Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature

We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ chain as a reference system. We consider open boundary conditions and in particular periodic boundary conditions. For both types of boundaries the identification with XXZ spectra is performed within isomorphic representations of the underlying Temperley-Lieb algebra. For open boundaries the spectra of these models differ from the spectrum of the associated XXZ chain only in the multiplicities of the eigenvalues. The periodic case is rather different. Here we show how the spectrum is obtained sector-wise from the spectra of globally twisted XXZ chains. As a spin-off, we obtain a compact formula for the degeneracy of the momentum operator eigenvalues. Our representation theoretical results allow for the study of the thermodynamics by establishing a TL-equivalence at finite temperature and finite field.Comment: 29 pages, LaTeX, two references added, redundant figures remove

Comparisons of log-normal mixture and Pareto tails, GB2 or log-normal body of Romania's all cities size distribution

Modeling demographic data has been on the agenda of statisticians for many years. Some of the distributions used are Pareto, reverse Pareto, q-exponential and log-normal models. An approach to this problem is to consider three statistical models: one for the upper tail, one for the middle range, and another for the lower tail. This paper deals with the size distribution of urban and rural agglomerations in Romania for the 1992–2017 period, by comparing the recently introduced three log-normal mixture (3LN), Pareto tails log-normal (PTLN), and threshold double Pareto Generalized Beta of second kind (tdPGB2) models. The tdPGB2 statistical model has the PTLN distribution as a limiting case. The maximum likelihood estimates of the distributions are computed, and goodness-of-fit tests are performed using the Kolmogorov–Smirnov (KS), Cramér–von Mises (CM) and Anderson–Darling (AD) statistics. Also, we use the Vuong and Bayes factor log-likelihood tests. Using both graphical and formal statistical tests, our results rigorously confirm that the 3LN model is statistically equivalent to PTLN and tdPGB2 distributions, the preferred model being the PTLN probability law. Both the PTLN and tdPGB2 distributions have Pareto tails but the 3LN model does not. All the three models prove to be very well suited parameterizations of Romania's city size data

Stimulation of TRPV1 by green laser light

Low-level laser irradiation of visible light had been introduced as a medical treatment already more than 40 years ago, but its medical application still remains controversial. Laser stimulation of acupuncture points has also been introduced, and mast-cells degranulation has been suggested. Activation of TRPV ion channels may be involved in the degranulation. Here, we investigated whether TRPV1 could serve as candidate for laser-induced mast cell activation. Activation of TRPV1 by capsaicin resulted in degranulation. To investigate the effect of laser irradiation on TRPV1, we used the Xenopus oocyte as expression and model system. We show that TRPV1 can functionally be expressed in the oocyte by (a) activation by capsaicin (K 1/2 = 1.1 μM), (b) activation by temperatures exceeding 42°C, (c) activation by reduced pH (from 7.4 to 6.2), and (d) inhibition by ruthenium red. Red (637 nm) as well as blue (406 nm) light neither affected membrane currents in oocytes nor did it modulate capsaicin-induced current. In contrast, green laser light (532 nm) produced power-dependent activation of TRPV1. In conclusion, we could show that green light is effective at the cellular level to activate TRPV1. To which extend green light is of medical relevance needs further investigation

Mendirikan Perguruan Tinggi Luar Negeri di Indonesia

Pemerintah telah memberi wewenang kepada perguruan tinggi luar negeri (PTLN) untuk mendirikan kampus fisik di Indonesia, sebagaimana diatur dalam Peraturan Menteri Riset, Teknologi, dan Pendidikan Tinggi (Permenristekdikti) No. 53/2018. Melihat rendahnya kualitas perguruan tinggi dalam negeri, yang disebabkan oleh sejumlah faktor seperti rendahnya mutu pengajaran, riset, dan sumber daya manusia, keterbatasan pendanaan, dan tata kelola yang buruk, hadirnya PTLN di Indonesia membuka peluang bagi para mahasiswa Indonesia untuk memperoleh pendidikan kelas dunia di dalam negeri—opsi yang sebelumnya tidak tersedia. Permenristekdikti No. 53/2018 mewajibkan semua PTLN untuk menjalin kemitraan dengan perguruan tinggi lokal di bidang akademik, penelitian dan inovasi. Akan tetapi, peraturan ini tidak berlaku untuk PTLN yangdidirikan di Kawasan Ekonomi Khusus (KEK) sebagaimana diatur dalam Peraturan Menteri Pendidikan dan Kebudayaan (Permendikbud) No. 10/2021. Karena kemitraan ini dapat menjadi sulit untuk diselenggarakan tanpa adanya ketentuan yang mengatur, Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi (Kemendikbudristek) dapat mengambil peran untuk memfasilitasinya. PTLN dapat memainkan peran penting dalam mendorong universitas-universitas lokal untuk meningkatkan kualitas, serta menjadi mitra strategis guna memperbaiki mutu perguruan- perguruan tinggi Indonesia dan menggenjot pembangunan ekonomi lokal. Kemitraan antara Monash University Indonesia dan Universitas Sultan Ageng Tirtayasa mencerminkan hal tersebut dengan diselenggarakannya berbagai kegiatan bersama, mulai dari riset hingga program-program mobilitas mahasiswa dan akademik, dan komitmen Monash University untuk mengembangkan talenta dan potensi lokal Provinsi Banten. Guna memanfaatkan keberadaan PTLN di Indonesia secara maksimal, Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi (Kemendikbudristek) perlu memfasilitasi kerja sama produktif antara PTLN dengan perguruan tinggi Indonesia. Fasilitasi ini penting untuk membina transfer pengetahuan dan teknologi serta membantu mengembangkan ekosistem riset di Indonesia melalui berbagai pengaturan yang saling menguntungkan antara kedua belah pihak. Di saat yang sama, ini membutuhkan perhatian khusus dari Kemendikbudristek terhadap upaya pengembangan kapasitas sumber daya manusia universitas lokal untuk memastikan bahwa mereka memiliki keterampilan yang dibutuhkan dalam bekerja sama dengan PTLN. Kemendikbudristek juga perlu memasukkan PTLN ke dalam program-program pendidikan tinggi Indonesia, seperti menjadikan PTLN sebagai destinasi beasiswa pascasarjana dan program mobilitas untuk memperkenalkan pendidikan berkualitas kelas dunia kepada para mahasiswa dan akademisi Indonesia lainnya

췌관선암 주변 림프절에 대한 종양의 직접 침윤이 환자의 생존결과에 미치는 영향

학위논문 (석사) -- 서울대학교 대학원 : 의과대학 의학과, 2020. 8. 장진영.배경: 림프절 전이는 비교적 잘 알려진 췌장암의 예후 인자 중 하나이다. 이 중 종양 주변 림프절에 췌장암이 직접 침습하는 경우의 림프절 전이 형태는 림프절 채널을 통해 전이되는 다른 림프절의 전이와는 차이가 있음에도 불구하고 병기 설정이나 치료 방침에 있어서 똑같이 취급되고 있다. 이와 관련된 기존의 연구들은 연구의 대상자 수가 적거나 뚜렷한 결론을 내리지 못하고 있어 종양 주변 림프절의 직접 침습에 대한 종양학적 의미를 확인하기 위해 본 연구를 진행하였다. 방법: 본 연구는 2012년부터 2018년까지 서울대학교 병원에서 췌관선암으로 근치적 수술을 받은 506명의 환자를 대상으로 의무기록 검토를 통해 진행되었다. 환자 중 최종 병리 진단이 췌관선암이 아니거나 근치적 목적의 수술이 아닌 환자, 수술 전 항암화학치료를 받은 환자, 남은 췌장에 새로운 췌장암이 발병하여 추가 수술을 받은 환자, 림프절 절제가 이루어지지 않은 환자, 병변의 위치가 다발성인 환자는 분석에서 제외하였다. 결과: 전체 506명의 환자 중 림프절 병기 분포는 176명 (35%)이 N0, 237명 (47%)이 N1, 93명 (18%)이 N2인 것으로 나타났다. 이 중 112명 (22%)에서 종양 주변 림프절의 직접 침윤이 있는 것으로 나타났다. N1 병기 환자들에서, 종양 주변 림프절의 직접 침윤만 있는 환자들은 다른 림프절 전이가 확인된 환자 또는 두 가지 형태의 림프절 전이가 함께 동반된 환자에 비해 2년 생존율이 통계적으로 유의하게 더 나은 결과를 보였다 (2년 생존율: 종양 주변 림프절의 직접 침윤만 있는 경우 74%, 다른 림프절 전이만 있는 경우 47%, 두 가지 형태가 함께 동반된 경우 46%, p=0.006). 하지만, 림프절 전이가 없는 N0 환자와 종양 주변 림프절의 직접 침윤만 있는 환자의 생존율은 유의한 차이가 없었다 (종양 주변 림프절의 직접 침윤만 있는 경우 74%, 림프절 전이가 없는 경우 69%, p=0.483). 결론: 종양 주변 림프절의 직접 침윤은 다른 림프절 전이와 비교하여 생존 결과에 나쁜 영향을 미치지 않기 때문에, 이를 다른 림프절 전이와 똑같이 취급하는 현재의 췌장암 림프절 병기 시스템은 과장될 우려가 있다. 따라서 현재의 췌장암 림프절 병기에서 종양 주변 림프절의 직접 침윤은 따로 취급되어야 한다.Background Lymph node (LN) metastasis is well-known to negatively affect the prognosis of pancreatic cancer. LN metastasis through direct invasion of tumor cell to peritumoral lymph nodes (PTLN) are treated as the same as those which spread through lymphatic channels. Previous studies were based on small number of cases without definitive conclusions. This study aimed to evaluate the impact of PTLN invasion on the oncologic outcome of pancreatic cancer. Methods Medical records of 506 patients who received radical resection for pancreatic ductal adenocarcinoma from January 2012 to December 2018 were reviewed. Pathologic review was performed by one experienced pathologist. PTLN invasion was defined as a direct invasion of tumor cells in contact with main tumor. Results Of the 506 patients, 176 (34.8%) were N0, 237 (46.8%) were N1, and 93 (18.3%) were N2. One-hundred twelve patients (22.1%) had PTLN invasion. In N1 stage, PTLN invasion group (PTLNI) had a significantly better 2- year survival than regional LN metastasis group (RLNM) and combined LN metastasis group (CLNM) (PTLNI 73.8% vs. RLNM 47.0% vs. CLNM 45.7%, p=0.006). There was no significant difference between N0 and PTLNI (PTLNI 73.8% vs. N0 69.4%, p=0.483). In multivariate analysis, the PTLNI was found to be a better prognostic factor (Hazard ratio 0.322 [0.182-0.570], p<0.001). Conclusion Because PTLN invasion does not adversely affect survival as LN metastasis, pancreatic cancer can be over-staged if it were dealt like metastatic LN. Therefore, PTLN invasion should be disregarded from current nodal staging system. 1. Introduction 1 2. Methods 2 3. Results 5 4. Discussion 8 5. References 13Maste

A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

Intermediate Subfactors with No Extra Structure

If $N \subset P,Q \subset M$ are type II_1 factors with $N' \cap M = C id$ and $[M:N]$ finite we show that restrictions on the standard invariants of the elementary inclusions $N \subset P$, $N \subset Q$, $P \subset M$ and $Q \subset M$ imply drastic restrictions on the indices and angles between the subfactors. In particular we show that if these standard invariants are trivial and the conditional expectations onto $P$ and $Q$ do not commute, then $[M:N]$ is 6 or $6 + 4\sqrt 2$. In the former case $N$ is the fixed point algebra for an outer action of $S_3$ on $M$ and the angle is $\pi/3$, and in the latter case the angle is $cos^{-1}(\sqrt 2-1)$ and an example may be found in the GHJ subfactor family. The techniques of proof rely heavily on planar algebras.Comment: 51 pages, 65 figure

Tied--boxed algebras

We introduce two new algebras that we call \emph{tied--boxed Hecke algebra} and \emph{tied--boxed Temperley--Lieb algebra}. The first one is a subalgebra of the algebra of braids and ties introduced by Aicardi and Juyumaya, and the second one is a tied--version of the well known Temperley--Lieb algebra. We study their representation theory and give cellular bases for them. Furthermore, we explore a strong connection between the tied--boxed Temperley--Lieb algebra and the so--called partition Temperley--Lieb algebra given by Juyumaya. Also, we show that both structures inherit diagrammatic interpretations from a new class of monoids that we call \emph{boxed ramified monoids}. Additionally, we give presentations for the singular part of the ramified symmetric monoid and for the boxed ramified monoid associated to the Brauer monoid.Comment: 35 figure