Standardization problem: Ressource Allocation in a Network

We consider the standardization problem (SP) which can be formulated as follows. It is known demand bi in each type i in {1, 2, ..., n} of items. Production of yi items of the ith type brings a profit fi (yi), where fi is a nondecreasing concave function for each i in {1, 2, ..., n}.It is necessary to satisfy the demand and to maximize the total profit provided that there exist >standardization possibilities< . These possibilities means that some types of items can be replaced by some another types. We introduce generalized standardization problem (GSP) in which titems demand is given as the set of admissible demand vectors. We show that GSP and SP are special cases of the resource allocation problem over a network polymatroid. Ibasing on this observation we propose a polynomial time solution algorithm for GSP and SP

Standardization problem: Ressource Allocation in a Network

We consider the standardization problem (SP) which can be formulated as follows. It is known demand bi in each type i in {1, 2, ..., n} of items. Production of yi items of the ith type brings a profit fi (yi), where fi is a nondecreasing concave function for each i in {1, 2, ..., n}.It is necessary to satisfy the demand and to maximize the total profit provided that there exist >standardization possibilities< . These possibilities means that some types of items can be replaced by some another types. We introduce generalized standardization problem (GSP) in which titems demand is given as the set of admissible demand vectors. We show that GSP and SP are special cases of the resource allocation problem over a network polymatroid. Ibasing on this observation we propose a polynomial time solution algorithm for GSP and SP

Efficiency Estimation of the Single- and Multicomponent Anti-hydrate Reagents

Different types of technological and technical problems in the oil, gas and chemical industries are connected with the hydrate formation process and with the using of anti-hydrate chemicals. That is why, it is necessary to estimate thermobaric ranges within which reagents does not let hydrate to grow or is their dissociation. Also, to estimate anti-hydrate influence we need to determine the chemicals’ anti-hydrate efficiency and chose the best one. They make the reagents consisting of several chemical components depending on the purpose of their application – for prevention of formation and (or) elimination of hydrates. It demands calculations of the optimum concentration and expenses and also the intensity (speed) of hydrates dissociation causing with the reagents. The analytical method of the anti-hydrate chemical reagents efficiency determination containing one or several components from different classes of chemical compounds – alcohols, salts, acids, compounds of nitrogen and oxygen – is presented in this paper. With its help it is possible to define decrease in temperature of hydrate formation from reagents influence, to count key parameters of reagents anti-hydrate efficiency depending on component compositions of hydrate gas and a phase condition of a hydrate-gas system, to select types of chemical components and their quantity in multicomponent reagents, i.e., to make new compounds. The method can be used for express assessment of anti-hydrate chemical reagents efficiency on criteria sign for practical application in oil, gas and processing industry

Determination of aircraft current location on the basis of its acoustic noise

In this paper the algorithm of signal detection by means passive acoustics and digital data processing is proposed. This algorithm is original and contains the processing of signals, which are received by several acoustic aerials. For signal detection the calculation of wide-band ambiguity function together with its projection on time axis are used. All the calculations are executed with the real signals. As the result the location of the aircraft on Cartesian coordinate plane is observed. The suggested algorithm is also proposed to use for measuring of aircraft noise with the aim of environmental protection

СУЧАСНІ АСПЕКТИ АНТИКРИЗОВОГО ФІНАНСОВОГО УПРАВЛІННЯ ПРОМИСЛОВИМИ ПІДПРИЄМСТВАМИ

The article studies existing methods of anti-crisis financial management of industrial enterprises and developed methodological support to assessment of the level of anti-crisis financial management. Provided that industry is one of the leading industries in national economy of Ukraine. All conversions that occur in industrial plants always lead to significant changes in the socio-economic situation of the country. The author’s definition anti-crisis financial management of industrial enterprise at which you want to understand the complex system of actions aimed at preventing or eliminating the negative phenomena for commercial and business activities. The algorithm of crisis financial management, which allows the development of a system crisis financial management of industrial enterprise to consider the impact of external and internal factors of the environment in which operates an industrial enterprise, with the aim prompt identification of threats to prevent or troubleshoot to prevent, or overcoming the crisis. Noted that an important role in the financial crisis management play the financial risks that occur throughout the entire production cycle. The developed methodological support of anti-crisis financial management, which is an estimate of the influence of groups of indicators for the deployment of crisis on the industrial enterprise.. It is concluded that the use of the proposed methodological support of anti-crisis financial management of industrial enterprises allows to reduce the likelihood of crisis situations and significantly reduce the size of the potential loss. That is, it application gain the opportunity for industrial enterprises to respond quickly to the emergence of the crisis and to consider all types of financial risk in the implementation industrial and commercial activities.Досліджено наявні&nbsp;методики антикризового фінансового управління промисловими підприємствами і розроблено методичне забезпечення до оцінки рівня антикризового фінансового управління підприємством. Зазначено, що промисловість є однією з провідних галузей у національному господарстві України. Усі перетворення, які відбуваються на промислових підприємствах, завжди призводять до суттєвих змін у соціально-економічному становищі країни. Надано авторське визначення антикризового фінансового управління промисловим підприємством, під яким слід розуміти комплексну систему дій, спрямованих на запобігання або усунення негативних явищ для комерційної діяльності та бізнесу. Розроблено алгоритм антикризового фінансового управління, який дає можливість при розробленні системи антикризового фінансового управління промисловим підприємством ураховувати вплив зовнішніх і внутрішніх факторів середовища, у якому функціонує промислове підприємство, з метою своєчасного визначення загроз для їх попередження або усунення з ціллю недопущення чи подолання кризи. Зазначено, що важливу роль в антикризовому фінансовому управлінні відіграють фінансові ризики, які мають місце протягом усього виробничого циклу. Розроблено методичне забезпечення антикризового фінансового управління, яке являє собою оцінку впливу груп показників на розгортання кризових явищ на промисловому підприємстві. Зроблено висновок, що використання запропонованого методичного забезпечення антикризового фінансового управління промисловими підприємствами дозволяє знизити ймовірність виникнення кризових ситуацій та значно зменшити розмір можливого збитку. Тобто його застосування надасть можливість промисловим підприємствам швидко реагувати на виникнення кризових явищ і враховувати всі види фінансових ризиків при здійсненні виробничо-господарської та комерційної діяльності

Navigating protein landscapes with a machine-learned transferable coarse-grained model

The most popular and universally predictive protein simulation models employ all-atom molecular dynamics (MD), but they come at extreme computational cost. The development of a universal, computationally efficient coarse-grained (CG) model with similar prediction performance has been a long-standing challenge. By combining recent deep learning methods with a large and diverse training set of all-atom protein simulations, we here develop a bottom-up CG force field with chemical transferability, which can be used for extrapolative molecular dynamics on new sequences not used during model parametrization. We demonstrate that the model successfully predicts folded structures, intermediates, metastable folded and unfolded basins, and the fluctuations of intrinsically disordered proteins while it is several orders of magnitude faster than an all-atom model. This showcases the feasibility of a universal and computationally efficient machine-learned CG model for proteins

Convex hulls of random walks, hyperplane arrangements, and Weyl chambers

We give an explicit formula for the probability that the convex hull of an n-step random walk in Rd does not contain the origin, under the assumption that the distribution of increments of the walk is centrally symmetric and puts no mass on affine hyperplanes. This extends the formula by Sparre Andersen (Skand Aktuarietidskr 32:27–36, 1949) for the probability that such random walk in dimension one stays positive. Our result is distribution-free, that is, the probability does not depend on the distribution of increments. This probabilistic problem is shown to be equivalent to either of the two geometric ones: (1) Find the number of Weyl chambers of type Bn intersected by a generic linear subspace of Rn of codimension d; (2) Find the conic intrinsic volumes of a Weyl chamber of type Bn. We solve the first geometric problem using the theory of hyperplane arrangements. A by-product of our method is a new simple proof of the general formula by Klivans and Swartz (Discrete Comput Geom 46(3):417–426, 2011) relating the coefficients of the characteristic polynomial of a linear hyperplane arrangement to the conic intrinsic volumes of the chambers constituting its complement. We obtain analogous distribution-free results for Weyl chambers of type An−1 (yielding the probability of absorption of the origin by the convex hull of a generic random walk bridge), type Dn, and direct products of Weyl chambers (yielding the absorption probability for the joint convex hull of several random walks or bridges). The simplest case of products of the form B1 ×···× B1 recovers the Wendel formula (Math Scand 11:109–111, 1962) for the probability that the convex hull of an i.i.d. multidimensional sample chosen from a centrally symmetric distribution does not contain the origin. We also give an asymptotic analysis of the obtained absorption probabilities as n → ∞, in both cases of fixed and increasing dimension d