But matters would appear to stand somewhat differently with respect to the program-based variant of the algorithms-as-abstracts view. To get an impression for why this is so, note first that as with the notion of machine model, the num- ber of programming languages which have been introduced in computer science numbers at least into the hundreds. However, the characteristics which qualify a formalism as a programming language seem to be less well defined than in the case of machine models. This is witnessed, for instance, by the existence of differ- ent programming paradigms – e.g. declarative, functional, object-oriented, etc. – each of which can be understood to be based on a fundamentally different concep- tion of what is involved with providing a linguistic description of a mathematical procedure (cf., e.g., ). Given that these languages employ primitive constructs drawn from a wide range of developments in logic and mathematics – e.g. the typed and untyped-lambda calculus (LISP and Haskell), first- and higher-order logic ( ProLog , HiLog ), graph rewriting (GP), linear algebra ( Fortran ) – it seems unlikely that we can find an overarching mathematical definition analogous to
In communication and computer network research, network simulation is a technique where a programmodels the behavior of a network either by calculating the interaction between the different network entities (hosts/routers, data links, packets, etc) using mathematical formulas, or actually capturing and playing back observations from a production network. The behavior of the network and the various applications and services it supports can then be observed in a test lab; various attributes of the environment can also be modified in a controlled manner to assess how the network would behave under different conditions. When a simulation program is used in conjunction with live applications and services in order to observe end-to-end performance to the user desktop, this technique is also referred to as network emulation.
When speaking about the tumour environment, we tend to focus on the tissue that is in close spatial prox- imity to the cancer cells (microenvironment). However, we should not forget that the blood circulation system connects the metabolism in the cancer tissue with the organism metabolism (macroenvironment). In other words, a complete mathematical description of the tumour microenvironment should take into account the interaction between cancer cells and distant organs via the circulatory system and, by extrapolation, with nutri- tion. The manifestation of the muscle-wasting syndrome of cachexia in cancer patients is a demonstration of these distant interactions . Therefore, a definitive model of cancer metabolism should account for the in- teractions between cancer cells and distant organs. From the technical point of view, this will require to link metabolic models for the cancer cells, the stroma cells and the relevant distant organs such as the liver. The good news is that the community efforts in the recon- struction of the human metabolic network have already provided the first drafts of tissue-specific metabolic models , and some advanced refinements are already available for liver metabolism .
Unfortunately, the commercial world was not ready for data networks, and my work lay dormant for most of the 1960s as I continued to publish my results on networking technol- ogy while at UCLA where I had joined the faculty in 1963. In the mid-1960s, the Advanced Research Projects Agency (ARPA)—which was created in 1958 as the United States’ response to the Soviet Union’s 1957 launch of Sputnik— became interested in networks. ARPA had been support- ing a number of computer scientists around the country, and as new researchers were brought in they naturally asked ARPA to provide a computer on which they could do their research and moreover asked that their comput- ers contain all the hardware and software capabilities of all the other supported computers. Rather than duplicat- ing all these capabilities, ARPA reasoned that this com- munity of scientists would be able to share these special- ized and expensive computing resources if the computers were connected together by means of a data network. In 1966 ARPA enlisted the services of my former ofﬁce mate at MIT, Lawrence G. Roberts (1974), to lead the effort to develop, manage, fund, and deploy this data network. It was largely through Larry’s leadership and vision that this net- work came about. Because of my expertise in data network- ing, Larry called me to Washington to play a key role in preparing a functional speciﬁcation for this network, which was to be called the ARPANET (1970)—a government- supported data network that would use the technology I had elucidated in my research, which by then had come to be known as “packet switching.”
Abstract: The paper presents the results of mathematical and computer simulation of the interaction of radio pulses of an arbitrary nature. Pulses of a rectangular and Gaussian shape are considered. We also consider the evolution of the wave packet formed as a result of the decay of the bound quantum state. The main reason for the distortion of the pulse shape is the interaction of narrow-band spectral components of pulses.
We consider (5a–d) incorporating necessary conditions for an extremum, and examine the sufficiency conditions for a solution X * , Y * , L * , * to be a maximum (or minimum). Again we follow closely the discussion of this matter given by Baxley and Moorhouse (1984), but we make the calculations more explicit so that the novice or the economist not sufficiently familiar with mathematical concepts and manipulations can follow the steps relatively easily.
The absorbing ball property concerns only the signal dynamics. It is satisfied by many dissipative models of the form (2.2.4) —see Section 2.5. The squeezing property involves both the signal dynamics and the observation operator P. It is satisfied by several problems of interest provided that the assimilation time h is sufficiently small and that the ‘right’ parts of the system are observed; see again Section 2.5 for examples. We remark that several forms of the squeezing property can be found in the dissipative dynamical systems literature. They all refer to the existence of a contracting part of the dynamics. Their importance for filtering has been explored in [Hayden et al., 2011], [Brett et al., 2013] and [Chueshov, 2014]. It also underlies the analysis in [Kelly et al., 2014] and [Law et al., 2016], as we make apparent here. We have formulated the squeezing property to suit our analyses and with the intention of highlighting the similar role that it plays to detectability for linear problems, as explained in Subsection 2.4.2. The function V will represent a Lyapunov type function in Section 2.4. For all the chaotic examples in Section 2.5 the operator D will be chosen as the identity, but other choices are possible. As we shall see, the absorbing ball property is not required when a global form of the squeezing property, as may arise for linear problems, is satisfied.
To obtain more practice and experience of this type, experimentalists and modelers should collaborate more closely. On the one hand, modelers will need experi- ments specifically performed for some modeling aspects. At present, many data are available, and the data flow from -omics experiments can be overwhelming. How- ever, not all data are useful for the type of modeling out- lined in this article, and modelers will be dependent on experimentalists to perform other types of experiments . On the other hand, experimentalists will want to see genuinely new results coming out of models, especially if they had contributed data to the modeling effort. They will benefit from new, integrative interpretations of their data and from reliable modeling results and computa- tionally achieved hypotheses guiding the “next steps” in their research programs. The generic differences between laboratory or field experiments and computational approaches render it evident that this type of collabo- ration has true potential, but that it will take time and patience on both sides to make progress toward reaching some of this potential.
In most models leaflet symmetry is assumed, and only one leaflet or one-half of the leaflet is modeled to reduce computation time. Models that consider hemodynamic differences when the valves do not coapt centrally need to include at least two adjacent leaflets . One leaflet can close faster if an asymmetric retrograde blood flow is directed towards it . Asymmetric vortices contributed to higher flow shear stress on the leaflets of asymmetric bicuspid aortic valves, a congenital disorder known to have a high incidence of stenosis due to calcification . Modeling patient-specific valves from imaging data are inherently asymmetric and need to include all leaflets.
The publications of nutrition science often do not approach the real problems. The purely empirical descriptions are not sufficient any more; it is now necessary to dwell on the knowledge of the biological mechanisms. It is naive to study nitrogen metabolism in rumen independently of carbon metabolism; same, the energy and protein inputs are arbitrary limited when animal performance is determined. The research was thus directed to the possible contribution of the mathematical modelling, of the kind used so successfully in the physical sciences.
Here, a new definition of the approximation of finite-difference schemes arises: the approximation of asymptotic sets. At present, unfortunately, the theorems of closeness of the attractors of differential problems and their finite-dimensional operators have not been proved for all well-known climate models. The establishment of closeness between invariant measures on attractors seems to be a much more complicated problem. Since such theorems are also absent, the construction of finite-dimensional approximations of differential climatic models is a nontrivial task. The approximation of energy intensive large-scale processes and the conception of a group of invariants of climate model in the absence of dissipation and forcing is the basis of such constructions.
The flight dynamics mathematical model o f a helicopter that would be strictly determined would comprise a system o f non-linear, non-stationary, partial differential equations. To sim plify these equations we introduce a number o f assumptions. Ig n o re d are th e ela stic c h a ra c te ris tic s o f the helicopter so the helicopter can be thought as a rigid body and, in this way, the dispersal o f parameters is eliminated. Also, fuel consumption is disregarded and so is the non-stationarity due to the temporal change in helicopter mass being eliminated.
The mathematical model approach consists in constructing the models of occurrent physical processes with the use of mathematical formalism. The most effective forecast model of emergency situation presents a set of equations that take into account the physical processes taking place at a the accident object and in the environment. In meteorological forecasting, this is the set of equations for atmospheric hydrothermodynamics. The initial data for constructing the models are the dynamic and energy characteristics of the release, as well as the initial spatial distribution of pollutants and meteorological parameters.
The authors do not give any particular Hardware specification. As VegAna programs are written in Java language, it is therefore necessary to have a Java Virtual Machine to execute them. To run VegAna you should have JRE 1.4.x or a later version. Unlike previous re- leases, JRE comes with Java Web Start (JWS). JWS is used to launch VegAna modules and maintain program updates.
Pupils' ability to solve problems is weak. Teachers should focus on cultivating students' problem-solving skills. Learn to build mathematicalmodels in their daily learning, students can solve problems by analyzing some practical problems in real life. In the process of solving mathematical problems, students can find a learning method and then set up a new math problem. Many students have difficulties in solving problems. Researchers engaged in solving mathematical problems present several models in mathematical psychology, namely understanding models, schema models, process models, and strategy models. Study of these models can help students improve their problem-solving skills. The establishment of mathematicalmodels in the process of solving problems is helpful for improving students’ ability of problem-solving  .
MATHEMATICAL MODELS FOR BALKAN PHONOLOGICAL CONVERGENCE 0 0 Phonolo$ical typologies~ statistical counts and mathematical models The high structuring of phonology, the obvious classes of sounds, and th[.]