Integer Programming Formulations For The Frobenius Problem

The Frobenius number of a set of relatively prime positive integers α1,α2,…,αn such that α1< α2< …< αn, is the largest integer that can not be written as a nonnegative integer linear combination of the given set. Finding the Frobenius number is known as the Frobenius problem, which is also named as the coin exchange problem or the postage stamp problem. This problem is closely related with the equality constrained integer knapsack problem. It is known that this problem is NP-hard. Extensive research has been conducted for finding the Frobenius number of a given set of positive integers. An exact formula exists for the case n=2 and various formulas have been derived for all special cases of n = 3. Many algorithms have been proposed for n≥4. As far as we are aware, there does not exist any integer programming approach for this problem which is the main motivation of this paper. We present four integer linear programming formulations about the Frobenius number of a given set of positive integers. Our first formulation is used to check if a given positive integer is the Frobenius number of a given set of positive integers. The second formulation aims at finding the Frobenius number directly. The third formulation involves the residue classes with respect to the least member of the given set of positive integers, where a residue table is computed comprising all values modulo that least member, and the Frobenius number is obtained from there. Based on the same approach underlying the third formulation, we propose our fourth formulation which produces the Frobenius number directly. We demonstrate how to use our formulations with several examples. For illustrative purposes, some computa-tional analysis is also presented.

Ironia jako dekonstrukcja umierania w Listach Witolda Wirpszy

This paper focuses on Witold Wirpsza’s Letters from the volume Second Resistance. Poems 1960–1964 (1965) and shows how irony becomes a deconstruction of dying, and at the same time of itself and of literary communication in general. The persiflage-oriented ars moriendi turns out to be a diagnosis directed against the discourses of thanatology, operating in institutions of power, medicine or religion (public letters) and family (private letters). Wirpsza designed it as a play of signs and communication noise in which meanings embedded in surface and deeper semantic levels intersect and contradict each other. This is accomplished by writing about death through epistolary, postal, philatelic tropes, concerning message, mediation and transmission. What are particularly important are the metaliterary parts, parabases intensifying the irony, which contain the vision of a postage stamp robbery as reality transformed into signs. The interpretation of the Letters reveals that the deconstructive irony makes epistolary poetry a literary event – the letter, writing that is to be stolen, killed, read by the reader in her or his own way.

Maps of the West Bank in Jordanian Postage Stamps, 1952–1985

This article examines Jordanian postage stamp depiction of the West Bank as part of the Hashemite Kingdom from 1952 to 1985. The majority of maps of the West Bank are featured as part of Jordan, both during Jordanian rule of the West Bank (1948–1967) and after Israel conquered the land during the 1967 war. Sometimes the West Bank is delineated from Jordan to suggest a territorial dispute with Israel, while other times, the West Bank is shown as part of Palestine. The ambiguous representations of the West Bank as Jordanian territory, disputed territory, and Palestinian territory reinforce Hashemite sovereignty claims to the West Bank while also supporting Palestinian rights and acknowledging Jordanian rule of the West Bank was conditional upon settlement of the Palestinian issue. Finally, this analysis seeks to explain why stamps stopped showing the West Bank as part of Jordan in 1985, three years before the kingdom formally severed all legal and administrative ties to the land.

Extending the Frequency Limits of "Postage-Stamp PIV" to MHz Rates

The effective frequency limits of postage-stamp PIV, in which a pulse-burst laser and very small fields of view combine to achieve high repetition rates, have been extended by increasing the PIV acquisition rate to very nearly MHz rates (990 kHz) by using a faster camera. Charge leaked through the camera shift register at these framing rates but this was shown not to bias the measurements. The increased framing rate provided oversampled data and enabled use of multi-frame correlation algorithms for a lower noise floor, increasing the effective frequency response to 240 kHz where the interrogation window size begins to spatially filter the data. The velocity spectra suggest turbulence power-law scaling in the inertial subrange steeper than the theoretical -5/3 scaling, attributed to an absence of isotropy.

Stamping out disease: health education and promotion by miniature messengers

<p><b>Abstract </b></p><p>This study explores the role of the ubiquitous postage stamp as a messenger of health promotion and education. It examines the way that postal material has been modified to act as a medium for health education, with images and texts appropriate to the specific health problems. The methodology used included a search for all postage stamps listed in established catalogues that fitted the described criterion. Selection for further study was drawn from those stamps that covered the topics of infection, immunisation, tobacco cessation, growth and nutrition. </p><p>It was clearly recognised that by simply presenting information on a stamp, would not necessarily bring about the desired behavioural change. Thus, the currently accepted health promotion models were examined to find an appropriate explanation for/ and a rationale to explain the use of postage stamp in health promotion and education. The strategy called “media advocacy” was the nearest best fit for the bulk of postage stamps carrying health information. This finding could explain why stamps have been perceived, over many years, as being a useful and successful element in health promotion and education by their frequent and continued use over a period of some fifty years. </p><p>Postage stamps are frequently used worldwide and have a clear role in carrying health information and thus play a small, but important and unique, role in the field of health promotion. </p>

Stamping out disease: health education and promotion by miniature messengers

<p><b>Abstract </b></p><p>This study explores the role of the ubiquitous postage stamp as a messenger of health promotion and education. It examines the way that postal material has been modified to act as a medium for health education, with images and texts appropriate to the specific health problems. The methodology used included a search for all postage stamps listed in established catalogues that fitted the described criterion. Selection for further study was drawn from those stamps that covered the topics of infection, immunisation, tobacco cessation, growth and nutrition. </p><p>It was clearly recognised that by simply presenting information on a stamp, would not necessarily bring about the desired behavioural change. Thus, the currently accepted health promotion models were examined to find an appropriate explanation for/ and a rationale to explain the use of postage stamp in health promotion and education. The strategy called “media advocacy” was the nearest best fit for the bulk of postage stamps carrying health information. This finding could explain why stamps have been perceived, over many years, as being a useful and successful element in health promotion and education by their frequent and continued use over a period of some fifty years. </p><p>Postage stamps are frequently used worldwide and have a clear role in carrying health information and thus play a small, but important and unique, role in the field of health promotion. </p>

GENDER AND IDEOLOGY: WOMEN ON POSTAGE STAMPS IN SERBIA: 2006-2018

In 2000 certain democratic changes happened in Serbia. They instilled hopes that everyday life will be more democratic in every segment, especially when gender equality is concerned (equality for the different, that is, women). The degree to which a society is democratic could be measured in different ways. One of them is the presence of visuals (drawings, etc.) or presence of any other form of material culture.The aim of this paper is to examine the degree of democratic changes in multinational, multi-confessional and multilingual Serbia during the last decade as it relates to the absence of linguistic codes, and using postage stamps to depict women (2006-2018). The corpus consists of all the postage stamps printed during the period, but only those depicting women were analysed. The analysis of the text on postage stamps opens up a theoretical question “What is text”?We here introduce the criterion of ‘implied knowledge’ as a measure for the understanding of the meaning of text on a stamp, more accurately, as a measure of the presence of an implicit discrimination towards notable women.The results reveal the following: 1. there are only several women who got the privilege to be presented on a postage stamp in this period; 2. all of them originate from the Serbian culture and none from other national communities. This clearly shows that the ideological decision is in question.

Structured variational inference for simulating populations of radio galaxies

ABSTRACT We present a model for generating postage stamp images of synthetic Fanaroff–Riley Class I and Class II radio galaxies suitable for use in simulations of future radio surveys such as those being developed for the Square Kilometre Array. This model uses a fully connected neural network to implement structured variational inference through a variational autoencoder and decoder architecture. In order to optimize the dimensionality of the latent space for the autoencoder, we introduce the radio morphology inception score (RAMIS), a quantitative method for assessing the quality of generated images, and discuss in detail how data pre-processing choices can affect the value of this measure. We examine the 2D latent space of the VAEs and discuss how this can be used to control the generation of synthetic populations, whilst also cautioning how it may lead to biases when used for data augmentation.

Sparse Array Design for DOA Estimation of Non-Gaussian Signals: From Global Postage-Stamp Problem Perspective

In this paper, a sparse array design problem for non-Gaussian signal direction of arrival (DOA) estimation is investigated. Compared with conventional second-order cumulant- (SOC-) based methods, fourth-order cumulant- (FOC-) based methods achieve improved DOA estimation performance by utilizing all information from received non-Gaussian sources. Considering the virtual sensor location of vectorized FOC-based methods can be calculated from the second order difference coarray of sum coarray (2-DCSC) of physical sensors, it is important to devise a sparse array design principle to obtain extended degree of freedom (DOF). Based on the properties of unfolded coprime linear array (UCLA), we formulate the sparse array design problem as a global postage-stamp problem (GPSP) and then present an array design method from GPSP perspective. Specifically, for vectorized FOC-based methods, we divide the process of obtaining physical sensor location into two steps; the first step is to obtain the two consecutive second order sum coarrays (2-SC), which can be modeled as GPSP, and the solutions to GPSP can also be utilized to determine the physical sensor location sets without interelement spacing coefficients. The second step is to adjust the physical sensor sets by multiplying the appropriate coprime coefficients, which is determined by the structure of UCLA. In addition, the 2-DCSC can be calculated from physical sensors directly, and the properties of UCLA are given to confirm the degree of freedom (DOF) of the proposed geometry. Simulation results validate the effectiveness and superiority of the proposed array geometry.