On homology 3-spheres defined by two knots

We show that if each of $K_1$ and $K_2$ is a trefoil knot or figure eight knot, the homology 3-sphere defined by the Kirby diagram which is a simple link of $K_1$ and $K_2$ with framing (0, n) is represented by an n-twisted Whitehead double of $K_2$ .Comment: 21 pages, 102 figure

Cayley sums and Minkowski sums of 22-convex-normal lattice polytopes

In this paper, we discuss the integer decomposition property for Cayley sums and Minkowski sums of lattice polytopes. In fact, we characterize when Cayley sums have the integer decomposition property in terms of Minkowski sums. Moreover, by using this characterization, we consider when Cayley sums and Minkowski sums of $2$-convex-normal lattice polytopes have the integer decomposition property. Finally, we also discuss the level property for Minkowski sums and Cayley sums.Comment: 10 page

“What is it like to be a bat?”—a pathway to the answer from the integrated information theory

What does it feel like to be a bat? Is conscious experience of echolocation closer to that of vision or audition? Or do bats process echolocation nonconsciously, such that they do not feel anything about echolocation? This famous question of bats' experience, posed by a philosopher Thomas Nagel in 1974, clarifies the difficult nature of the mind–body problem. Why a particular sense, such as vision, has to feel like vision, but not like audition, is totally puzzling. This is especially so given that any conscious experience is supported by neuronal activity. Activity of a single neuron appears fairly uniform across modalities and even similar to those for non-conscious processing. Without any explanation on why a particular sense has to feel the way it does, researchers cannot approach the question of the bats' experience. Is there any theory that gives us a hope for such explanation? Currently, probably none, except for one. Integrated information theory has potential to offer a plausible explanation. IIT essentially claims that any system that is composed of causally interacting mechanisms can have conscious experience. And precisely how the system feels is determined by the way the mechanisms influence each other in a holistic way. In this article, I will give a brief explanation of the essence of IIT. Further, I will briefly provide a potential scientific pathway to approach bats' conscious experience and its philosophical implications. If IIT, or its improved or related versions, is validated enough, the theory will gain credibility. When it matures enough, predictions from the theory, including nature of bats' experience, will have to be accepted. I argue that a seemingly impossible question about bats' consciousness will drive empirical and theoretical consciousness research to make big breakthroughs, in a similar way as an impossible question about the age of the universe has driven modern cosmology

Gorenstein simplices and the associated finite abelian groups

It is known that a lattice simplex of dimension $d$ corresponds a finite abelian subgroup of $(\mathbb{R}/\mathbb{Z})^{d+1}$. Conversely, given a finite abelian subgroup of $(\mathbb{R}/\mathbb{Z})^{d+1}$ such that the sum of all entries of each element is an integer, we can obtain a lattice simplex of dimension $d$. In this paper, we discuss a characterization of Gorenstein simplices in terms of the associated finite abelian groups. In particular, we present complete characterizations of Gorenstein simplices whose normalized volume equals $p,p^2$ and $pq$, where $p$ and $q$ are prime numbers with $p \neq q$. Moreover, we compute the volume of the dual simplices of Gorenstein simplices.Comment: 18 pages, to appear in European Journal of Combinatoric

Role of pharmacotherapy in Brugada syndrome

In patients who undergo aborted sudden cardiac death or syncope of unknown origin (symptomatic Brugada syndrome), no one argues that the implantation of an ICD is the first-line therapy regardless of the findings of the EP study. For those patients, drug therapy plays not a contradictory but a complimentary role to the ICD by reducing the number of ICD shock deliveries. Prevention of VF contributes to the improvement in the quality of life of the patients by avoiding uncomfortable ICD shock deliveries. As mentioned above, Belhassen et al. 11, performed EP-guided medical therapy in 34 patients with idiopathic VF, in 5 of whom the criterion of Brugada syndrome were fulfilled, and reported excellent long-term results. Although medical therapy requires markers that can accurately predict the preventive effect of VF over a long-term period, there, however, seems to be no reliable marker. An EP study is usually used to examine the preventive effects of antiarrhythmic agents on sustained ventricular tachycardia in patients with structural heart disease, whereas the prognostic value of the EP study in predicting life-threatening events in Brugada syndrome is still controversial. Brugada et al., 3 suggested that among the asymptomatic patients, the inducibility of VT during the EP study might be a prognostic marker of risk. Studies by Priori et al., 22 and Kanda et al., 23 failed to find an association between the inducibility and recurrence of VT/VF in patients with Brugada syndrome regardless of whether it was symptomatic or asymptomatic. As Belhassen suggested 13, the difference might be due to the VF induction protocol in the EP study, in which Belhassen et al., used a stimulus current intensity of five times the diastolic threshold along with the use of repetition of double and triple extrastimulation at the shortest coupling intervals that resulted in ventricular capture. Further appropriate clinical trials are needed to clarify this issue. In patients with asymptomatic Brugada syndrome who are family members of symptomatic Brugada syndrome patients, the same strategy as that for the symptomatic Brugada syndrome patients should be considered 2,3,4. In another asymptomatic-patient group in whom an ECG that discloses the Brugada sign is performed for routine reasons such as a workup prior to surgery or sport license or screening for insurance, risk stratification to find the patients at high risk is needed because in most cases these patients have a benign prognosis3,22,23. Antzelevitch et al. 4, recommended that all asymptomatic patients with the Brugada sign should undergo an EP study for risk stratification, and, if inducible, an ICD should be implanted since Brugada et al.3, reported that an overall 8% life-threatening event rate was found in initially asymptomatic patients. Belhassen et al.,13 suggested that EP study-guided quinidine therapy might become an alternative to ICD therapy for prophylaxis of arrhythmic events in these patients. Further appropriate clinical trials are needed