Reconstructing GKZ via topological recursion

In this article, a novel description of the hypergeometric differential equation found from Gel'fand-Kapranov-Zelevinsky's system (referred to GKZ equation) for Givental's $J$-function in the Gromov-Witten theory will be proposed. The GKZ equation involves a parameter $\hbar$, and we will reconstruct it as the WKB expansion from the classical limit $\hbar\to 0$ via the topological recursion. In this analysis, the spectral curve (referred to GKZ curve) plays a central role, and it can be defined as the critical point set of the mirror Landau-Ginzburg potential. Our novel description is derived via the duality relations of the string theories, and various physical interpretations suggest that the GKZ equation is identified with the quantum curve for the brane partition function in the cohomological limit. As an application of our novel picture for the GKZ equation, we will discuss the Stokes matrix for the equivariant $\mathbb{C}\textbf{P}^{1}$ model and the wall-crossing formula for the total Stokes matrix will be examined. And as a byproduct of this analysis we will study Dubrovin's conjecture for this equivariant model.Comment: 66 pages, 13 figures, 6 tables; v2: new subsections added, minor revisions, typos corrected; v3: minor revisions, typos correcte

Partial chord diagrams and matrix models

In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two types of spectra. We introduce matrix models that encode generating functions of partial chord diagrams filtered by each of these spectra. Using these matrix models, we derive partial differential equations - obtained independently by cut-and-join arguments in an earlier work - for the corresponding generating functions.Comment: 42 pages, 14 figure

Quantum Circuit Simulation by SGEMM Emulation on Tensor Cores and Automatic Precision Selection

Quantum circuit simulation provides the foundation for the development of quantum algorithms and the verification of quantum supremacy. Among the various methods for quantum circuit simulation, tensor network contraction has been increasing in popularity due to its ability to simulate a larger number of qubits. During tensor contraction, the input tensors are reshaped to matrices and computed by a GEMM operation, where these GEMM operations could reach up to 90\% of the total calculation time. GEMM throughput can be improved by utilizing mixed-precision hardware such as Tensor Cores, but straightforward implementation results in insufficient fidelity for deep and large quantum circuits. Prior work has demonstrated that compensated summation with special care of the rounding mode can fully recover the FP32 precision of SGEMM even when using TF32 or FP16 Tensor Cores. The exponent range is a critical issue when applying such techniques to quantum circuit simulation. While TF32 supports almost the same exponent range as FP32, FP16 supports a much smaller exponent range. In this work, we use the exponent range statistics of input tensor elements to select which Tensor Cores we use for the GEMM. We evaluate our method on Random Circuit Sampling (RCS), including Sycamore's quantum circuit, and show that the throughput is 1.86 times higher at maximum while maintaining accuracy.Comment: This paper has been accepted to ISC'2

Prospective longitudinal comparative study of health-related quality of life in patients treated with radical prostatectomy or permanent brachytherapy for prostate cancer

To determine health-related quality of life (HRQOL) after radical retropubic prostatectomy (RRP) or permanent prostate brachytherapy (BT), third party-conducted QOL surveys were prospectively compared. Between 2004 and 2005, 37 patients underwent RRP and 36 were treated with BT. A QOL survey consisting of the Medical Outcomes Study 36-Item Short Form (SF-36), the University of California, Los Angeles, Prostate Cancer Index (UCLA-PCI) and the International Prostate Symptoms Score (IPSS) was completed prospectively by a research coordinator at baseline, and at 1, 3, 6 and 12 months after treatment. The RRP patients scored well in general QOL except at 1 month after surgery, with their mental health better than at baseline by 6 months after surgery. Disease-specific QOL in RRP patients received a low score at 1 month for both urinary and sexual function, though urinary function rapidly recovered to baseline levels. BT patient QOL was not affected by the therapy except in the IPSS score. However, general and mental health scores in BT patients were inferior to those in RRP patients. This prospective study revealed differences in QOL after RRP and BT. These results will be helpful in making treatment decisions.</p

ペルーの人工変形頭蓋正中矢状面輪郭における若干の顔面角について

ペルー人男性の前頭後頭型人工変形頭蓋における頭蓋型と，正中矢状面輪郭上の歯槽性突顎に関連する若干の角について調べた．変形頭蓋は非常に大きな頭蓋示数を有するが，頭蓋モズルスは非変形頭蓋との間に有意差がなかった．Basion （Ba）-Nasion （Na）-Prosthion （Pr）角とBa-Na-Subspinale （Ss）角における両頭蓋間の差は有意であった．これに対し，Na-Pr線，Na-Ss線とフランクフルト面（FHP）のなす角度の差は有意でなかった．また，Na-Ba線とFHPとのなす角に有意差が認められた．これらの結果から人工変形はNa-Ba線の位置変化をもたらすが，歯槽性突顎の形態には影響を与えないことが示唆される．Three principal cranial dimensions and six angles on sagittal cranial profile related with facial prognathism, between artificially front-occipital deformed and undeformed Peruvian skulls were examined. The deformed skull group was characterized by a shorter and wider neurocranial vault. Angular analyses suggested that the skull deformation caused displacement of the basion-nasion line. However, the significant difference in the facial prognathism between the deformed and undeformed skulls could not be confirmed in this craniogeometric study

The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings

We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard-Orantin topological recursion relation. We check the correspondence for the figure eight knot complement and the once punctured torus bundle over S^1 with the holonomy L^2R up to the fourth order. For the torus knots, we find trivial the recursion relations on both sides.Comment: 48 pages, 7 figure

解剖実習体の膝関節にみられた円板状外側半月の一例について-特に関節内靱帯との関係-

65歳男性遺体の右膝に見いだされた円板状外側半月を観察し，特に関節内付属靱帯との関係を記載した．円板状外側半月は比較的幅広く，脛骨の外側顆上関節面をほぼ完全に被い，肉眼的観察およびX線撮影ではその損傷や石灰化などの異常は見られなかった．本例では，全体的に半月の固定に関係する靱帯の発達が良好であった．すなわち，半月の前角と後角は靱帯を介して強固に脛骨に付着し，さらに，強い半月横靱帯が内・外側半月の前部を連結していた．後方では外側半月後角から起こる太い後半月大腿靱帯が認められた．加えて，内側・外側半月の前角から起こり前十字靱帯に合流する靱帯小束が認められたが，これらは半月の前部固定に関与すると考えられた．The right knee, from a male cadaver aged 65, with discoid lateral meniscus was carefully dissected. The meniscus and its anatomical relationships with some associated ligaments of the knee are described. The discoid meniscus was a wide structure covering nearly the articular surface of the tibia and was almost intact macroscopically. Neither meniscal calcification nor ossification was demonstrated by radiography. There were strong transverse ligament, solid attachments from both anterior and posterior horns to the tibia, distinct posterior menisco-femoral ligament, and ligamentous slips from both anterior horns of the medial and lateral menisci to the anterior cruciate ligament. The knee anatomy was characterized by the well-development attachment system of the menisci. The medial meniscus was anatomically normal

Iodine-125 Seed Implantation (Permanent Brachytherapy) for Clinically Localized Prostate Cancer

From January 2004 to March 2007, 308 patients with clinically localized prostate cancer were treated using iodine-125 (125I) seed implantation (permanent brachytherapy) at Okayama University Graduate School of Medicine, Dentistry and Pharmaceutical Sciences. We evaluated the treatment’s effi cacy and morbidity in 300 prostate cancer patients who were followed up for more than 1 month after brachytherapy. Based on the National Comprehensive Cancer Network (NCCN) guidelines, patients with a prostate volume of less than 40 ml in transrectal ultrasound imaging were classifi ed as low or intermediate risk. The median patient age was 67 years (range 50 to 79 years), the median prostate-specific antigen (PSA) value before biopsy was 6.95 ng/ml (range 1.13 to 24.7 ng/ml), and the median prostate volume was 24.33 ml (range 9.3 to 41.76 ml). The median follow-up was 18 months (range 1 to 36 months) and the PSA levels decreased in almost all patients after brachytherapy. Although 194 of 300 patients (64.7%) complained of diffi culty in urination, pollakisuria/urgency, miction pain, and/or urinary incontinence, all of which might be associated with radiation prostatitis during the fi rst month after brachytherapy, these symptoms gradually improved. 125I seed implantation brachytherapy is safe and eff ective for localized prostate cancer within short-term follow up.</p

Two New Tryptamine Derivatives, Leptoclinidamide and (-)-Leptoclinidamine B, from an Indonesian Ascidian Leptoclinides dubius

Two new tryptamine-derived alkaloids, named as leptoclinidamide (1) and (-)-leptoclinidamine B (2), were isolated from an Indonesian ascidian Leptoclinides dubius together with C2-α-D-mannosylpyranosyl-L-tryptophan (3). The structure of 1 was assigned on the basis of spectroscopic data for 1 and its N-acetyl derivative (4). Compound 1 was an amide of tryptamine with two β-alanine units. Although the planar structure of 2 is identical to that of the known compound (+)-leptoclinidamine B (5), compound 2 was determined to be the enantiomer of 5 based on amino acid analysis using HPLC methods. Compounds 1 to 4 were evaluated for cytotoxicity against two human cancer cell lines, HCT-15 (colon) and Jurkat (T-cell lymphoma) cells, but none of the compounds showed activity