Fisher Model Research Articles

Strong convergence and stationary distribution of an explicit scheme for the Wright–Fisher model

A novel explicit time-stepping scheme, called Lamperti smooth sloping truncation (LSST) scheme, is devised in this paper to strongly approximate the Wright–Fisher model, whose coefficients violate the Lipschitz condition and whose solution process takes values in a bounded domain. The LSST scheme is constructed by combining the Lamperti-type transformation and the smooth sloping truncation. Under appropriate condition, it is proved that the convergence order of the LSST scheme can be up to one. Moreover, it is shown that the proposed scheme has a unique stationary distribution, which converges to that of the original model. Numerical examples are reported to confirm our theoretical findings.

Glass component analysis based on Fisher's linear discriminant model and random forest classification model

The production of ancient glass is the crystallization of the wisdom of the majority of ancient working people in China. The differences in fluxes and the differences in the burial environment during weathering have a great impact on its chemical composition content. In this paper, a relevant classification model is established based on the data of various properties of glass. In this paper, Fisher linear discriminant model and random forest classification model were established according to the content of different chemical components, and Fisher linear discriminant model, which is easier to test for sensitivity analysis, was selected. Next, the clustering results were obtained by systematically clustering high potassium glass and lead-barium glass, and the classification basis was determined by drawing a line graph and then establishing a subclass classification model to classify high potassium glass into low potassium subclasses and high calcium subclasses. Sensitivity analysis was performed by changing the values of key parameters to check the reasonableness and stability of the subclass classification model. A discriminant model was established to initially determine the categories of eight unknown classified glass artifacts. Sensitivity analysis was performed by changing the key variables through the gradient descent method, and the model was obtained to have good sensitivity.

Traveling wave speed and profile of a “go or grow” glioblastoma multiforme model

Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction–diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction–diffusion GBM model based on the ‘go or grow’ hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.

In depth analysis of Fisher model and explore its limitation

This paper shows how people develop the concept of time value of money or the interest rate in the financial market model, how to derive individual savings decisions from corporate investment decisions, and why the net present value rule applies to decision-making. Specifically analyze the relationship between capital market line and Fisher model. And based on the Chinese stock market to further study the Fisher model and show its role.

Time-Series Sequences for Evolutionary Inferences.

The application of genomics to evolutionary biology has provided unprecedented power and resolution to investigate processes like mutation (Nachman and Crowell 2000; Rozhok and Degregori 2019), genetic drift (Whitney and Garland 2010; Funk et al. 2016), gene flow (Gallego-García et al. 2019; LaCava et al. 2021), and natural selection (Brauer et al. 2016; Martins et al. 2018). Evolutionary genomics has historically used contemporary or single-timepoint samples to study microevolutionary processes that most often depend on idealized model assumptions (e.g., Wright–Fisher model) (Butlin 2008; Hoban et al. 2016). For example, genome scanning methods aim to detect natural selection by assuming that the impact of selection can be discerned from the effects of neutral evolutionary processes on genetic differentiation (Hoban et al. 2016). However, different demographic scenarios can also produce signatures of selection, leading to false positives (Lotterhos and Whitlock 2015; Haasl and Payseur 2016). Similarly, when using measures of genetic differentiation to estimate gene flow, most models assume that population size is large enough that genetic drift is negligible—that is, not driving neutral divergence between populations (Whitlock and McCauley 1999; Ma et al. 2015).

Loss and fixation of strongly favoured new variants: Understanding and extending Haldane’s result via the Wright–Fisher model

The implications of Haldane’s analysis for the fixation of beneficial alleles lies at the heart of much of ‘population genetic thinking’ and underlies many approaches that have been tailored to the detection of positive selection. Within the framework of a branching process, Haldane gave an approximation for the probability that fixation ultimately occurs when the selective advantage of a beneficial allele is small (≪1). Here, we make no use of branching processes. Rather, we work solely within a finite-population Wright–Fisher framework. We use this framework to analyse where Haldane’s result applies, and extend Haldane’s analysis. In particular, we present results for: (i) the domain of applicability of Haldane’s analysis; (ii) the probability that loss occurs up to a given time; (iii) the probabilities that loss and fixation ultimately occur; (iv) an analytic approximation associated with the probability of loss and fixation ultimately occurring; (v) quantification of the crossover from weak to strong selection; (vi) determination of the number of invasive alleles that have a significant probability (>0.95) of invading a novel population. We note that the results obtained for (ii), (iii) and (iv) hold for an arbitrary initial number of mutations, and for selection that can be arbitrarily strong. Our results have fundamental implications for population and conservation genetics, and open up new avenues to identify traces of historically beneficial alleles through comparative genomics.

Research on Cost Optimization of Supply Chain Network in Dairy Industry

The domestic dairy consumption market is constantly expanding, but most dairy products are perishable and difficult to preserve. Therefore, the supply chain network of the dairy industry is special and its cost is relatively high. Based on Marshall L. Fisher's supply chain matching model, this paper constructs an agile supply chain network for the dairy industry, which is cost-optimized for each node and the whole.

Usury and the Paretian Objection

This paper has the following goals: 1) to prove that the contract of usury suffers from a self-contradiction, both from the viewpoint of the lender and the borrower; 2) to demonstrate the self-contradictory nature of the contract of usury by means of the Fisher model of the inter-temporal choice; 3) to prove that both the lender and the borrower pronounce the consent to the basic contract involuntarily because the former as well as the latter is acting under the indirect coercion; 4) to respond to Paretian objection that the Pareto improvement implies the mutual voluntariness, which is why there is no justification for the state to not enforce the contracts of usury. The author contends that from a subjective viewpoint, the contract of usury is a complex of two contracts which contradict each other: the basic contract and the super-contract. From the lender’s perspective, the basic contract is a loan and the super-contract is a sale of the loan. Since the lender negates his will to give a loan by the sale of the loan, the lender’s consent to the contract of usury as whole is self-contradictory. From the borrower’s perspective, the basic contract is a gift to the lender and the super-contract is a sale of this gift for a loan. Since the borrower negates his will to give a gift by the sale of the gift, the borrower’s consent to the contract of usury as a whole is self-contradictory. Next, the author contends that from an objective viewpoint, the contract of usury is an example of a non-equal “exchange”, i. e. a complex of an exchange (loan) and a transfer (usurious interest). Since the borrower does not give the transfer voluntarily, the lender violates the commutative justice by the contract of usury. To the Paretian objection that since both the lender and the borrower move onto a higher indifference curve thanks to the contract of usury, it must be a voluntary exchange, the author responds that the Pareto improvement does not imply the mutual voluntariness. The way how both the lender and the borrower move onto a higher indifference curve is not a voluntary exchange. There is no way to move onto a higher indifference curve in the contract of usury through a voluntary exchange. The contract of usury is neither an exchange, nor voluntary. It is not an exchange because it violates the equality in exchange. It is not voluntary, either, because it suffers from a double self-contradiction and voluntariness cannot be predicated to a self-contradictory (i. e. non-being) act of will. The author concludes that the state cannot and must not enforce the contracts of usury. It cannot because these contracts suffer from a double self-contradiction. It must not, either, because these contracts violate the commutative justice and it is the purpose of the state to protect the justice.

Diffusion approximations in population genetics and the rate of Muller’s ratchet

The Wright–Fisher binomial model of allele frequency change is often approximated by a scaling limit in which selection, mutation and drift all decrease at the same 1/N rate. This construction restricts the applicability of the resulting ‘Wright–Fisher diffusion equation’ to the weak selection, weak mutation regime of evolution. We argue that diffusion approximations of the Wright–Fisher model can be used more generally, for instance in cases where genetic drift is much weaker than selection. One important example of this regime is Muller’s ratchet phenomenon, whereby deleterious mutations slowly but irreversibly accumulate through rare stochastic fluctuations. Using a modified diffusion equation we derive improved analytical estimates for the mean click time of the ratchet.

TheWeight: A simple and flexible algorithm for simulating non‐ideal, age‐structured populations

Abstract The Wright–Fisher model, which directs how matings occur and how genes are transmitted across generations, has long been a lynchpin of evolutionary biology. This model is elegantly simple, analytically tractable and easy to implement, but it has one serious limitation: essentially no real species satisfies its many assumptions. With growing awareness of the importance of jointly considering both ecology and evolution in eco‐evolutionary models, this limitation has become more apparent, causing many researchers to search for more realistic simulation models. A recently described variation retains most of the Wright–Fisher simplicity but provides greater flexibility to accommodate departures from model assumptions. This generalized Wright–Fisher model relaxes the assumption that all individuals have identical expected reproductive success by introducing a vector of parental weights w that specifies relative probabilities different individuals have of producing offspring. With parental weights specified this way, expectations of key demographic parameters are simple functions of w. This allows researchers to quantitatively predict the consequences of non‐Wright–Fisher features incorporated into their models. An important limitation of the Wright–Fisher model is that it assumes discrete generations, whereas most real species are age structured. Here I show how an algorithm (TheWeight) that implements the generalized Wright–Fisher model can be used to model evolution in age‐structured populations with overlapping generations. Worked examples illustrate simulation of seasonal and lifetime reproductive success and show how the user can pick vectors of weights expected to produce a desired level of reproductive skew or a desired Ne/N ratio. Alternatively, weights can be associated with heritable traits to provide a simple, quantitative way to model natural selection. Using TheWeight, it is easy to generate positive or negative correlations of individual reproductive success over time, thus allowing explicit modelling of common biological processes like skip breeding and persistent individual differences. Code is provided to implement basic features of TheWeight and applications described here, including one scenario implemented in SLiM. However, required coding changes to the Wright–Fisher model are modest, so the real value of the new algorithm is to encourage users to adopt its features into their own or others' models.

New quinary cesium vanadium (IV) fluorophosphates, CsVOF(PO3F) and CsV2O2F(PO3F)2·H2O

Two new quinary cesium vanadium fluorophosphates CsVOF(PO3F) and CsV2O2F(PO3F)2·H2O were prepared through hydrothermal reactions. The crystal structure of CsVOF(PO3F) consists of two-dimensional [VPO4F2]- sheets, formed by isolated V2F2O8 dimers. However, The anionic framework structure {V2O3(PO3F)2}3- in CsV2O2F(PO3F)2·H2O contains one-dimensional parallel ∞[V2O6F]5- chains, bidentate-bridged and unidentate-bridged with PO3F tetrahedral, respectively. The magnetic data have been analyzed with two different equations, i.e. the dimeric Bleaney-Bowers expression and the Fisher model with interchain mean-field corrections. The magnetism of CsVOF(PO3F) can best be described with the dimeric Bleaney-Bowers expression (J/kB ​= ​-4.1 (1) K, and g ​= ​1.80(1)). For the compounds CsV2O2F(PO3F)2·H2O, excellent fits are obtained with the Fisher model with interchain mean-field corrections, yielding Jintra/kB ​= ​−4.5(1) K and Jinter/kB ​= ​0.11(2) K, and g ​= ​2.19(1) .

Synthesis, crystal structure and magnetic properties of coordination compounds of Mn(NCS)2 with the 3-bromopyridine ligand

Abstract Reactions of Mn(NCS)2 with 3-bromopyridine in acetonitrile lead to the formation of Mn(NCS)2(3-bromopyridine)4 (1) and Mn(NCS)2(3-bromopyridine)2(MeCN)2 (2) that were characterized by single crystal X-ray diffraction. Compounds 1 and 2 consist of discrete complexes, in which the Mn(II) cations are octahedrally coordinated by two trans-N-bonding thiocyanate anions and four pyridine (1) or two pyridine and two acetonitrile ligands (2). Thermoanalytical measurements on 1 and 2 have shown that upon heating half of the 3-bromopyridine co-ligands from 1 or both acetonitrile ligands from 2 are removed leading to a crystalline phase with the composition [Mn(NCS)2(3-bromopyridine)2] n (3-II). From dry n-butanol a phase with the same composition was obtained (3-I) that corresponds to a polymorphic or isomeric form of 3-II. Crystal structure analysis of 3-I shows that in this form the Mn cations are linked by pairs of anionic ligands into linear chains. The results of magnetic measurements on 3-I show antiferromagnetic interactions along the chains and the analysis of the magnetic susceptibility using the Fisher model for chains gave a J value of −5.76(5) K.

Procrustes Analysis for High-Dimensional Data

The Procrustes-based perturbation model (Goodall in J R Stat Soc Ser B Methodol 53(2):285–321, 1991) allows minimization of the Frobenius distance between matrices by similarity transformation. However, it suffers from non-identifiability, critical interpretation of the transformed matrices, and inapplicability in high-dimensional data. We provide an extension of the perturbation model focused on the high-dimensional data framework, called the ProMises (Procrustes von Mises–Fisher) model. The ill-posed and interpretability problems are solved by imposing a proper prior distribution for the orthogonal matrix parameter (i.e., the von Mises–Fisher distribution) which is a conjugate prior, resulting in a fast estimation process. Furthermore, we present the Efficient ProMises model for the high-dimensional framework, useful in neuroimaging, where the problem has much more than three dimensions. We found a great improvement in functional magnetic resonance imaging connectivity analysis because the ProMises model permits incorporation of topological brain information in the alignment’s estimation process.

Extinction threshold and large population limit of a plant metapopulation model with recurrent extinction events and a seed bank component

We introduce a new model for plant metapopulations with a seed bank component, living in a fragmented environment in which local extinction events are frequent. This model is an intermediate between population dynamics models with a seed bank component, based on the classical Wright–Fisher model, and Stochastic Patch Occupancy Models (SPOMs) used in metapopulation ecology. Its main feature is the use of “ghost” individuals, which can reproduce but with a very strong selective disadvantage against “real” individuals, to artificially ensure a constant population size. We show the existence of an extinction threshold above which persistence of the subpopulation of “real” individuals is not possible, and investigate how the seed bank characteristics affect this extinction threshold. We also show the convergence of the model to a SPOM under an appropriate scaling, bridging the gap between individual-based models and occupancy models.

The Impulse Response of Domestic and Foreign Interest Rate in Output, Price, Exchange Rate Model, a Deconstructed Derivation and Economic Calibration of Vector Error Correction Model

How to assess external shocks, whether they are inflationary shocks or interest rate shocks without warning, is crucial to construct smooth and predictable financial market. The purpose of this paper is to analyze the short-run and long-run effects of shocks on an economy under chaotic conditions of uncertainty using the Vector Error Correction Model (VECM). A comprehensive and detailed derivation process is presented for VECM and reveals the dynamics of interest rates and inflation in the face of external shocks, through Cholesky ordering and impulse response decomposition. With a constraint, the VECM model is also used to derive its two applications in well-known theoretical fields, the Fisher model and the uncovered interest rate parity (UIP) theory.

Research on Financial Risk Early Warning in the Online Game Industry Based on Random Forest and Fisher Discriminant Method

With the rapid rise of the online game industry and the intensification of market competition, online game enterprises face different degrees of financial risks. It is necessary to establish an effective financial risk early warning model. Based on the online game industry, this paper constructs an index system from six dimensions, and makes an empirical study on financial risk early warning. First of all, a financial risk early warning model based on the random forest is constructed, and the prediction accuracy is as high as 100%, but the machine learning model has poor explanatory ability. Therefore, according to the index of random forest screening, a financial risk warning model based on the Fisher discriminant method is established. This model optimized the prediction effect of the original fisher's discriminant model and the prediction accuracy reached 87.5%. Finally, suggestions are made from the three aspects of cash flow, solvency and profitability of online game enterprises, and national support policies.

Correcting Bias in Allele Frequency Estimates Due to an Observation Threshold: A Markov Chain Analysis.

There are many problems in biology and related disciplines involving stochasticity, where a signal can only be detected when it lies above a threshold level, while signals lying below threshold are simply not detected. A consequence is that the detected signal is conditioned to lie above threshold, and is not representative of the actual signal. In this work, we present some general results for the conditioning that occurs due to the existence of such an observational threshold. We show that this conditioning is relevant, for example, to gene-frequency trajectories, where many loci in the genome are simultaneously measured in a given generation. Such a threshold can lead to severe biases of allele frequency estimates under purifying selection. In the analysis presented, within the context of Markov chains such as the Wright–Fisher model, we address two key questions: (1) “What is a natural measure of the strength of the conditioning associated with an observation threshold?” (2) “What is a principled way to correct for the effects of the conditioning?”. We answer the first question in terms of a proportion. Starting with a large number of trajectories, the relevant quantity is the proportion of these trajectories that are above threshold at a later time and hence are detected. The smaller the value of this proportion, the stronger the effects of conditioning. We provide an approximate analytical answer to the second question, that corrects the bias produced by an observation threshold, and performs to reasonable accuracy in the Wright–Fisher model for biologically plausible parameter values.

Impulsive fishery resource transporting strategies based on an open‐ended stochastic growth model having a latent variable

In inland fisheries, transporting fishery resource individuals from a habitat to spatially apart habitat(s) has recently been considered for fisheries stock management in the natural environment. However, its mathematical optimization, especially finding when and how much of the population should be transported, is still a fundamental unresolved issue. We propose a new impulse control framework to tackle this issue based on a simple but new stochastic growth model of individual fishes. The novel growth model governing individuals' body weights uses a Wright–Fisher model as a latent driver to reproduce plausible growth dynamics. The optimization problem is formulated as an impulse control problem of a cost–benefit functional constrained by a degenerate parabolic Fokker–Planck equation of the stochastic growth dynamics. Because the growth dynamics have an observable variable and an unobservable variable (a variable difficult or impossible to observe), we consider both full‐information and partial‐information cases. The latter is more involved but more realistic because of not explicitly using the unobservable variable in designing the controls. In both cases, resolving an optimization problem reduces to solving the associated Fokker–Planck and its adjoint equations, the latter being nontrivial. We present a derivation procedure of the adjoint equation and its internal boundary conditions in time to efficiently derive the optimal transporting strategy. We finally provide a demonstrative computational example of a transporting problem of Ayu sweetfish Plecoglossus altivelis altivelis based on the latest real data set.

Hemopoiesis and Immune Cell Perturbations during Venetoclax Plus Azacytidine Treatment in Acute Myeloid Leukemia

Treatment of acute myeloid leukemia (AML) in elderly is still challenging. Indeed, high-dose chemotherapy followed by hematopoietic stem cell transplantation with myeloablative regimens is not always feasible because patients are often unfit and have several comorbidities; however, they frequently show multiple negative prognostic factors and have a worse overall survival compared to younger adults. Venetoclax, the first-in-class Bcl-2 antagonist and first approved for treatment of chronic lymphocytic leukemia, inhibits the anti-apoptotic functions of Bcl-2 inducing apoptosis and tumor growth arrest. Venetoclax is also used in combination with azacytidine, or decitabine, or low-dose cytarabine for treatment of elderly newly diagnosed AML. However, several mechanisms of resistance have already been described, such as increased expression of other anti-apoptotic proteins by the leukemic clone. In this case series, we investigated hematopoiesis and immune cell perturbations during venetoclax plus azacytidine treatment in elderly AML patients.A total of six AML patients (M/F, 2/4; median age, 71 years old; range, 63-79 years) were retrospectively evaluated at the Hematology and Transplant Center, University Hospital “San Giovanni di Dio e Ruggi d'Aragona”, Salerno, Italy. Patients received a diagnosis of AML based on the 2016 World Health Organization (WHO) criteria and chemotherapy with azacytidine 75 mg/m 2 daily for 7 days per cycle and venetoclax 70 mg/daily. Two patients were NPM1 mutated (one of them also had mutated IDH1, VAF 27.2%), while all subjects had FLT3 wild type. Based on the 2017 European LeukemiaNet risk classification, two patients had favorable risk and four intermediate. Median follow-up was 10.1 months (range, 4.9-16.6 months), and all patients were in partial or complete remission at the time of writing. Flow cytometry immunophenotype, complete blood counts (CBCs), and WT1 expression levels were performed at diagnosis and after every cycle of therapy as per our institutional guidelines.In our case series, leukemic cells were already decreased after the first cycle of therapy (blasts by flow cytometry + SD, 54.7+39.9% vs 4.2+5.4%, diagnosis vs post I cycle; P = 0.0671; paired t-test performed), while normal granulocytes detected by flow cytometry recovered only after the third cycle of therapy (20.7+23.7% vs 53+6.6%, diagnosis vs post III cycle; P = 0.1396; uncorrected Fisher's mixed model performed). Treated patients also displayed a contextual decreased in WT1 expression levels (normalized WT1 copy number + SD, 1810+2723 copies vs 201+132.9 copies, diagnosis vs post I cycle; P = 0.2660; paired t-test performed). Platelet count tended to increase after the first cycle (P = 0.0680); however, at the end of the second cycle, half of patients were again thrombocytopenic (platelets < 100 x 10 3/µL). Interestingly, percentage of lymphocytes detected by flow cytometry were significantly increased after the second cycle of azacytidine plus venetoclax compared to baseline and after the first cycle of therapy (mean+SD, 13.5+13.3% vs 48+8.7%, diagnosis vs post II cycle; P = 0.0167; and vs 28+11.3%, vs post III cycle; P = 0.0480), likely because an increase in Natural Killer (NK) cell frequency peaking after the second cycle (mean+SD, 19.4+4.4% vs 32.5+15.1%, diagnosis vs post II cycle; P = 0.1383). Moreover, five out of six patients displayed expansion of plasma cells detected by flow cytometry in the bone marrow after the first cycle: in particular, one case patient had expansion of aberrant CD45-/dimCD38++CD138++CD56+CD19- plasma cells, while one subject showed only a transient appearance of clonal plasma cells after the second cycle. No differences in bone marrow monocyte frequencies were described during treatment.Our preliminary results added evidence to efficacy and safety of the combination of venetoclax and azacytidine in treatment of elderly AML in a real-world setting. These drugs might synergistically function on hematopoiesis by inducing apoptosis of neoplastic cells while favoring differentiation of other lineages, as suggested by the expansion of plasma cells, or triggering NK-mediated immunosurveillance. However, prognostic and clinical significance of plasma cell and NK cell expansion in the setting of AML treatment needs to be further explored in larger prospective cohorts. DisclosuresNo relevant conflicts of interest to declare.

Coalescent models derived from birth–death processes

A coalescent model of a sample of size n is derived from a birth–death process that originates at a random time in the past from a single founder individual. Over time, the descendants of the founder evolve into a population of large (infinite) size from which a sample of size n is taken. The parameters and time of the birth–death process are scaled in N0, the size of the present-day population, while letting N0→∞, similarly to how the standard Kingman coalescent process arises from the Wright–Fisher model. The model is named the Limit Birth–Death (LBD) coalescent model. Simulations from the LBD coalescent model with sample size n are computationally slow compared to standard coalescent models. Therefore, we suggest different approximations to the LBD coalescent model assuming the population size is a deterministic function of time rather than a stochastic process. Furthermore, we introduce a hybrid LBD coalescent model, that combines the exactness of the LBD coalescent model model with the speed of the approximations.