Poisson distribution and process as a well-fitting pattern for counting variables in biologic models

One of the major criticisms directed to basic research on high dilution effects is the lack of a steady statistical approach; therefore, it seems crucial to fix some milestones in statistical analysis of this kind of experimentation. Since plant research in homeopathy has been recently developed and one of the mostly used models is based on in vitro seed germination, here we propose a statistical approach focused on the Poisson distribution, that satisfactorily fits the number of non-germinated seeds. Poisson distribution is a discrete-valued model often used in statistics when representing the number X of specific events (telephone calls, industrial machine failures, genetic mutations etc.) that occur in a fixed period of time, supposing that instant probability of occurrence of such events is constant. If we denote with λ the average number of events that occur within the fixed period, the probability of observing exactly k events is: P(k) = e-λ λk /k! , k = 0, 1,2,… This distribution is commonly used when dealing with rare effects, in the sense that it has to be almost impossible to have two events at the same time. Poisson distribution is the basic model of the socalled Poisson process, which is a counting process N(t), where t is a time parameter, having these properties: - The process starts with zero: N(0) = 0; - The increments are independent; - The number of events that occur in a period of time d(t) follows a Poisson distribution with parameter proportional to d(t); - The waiting time, i.e. the time between an event and another one, follows and exponential distribution. In a series of experiments performed by our research group ([1], [2]., [3], [4]) we tried to apply this distribution to the number X of non-germinated seeds out of a fixed number N* of seeds in a Petri dish (usually N* = 33 or N* = 36). The goodness-of-fit was checked by different tests (Kolmogorov distance and chi-squared), as well as with the Poissonness plot proposed by Hoaglin [5]. The goodness-of-fit of Poisson distribution allows to use specific tests, like the global Poisson test (based on a chi-squared statistics) and the comparison of two Poisson parameters, based on the statistic z = X1–X2 / (X1+X2)1/2 which is, for large samples (at least 20 observations) approximately standard normally distributed. A very clear review of these tests based on Poisson distribution is given in [6]. This good fit of Poisson distribution suggests that the whole process of germination of wheat seeds may be considered as a non-homogeneous Poisson process, where the germination rate is not constant but changes over time. Keywords: Poisson process, counting variable, goodness-of-fit, wheat germination References [1] L.Betti, M.Brizzi, D.Nani, M.Peruzzi. A pilot statistical study with homeopathic potencies of Arsenicum Album in wheat germination as a simple model. British Homeopathic Journal; 83: 195-201. [2] M.Brizzi, L.Betti (1999), Using statistics for evaluating the effectiveness of homeopathy. Analysis of a large collection of data from simple plant models. III Congresso Nazionale della SIB (SocietàItaliana di Biometria) di Roma, Abstract Book, 74-76. [3] M.Brizzi, D.Nani, L.Betti, M.Peruzzi. Statistical analysis of the effect of high dilutions of Arsenic in a large dataset from a wheat germination model. British Homeopathic Journal, 2000;, 89, 63-67. [4] M.Brizzi, L.Betti (2010), Statistical tools for alternative research in plant experiments. “Metodološki Zvezki – Advances in Methodology and Statistics”, 7, 59-71. [5] D.C.Hoaglin (1980), A Poissonness plot. “The American Statistician”, 34, 146-149. [6] L.Sachs (1984) Applied statistics. A handbook of techniques. Springer Verlag, 186-189.

Modelling and iterative learning control of internal pressure for high-speed trains under excitation of varying-amplitude tunnel pressure waves

Traditional control algorithm of shutting down the air ducts for a fixed period is not applicable to take both the riding comfort and the air quality inside high-speed train carriages into account in long tunnels. Inspired by the morphological similarity of the tunnel pressure waves generated by the same train passes through the same tunnel, an upgraded iterative learning control algorithm for suppressing the air pressure variation excited by the quasi-periodic varying-amplitude tunnel pressure wave is developed. Firstly, the mathematical model of the control system is established, in which the air ducts, gaps and random interferences are considered. Then, the methodology of determining the goal in each iteration is formed, and the implementation of the iterative learning control algorithm is discussed. Finally, simulations of the algorithm are carried out. The simulation results show that in the upgraded iterative learning control algorithm, both the goal and the output of the air pressure inside the carriage will converge into a range determined by the amplitude and random interferences. By comparing with the traditional control algorithm, the upgraded iterative learning control algorithm is more adaptable to meet the needs of riding comfort.

The Systematic Risk at the Crisis - A Multifractal Non-uniform Wavelet Systematic Risk Estimation

The Capital Asset Pricing Model is a widely applied model to describe risky markets and to deduce their systematic risk. Its estimation, therefore, remains an important task in Econo-financial studies. Empirically, it focuses on the impact of return interval on the betas. Existing studies somehow turn around the same idea of measuring the value of the beta according to the uniform intervals of time during a fixed period. However, it is noticed easily, and especially in the last decade that many factors such as socio-political, and Econo-environmental ones have led to a perturbation in the timeline of the worldwide development, and especially in countries and regions having political changes. This led us to introduce a new idea of risk estimation taking into account the non-uniform changes in markets by introducing a non-uniform wavelet analysis. We aim to explain the Econo-political situation of Arab spring countries and the effect of the revolutions on the market beta. The main novelty is firstly the construction of a dynamic backward-forward model for missing data, and next the application of random non-uniform wavelets. The proposed procedure will be acted empirically on a sample corresponding to TUNINDEX stock as a representative index of the Tunisian market actively traded over the period January 14, 2016, to January 13, 2021. The chosen 5-years period is important as it constitutes the first 5-years-after the revolution and depends strongly on the Socio-Econo-political stability in the revolutionary countries.

Reproduction number for an age of infection structured model

We study the basic reproduction number ($R_0$) in an epidemic model where infected individuals are initially asymptomatic and structured by the time since infection. At the beginning of an epidemic outbreak the computation of $R_0$ relies on limited data based mostly on symptomatic cases, since asymptomatic infected individuals are not detected by the surveillance system. $R_0$ has been widely used as an indicator to assess the dissemination of infectious diseases. Asymptomatic individuals are assumed to either become symptomatic after a fixed period of time or they are removed (recovery or disease-related death).We determine $R_0$ , understood as the expected secondary symptomatic cases produced by a symptomatic primary case through a chain of asymptomatic infections. $R_0$ is computed directly by interpreting the model ingredients and also using a more systematic approach based on the next-generation operator. Reported Covid-19 cases data during the first wave of the pandemic in Spain are used to fit the model and obtain both values of $R_0$ before and after the severe lockdown imposed in March 2020. The results confirm that SARS-CoV-2 was expanding within the population before the lockdown whereas the virus spreading was controlled two weeks after the lockdown. p, li { white-space: pre-wrap; }

Enhancement of coherence resonance induced by inhibitory autapse in Hodgkin–Huxley model

Inhibitory effect often suppresses electronic activities of the nervous system. In this paper, the inhibitory autapse is identified to enhance the degree of coherence resonance (CR) induced by noise in the Hodgkin–Huxley (HH) model with Hopf bifurcation from resting state to spiking with nearly fixed period [Formula: see text]. Without noise, the inhibitory autapse can induce a post inhibitory rebound (PIR) spike from the resting state at time delay approximating [Formula: see text] and can inhibit a spike of spiking at time delay approximating [Formula: see text]. In the presence of noise, CR characterized by maximal value of power spectrum of spike trains appears in a wide range of both time delay and conductance of autapse. With increasing autaptic conductance, CR degree becomes stronger for time delay approximating [Formula: see text] plus integer (from 0) multiples of [Formula: see text], because the inhibitory autaptic current pulses can induce more PIR spikes. The decrease of CR degree at time delay approximating integer (from 1) multiples of [Formula: see text] can be explained by the inhibition effect. The promotion of coherence resonance degree and the underlying PIR mechanism induced by inhibitory self-feedback extends the paradoxical phenomenon of inhibitory autapse to stochastic system and presents potential measures to modulate CR degree and information processing.

Money creation and the revolution. Along the Path to Real Change

When you store your belongings in a private locker, does the owner of the locker pay you? On the contrary, you pay the owner, for he is providing you with a service called safe-keeping. In effect, the owner holds your belongings safe until you take them back. So, why is it that you accept money from a bank to hold your money for you? The obvious answer is that the bank is not holding your money; it is lending it out and rewarding you with a portion of what it collects in interest. If you are happy with this arrangement, you have likely sought out a bank in your neighborhood that provides you with the greatest return on your deposit. Unfor tunately, there are several things very wrong with this type of transaction. Most important is that you are engaging in a tran saction that is commercially unsound. You and your bank engage in a legally non-binding agreement when, on the one hand, your bank promises to return your deposit on demand, and on the other hand, loans a portion of it to others for a specified period of time. Contractually, these two acts are incompatible, as the same money cannot be both a de-mand deposit and a loan simultaneously. Either, you deposit your money, reserve the right to de-mand it back at any moment, and pay the bank for holding it on your behalf. This is called a demand deposit. Or, you surrender your right to your money for a specific period of time, permit your bank to lend it to others, and receive interest for your risk and sacrifice. This is called a time deposit. Commercially, treating your demand deposit as money that can be loaned to others is not an enforceable contract, for the law insists that there must be mutual assent when two parties enter into an agreement. You and the bank are simply at odds when you expect to retrieve your money at any moment on demand, and the bank lends a portion of it to others for a fixed period. Legally speaking, both parties to the transaction do not agree to the same contractual terms in the same sense.

ANALISIS PERENCANAAN PERSEDIAAN BAHAN BAKU PAKAN TERNAK DENGAN MENGGUNAKAN METODE LOT SIZING (Studi Kasus Pada PT. Japfa Comfeed Indonesia Tbk, Unit Makassar)

Permasalahan yang dihadapi perusahaan adalah tingginya total biaya persediaan pada bahan baku pakan ternak kategori mayor dalam penelitian ini bahan baku tersebut diantaranya Jagung Lokal, Wheat Bran Pellet, Biji Batu dan Katul. Oleh karena itu, penelitian ini bertujuan untuk mengoptimalkan kuantitas pemesanan (lot size) agar diperoleh total biaya yang minimum. Pada penelitian ini dilakukan perencanaan persediaan menggunakan Fixed Period Requirement (FPR) dan Algoritma Wagner-Whitin (AWW) dengan mempertimbangkan kuantitas pemesanan. Langkah awal yang dilakukan ialah peramalan permintaan menggunakan Weighted Moving Average dan Single Exponential Smoothing, kemudian dilakukan perbaikan terhadap manajemen persediaan bahan baku pakan ternak kategori mayor, dengan menentukan safety stock dan reorder point, kuantitas pemesanan optimal, dan total biaya persediaan. Hasil dari penelitian yang dilakukan ialah diperoleh safety stock dan reorder point setiap jenis material untuk mengantisipasi apabila terjadi stock out, serta lot size yang optimal agar tidak terjadi overstock. Hasil yang didapatkan setelah melakukan perhitungan menggunakan FPR adalah sebesar Rp. 68.836.795.791 dan AWW menunjukkan hasil sebesar Rp 3.216.795.791 Berdasarkan hasil tersebut maka metode yang menghasilkan total biaya minimum adalah AWW.

EXCITATION OF FREAK WAVE BY NATURAL OSCILLATIONS OF THE WATER BODY

In linear theory the formation of extreme waves their existence is interpreted as a local superposition of surface monochromatic waves. Natural water areas are resonators that have their own set of natural oscillations – standing waves of stable spatial structure and fixed period. In the spectra of waves of many water bodies of World Ocean observed double high waves, this is explained by the tidal-seiche resonance. During a storm, the energy of natural oscillations increases ten times the background energy, during a tsunami it can increase up to three orders of magnitude. Examples of the effects of natural oscillations on the coast are given, and it is reported about the increased probability of the occurrence on the coast freak waves. Additionally, it is noted that natural oscillations in water mass are a normal state for any body of water at any time of its existence. The corresponding indices of the water fluctuations of the water basins are given. The events of extreme waves during the accidents at DniproHES (Zaporizhia) on August 18, 1941, and the Kurenivsky dam (Kyiv) on March 13, 1961, are presented. The excitement of the freak wave can be interpreted as enhancing the natural oscillations of the water basin, represented by standing waves of stable spatial structure, fixed period and high probability of waves in the water body. This does not contradict the linear theory of the resonant formation of abnormally high waves. The purpose of the article is to investigate possible sources of the excitement of freak waves, the results are proposed to be implemented in the development of countermeasures to the destructive process. However, the waves carry out both destructive and creative work. A task is presented, which involves the development of measures to stimulate extreme waves. This will increase electricity generation. Affiliation of dam-break waves to freak waves can be doubtful. However, they formally correspond to the classical condition of double exceeding the significant wave height. Most water basins are integral anthropogenic sites. The variability of both natural and anthropogenic environments forces the overriding of systematization and definition. It is proposed to attribute extreme waves of dam-break waves to freak waves.