scholarly journals Multigraphs (Only) Satisfy a Weak Triangle Removal Lemma

10.37236/249 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Asaf Shapira ◽  
Raphael Yuster

The triangle removal lemma states that a simple graph with $o(n^3)$ triangles can be made triangle-free by removing $o(n^2)$ edges. It is natural to ask if this widely used result can be extended to multi-graphs. In this short paper we rule out the possibility of such an extension by showing that there are multi-graphs with only $n^{2+o(1)}$ triangles that are still far from being triangle-free. On the other hand, we show that for some slowly growing function $g(n)=\omega(1)$, if a multi-graph has only $g(n)n^2$ triangles then it must be close to being triangle-free. The proof relies on variants of the Ruzsa-Szemerédi theorem.

2020 ◽  
Vol 63 (1) ◽  
pp. 123-142
Author(s):  
Milos Bogdanovic

In this paper we will try to confront Quine?s and Davidson?s holistic position through Davidson?s thesis of mental as a non-ontological category. In this regard, since Davidson came to this position through the thesis of mental as a decidedly conceptual category, we will try to show how this approach does not, nevertheless, rule out the possibility of its interpretation in ontological terms. However, in what follows we will draw attention to the fact that mental can be interpreted so that it proves to be immune to ontologization in Quine?s sense. This would be the evidence of different ways, which are not necessarily compatible, to argue for Davidson?s central thesis - the thesis about holistic character of mental - as well as, which is closely related, a certain difference that exists between Davidson?s view of mental as a conceptual category on the one hand, and a holistic category on the other hand.


1962 ◽  
Vol 203 (4) ◽  
pp. 649-654 ◽  
Author(s):  
C. Raynaud

In rabbits, after rapid intravenous injection of Mg28, the plasma and urinary specific activities, corrected for transit time, are at all times in equilibrium. Injection of Mg28 during stop flow does not reveal any tubular zone permeable to magnesium. On the other hand, the magnesium behavior is in many ways comparable to that of a glomerular substance. These three arguments lead to the view that urinary magnesium is of essentially glomerular origin, and rule out any mechanism of tubular exchange or secretion.


2018 ◽  
Vol 15 (04) ◽  
pp. 1850060
Author(s):  
Koen Thas

Nearly every known pair of isospectral but nonisometric manifolds — with as most famous members isospectral bounded [Formula: see text]-planar domains which makes one “not hear the shape of a drum” [M. Kac, Can one hear the shape of a drum? Amer. Math. Monthly 73(4 part 2) (1966) 1–23] — arise from the (group theoretical) Gassmann–Sunada method. Moreover, all the known [Formula: see text]-planar examples (so counter examples to Kac’s question) are constructed through a famous specialization of this method, called transplantation. We first describe a number of very general classes of length equivalent manifolds, with as particular cases isospectral manifolds, in each of the constructions starting from a given example that arises itself from the Gassmann–Sunada method. The constructions include the examples arising from the transplantation technique (and thus in particular the known planar examples). To that end, we introduce four properties — called FF, MAX, PAIR and INV — inspired by natural physical properties (which rule out trivial constructions), that are satisfied for each of the known planar examples. Vice versa, we show that length equivalent manifolds with FF, MAX, PAIR and INV which arise from the Gassmann–Sunada method, must fall under one of our prior constructions, thus describing a precise classification of these objects. Due to the nature of our constructions and properties, a deep connection with finite simple groups occurs which seems, perhaps, rather surprising in the context of this paper. On the other hand, our properties define in some sense physically irreducible pairs of length equivalent manifolds — “atoms” of general pairs of length equivalent manifolds, in that such a general pair of manifolds is patched up out of irreducible pairs — and that is precisely what simple groups are for general groups.


1876 ◽  
Vol 24 (164-170) ◽  
pp. 451-455 ◽  

Since my communication of the above-cited Paper to the Royal Society on the 16th December, 1875, two important contributions to the Anatomy of Antedon have appeared—one by Dr. Ludwig, chiefly based on his study of Antedon Eschrichtii (“Zur Anatomie der Crinoiden,” Zeitschrift für Wissenschaftliche Zoologie, Bd. xxvi. 1876, p. 361, continued in Nachrichten von der Königl. Gesellschaft der Wissenschaf ten und der Gr. A.Universität-zu Göttingen, No. 5, Feb. 23, 1876), and the other by Prof. Greef, of Marburg (Sitzungsberichte der G-esellschaft zur Beförderung der gesammten Naturwissenschaften zu Marburg, January 1876), both of which seem to have been prompted by the appearance of Professor Semper’s short paper on the subject. These able observers fully concur with me, as to all essential particulars, in the account I have given of the triple canal-system of the arms, which M. Edmund Perrier not only could not himself find, but ventured to predict that no one else would find; in fact, Professor G-reef’s figure of a transverse section of an arm might have been copied from one of the drawings I have had by me for more than ten years, save for one slight additional feature. The German investigators also accept the correctness of the statements made by me in my First Memoir, that the “nerve” of Müller is really the genital rachis, and that Müller’s “vessel” in the arms is solid, not tubular, though neither is disposed to believe with me that this “axial cord” is a nerve. The character of a nerve, on the other hand, is assigned by Ludwig to a fibrillar band lying beneath the epithelial floor of the ventral furrow of the arms; which band had been independently noticed by my son, Mr. P. H. Carpenter (who is at present working in the laboratory of Professor Semper at Würzburg), in two of Professor Semper’s Philip-pine species, Actinometra armata and A. nigra , as also in Antedon Eschrichtii , in which it had been previously discovered by Ludwig. It is not nearly so distinct, however, in A. rosaceus ; but its existence in that species was also independently recognized by Professor Huxley, who, like Ludwig, was led by his general view of the homologies of the Crinoids to regard it as a nerve. My son regards both the ventral band of Ludwig and my “axial cord” as belonging to the nervous system, being led to that conclusion, as regards the former, by its homology with the radial nerves of other Echinoderms, and, as regards the latter, by the very definite branching he has discovered in the axial cord of the arms of Actinometra armata and A. nigra —two pairs of branches running on each side towards the dorsal surface, and two towards the ventral, where he has distinctly traced their ramifications as far as the leaflets bounding the ventral furrow. Prof. Greef, on the other hand, describes the whole epithelial floor of the ventral furrow as a nerve, on the ground that its histological character resembles that of the nerves of other Echinoderms. Having recently had an opportunity of examining at Würzburg the very thin sections prepared by my son, I can say with certainty that the fibrillar band is quite distinct from the layer of columnar epithelium which it underlies; but it appeared to me to send off very minute fibrils that pass up between the cells of which that layer is composed.


2020 ◽  
Vol 55 ◽  
pp. 343-368
Author(s):  
Łukasz Oleszczak ◽  
Marcin M. Przybyła ◽  
Igor Pieńkos ◽  
Konstantin V. Chugunov ◽  
Nina A. Zhogova

In 2019, Polish archaeologists took part in an expedition of the Hermitage Museum, led by K.V. Chugunov, in Chinge-Tey cemetery, Tuva (Russian Federation). This paper presents the results of magnetic surveys carried out within the so-called western chain of barrows and around the princely barrow of Chinge-Tey I. This method of non-invasive research is very well suited to the landscape and has produced a significant body of information. Among others, the survey of the western chain identified a stone mantle in barrow 8, which makes it different from other barrows from this group, whose mounds were built of earth. Another important result is the identification of a stone circle surrounding a cult feature (certainly associated with eschatological rituals) known as the northern complex. The presence of the circle came as a surprise for the investigators of the site, as it does not manifest itself at all on the surface of the site. On the other hand, worth noting is one negative result, which nevertheless allows for some conclusions, namely the lack of detectable anomalies connected with one of the tombs in the vicinity of Chinge-Tey I (barrow 15). Despite being clearly discernible in the landscape, and even more evident in LIDAR images, the barrow is invisible on images produced with a magnetometer. This means that one cannot rule out a possibility that other structures undetectable by magnetic surveys may be present within the investigated part of the cemetery. Nevertheless, one cannot but arrive at the conclusion that the results generated by the magnetic research provide significant information concerning the spatial arrangement of the cemetery and are helpful in planning of archaeological excavation.


1889 ◽  
Vol 6 (11) ◽  
pp. 490-492
Author(s):  
R. H. Traquair

In a short paper on the nomenclature of the Old Red Sandstone Fishes published in this Magazine for November, 1888, I expressed the opinion “that the scattered teeth and fragments of jaws known as Dendrodus and Lamnodus belong to fishes at present known to us by their scales as species of Holoptychius and Glyptolepis.” The family terms “Holoptychiidæ” and “Dendrodontidæ” I consider absolutely synonymous. On the other hand, the Rhizodontidæ (Gyroptychius, Tristichopterus, Rhizodus, etc.) present a somewhat different form of tooth-structure, and one which is, in the main, identical with that which, in so many Stegocephalous Amphibia, is called “labyrinthodont.”


2016 ◽  
Vol 2 (1) ◽  
pp. 141-150
Author(s):  
Fábio Henrique Bittes Terra

This short paper analysis the pamphlet Uma ponte para o futuro, which presents the basic guidelines of Michel Temer’s government – by now, mid-2016, yet a temporary government. The analysis will be done divided in three sections. On the one hand, it will present the diagnosis how the pamphlet looks at the current economic problems in Brazil and the solutions proposed to resolve them. On the other hand, the paper realizes a Keynesian analysis over the document. Finally, as its concluding remarks, the paper debates the current political circumstances in Brazil as they are fundamental to define whether the Ponte para o futuro will be implemented or not.


2020 ◽  
Vol 9 (1) ◽  
pp. 39-52
Author(s):  
Sutono Widjaja

Malpractice cases are a crime that is very common in Indonesia. Malpractice is basically the actions of professionals who contravene SOPs, codes of ethics, and applicable laws, whether intentional or as a result of negligence resulting in loss or death to others. On the other hand, in the implementation of health services, medical personnel, namely doctors and nurses do not rule out the possibility of an error or negligence. Errors or negligence by doctors in carrying out their professional duties can be fatal both to the body and soul of the patient (in medical/legal terms this incident is called malpractice) and this is of course very detrimental to the patient as a victim of malpractice. As a victim of malpractice that is harmed , of course the patient will demand what is his right. Patients who are victims of malpractice will demand compensation or ask for accountability from the doctor concerned. These demands can be in the form of civil claims, namely compensation, criminal charges, namely imprisonment for perpetrators of malpractice


2020 ◽  
Author(s):  
Huafang Li

This short paper highlights the importance and relevance of studying Chinese public administration. As China becomes an increasingly important member in the global village, more attention should be paid to the study of Chinese public administration. On the one hand, many studies will continually focus on studying Chinese public administration itself, and on the other hand comparative study between China and other countries will likely flourish as well.


Author(s):  
Rahmathulla Safiyul Rahman ◽  
Ali Saeed Alharbi ◽  
Bassam Ahmed Basaben ◽  
Ahmad Adnan Alsalman ◽  
Anas Sulaiman Aljohani ◽  
...  

Colon polyps might originate from the submucosa including lymphoid aggregates, carcinoids and lipomas. On the other hand, most polyps usually arise from the mucosa and include various types, whether neoplastic or not. The prognosis and treatment of these lesions depend on establishing an adequate diagnosis to rule out the presence of malignancy. Therefore, clinicians should be aware of each subclassification's different types and presentations to achieve the best outcomes. When conducting colonoscopy screening for colorectal cancer, colorectal polyps are commonly discovered. The prevalence of these lesions is high. However, most of them do not have any clinical significance. On the other hand, evidence shows that some polyps might have premalignant characteristics, which are usually challenging to manage in clinical practice. Therefore, evidence shows that the most appropriate approach to managing these lesions and achieving the best prognosis would be identifying and treating them as early as possible before complications appear to intervene against potential morbidities and mortality. Clinicians should consider the wide variations of colorectal cancer to establish the most appropriate diagnosis. A histological diagnosis is essential in these events to exclude malignancy and decide the most appropriate treatment plan.


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