trossulus × M. edulis hybrids. Species distribution did not correlate with year of settlement nor with salinities taken at the time of sampling. There were significant differences in species distribution due to site location and depth, with M. edulis being more frequent at 8 m depth and M. trossulus more common at shallower depths. These differences might be exploitable in management strategies for continuing production, for example to decrease the prevalence of M. trossulus at shellfish farms in favour of the more desirable M. edulis.

GMSB at a stable vacuum and MSSM without exotics from heterotic string

We show that it is possible to introduce the confining hidden sector gauge group SU(5)′ with the chiral matter 100′ plus 5¯0′, which are neutral under the standard model gauge group, toward a gauge mediated supersymmetry breaking (GMSB) in a Z12−I orbifold compactification of E8×E8′ heterotic string. Three families of MSSM result without exotics. We also find a desirable matter parity P (or R-parity) assignment. We note that this model contains the spectrum of the Lee–Weinberg model which has a nice solution of the μ problem.

A comparative analysis of demand estimation approaches in yield management

The objective of this paper is to provide a comparative analysis of demand estimation approaches in the context of yield management. We propose different theoretical modeling approaches for demand estimation. Demand is assumed to be function of price, time and inventory remaining. The proposed models are – intrinsically linear model, nonhomogeneous Poisson demand process (Leemis 1991), and a neural network approach. These are compared with three benchmark models: Swami and Khairnar (2003), Tretheway and Weinberg (1991) model, and price‐based model. Four representative demand data sets from the car rental business are used (Wang 2001). Our empirical analysis results show that the proposed intrinsically linear model and neural network approach provide good estimates of demand.

Alteration of SMRT Tumor Suppressor Function in Transformed Non-Hodgkin Lymphomas

Indolent non-Hodgkin lymphomas are characterized by a prolonged phase that is typically followed by a clinical progression associated with an accelerated clinical course and short survival time. Previous studies have not identified a consistent cytogenetic or molecular abnormality associated with transformation. The development of a transformed phenotype, evolving from the original low-grade component, most likely depends on multiple genetic events, including the activation of synergistic dominant oncogenes and a loss of tumor suppressor gene functions. Complex karyotypes and relatively bad chromosome morphology are typical of transformed non-Hodgkin lymphomas, rendering complete cytogenetic analysis difficult. Here, we report the use of transformed non-Hodgkin lymphoma cell lines and primary samples to identify the involvement of the silencing mediator of retinoic acid and thyroid hormone receptor (SMRT) gene that maps at chromosome 12q24 in transformed non-Hodgkin lymphomas. We also show that down-regulation of SMRT in the immortalized "Weinberg's model" cell lines induces transformation of the cells. Assessment of cDNA array profiles should further help us to design a working model for SMRT involvement in non-Hodgkin lymphoma transformation as a novel, nonclassical tumor suppressor.