Complex Integral

In this article, we defined complex curve and complex integral. Then we have proved the linearity for the complex integral. Furthermore, we have proved complex integral of complex curve's connection is the sum of each complex integral of individual complex curve.Yamazaki Masahiko - Shinshu University, Nagano, JapanYamazaki Hiroshi - Shinshu University, Nagano, JapanShidama Yasunari - Shinshu University, Nagano, JapanWasaki Katsumi - Shinshu University, Nagano, JapanCzesław Byliński. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Property of complex functions. Formalized Mathematics, 9(1):179-184, 2001.Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Yasunari Shidama and Artur Korniłowicz. Convergence and the limit of complex sequences. Series. Formalized Mathematics, 6(3):403-410, 1997.Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990

Difficulties and Coping Strategies Experienced by Employed People with HIV in Japan: A Qualitative Study Comparing High and Low Sense of Coherence Groups

People with HIV experience anxiety about discrimination in the workplace and disclosing their disease. Effective coping ability toward HIV-related challenges may be associated with a person’s sense of coherence (SOC). This study describes the range of difficulties HIV-positive individuals experience and their coping strategies, especially in the workplace. The experiences of those with high and low SOC are compared. Data were collected in Japan from 2007 to 2009 using a qualitative approach. Semistructured interviews were conducted with 40 participants with HIV with work experience. Interviews focused on individual’s perspectives, including self-perceptions of physical and mental functioning, work conditions, and perceived changes in their circumstances. Participants were divided into high and low SOC groups based on SOC-13 scores. A number of categories and subcategories of experiences were extracted, including “acute feeling of the severe social positioning of HIV,” with some categories specific to those with low SOC. Those with high SOC appeared to have a unique perspective that supported more successful coping, for example, “Awareness of death is linked to valuing living in the present,” “Do not be discouraged by uncertainties and difficulties,” and so on. It suggests that development of coping skills may help people with HIV

Acute Appendicitis in an Incarcerated Femoral Hernia: A Case of De Garengeot Hernia

Appendicitis and incarcerated hernia are frequently encountered reasons of emergency surgery for acute abdomen. The treatment in early stages of each condition is generally simple, but when these conditions are combined, the symptoms become slightly complicated, obscuring specific symptoms. Especially the lack of symptoms for appendicitis leads to delayed diagnosis, resulting in high morbidity. Amyand hernia, which contains appendix in its inguinal hernia sac, is perhaps more familiar to the general surgeons than De Garengeot hernia, which is an incarcerated femoral hernia with an appendix in its sac. We report the case of a 90-year-old female with incarcerated femoral hernia who underwent emergency hernioplasty only to reveal an inflamed appendix in its sac. The patient underwent both appendectomy and hernia repair simultaneously with synthetic mesh and was discharged on postoperative day 7 without any complications. We will also discuss the physical and radiological findings of De Garengeot hernia

Tumefactive multiple sclerosis requiring emergent biopsy and histological investigation to confirm the diagnosis: a case report

<p>Abstract</p> <p>Introduction</p> <p>Tumefactive multiple sclerosis is a demyelinating disease that demonstrates tumor-like features on magnetic resonance imaging. Although diagnostic challenges without biopsy have been tried by employing radiological studies and cerebrospinal fluid examinations, histological investigation is still necessary for certain diagnosis in some complicated cases.</p> <p>Case presentation</p> <p>A 37-year-old Asian man complaining of mild left leg motor weakness visited our clinic. Magnetic resonance imaging demonstrated high-signal lesions in bilateral occipital forceps majors, the left caudate head, and the left semicentral ovale on fluid-attenuated inversion recovery and T2-weighted imaging, and these lesions were enhanced by gadolinium-dimeglumin. Tumefactive multiple sclerosis was suspected because the enhancement indistinctly extended along the corpus callosum on magnetic resonance imaging and scintigraphy showed a low malignancy of the lesions. But oligoclonal bands were not detected in cerebrospinal fluid. In a few days, his symptoms fulminantly deteriorated with mental confusion and left hemiparesis, and steroid pulse therapy was performed. In spite of the treatment, follow-up magnetic resonance imaging showed enlargement of the lesions. Therefore, emergent biopsy was performed and finally led to the diagnosis of demyelinating disease. The enhanced lesion on magnetic resonance imaging disappeared after one month of prednisolone treatment, but mild disorientation and left hemiparesis remained as sequelae.</p> <p>Conclusions</p> <p>Fulminant aggravation of the disease can cause irreversible neurological deficits. Thus, an early decision to perform a biopsy is necessary for exact diagnosis and appropriate treatment if radiological studies and cerebrospinal fluid examinations cannot rule out the possibility of brain tumors.</p

Morphology for Image Processing. Part I

In this article we defined mathematical morphology image processing with set operations. First, we defined Minkowski set operations and proved their properties. Next, we defined basic image processing, dilation and erosion proving basic fact about them [5], [8].Yamazaki Hiroshi - Shinshu University, Nagano, JapanByliński Czesław - University of Białystok, PolandWasaki Katsumi - Shinshu University, Nagano, JapanCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Yuzhong Ding and Xiquan Liang. Preliminaries to mathematical morphology and its properties. Formalized Mathematics, 13(2):221-225, 2005.Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Formalized Mathematics, 11(1):23-28, 2003.H. J. A. M. Heijimans. Morphological Image Operators. Academic Press, 1994.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.P. Soille. Morphological Image Analysis: Principles and Applications. Springer, 2003.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990

Molecular mechanism of the recognition of bacterially cleaved immunoglobulin by the immune regulatory receptor LILRA2

金沢大学医薬保健研究域薬学系Human leukocyte immunoglobulin-like receptors (LILRs) typically regulate immune activation by binding to the human leukocyte antigen class I molecules. LILRA2, a member of the LILR family, was recently reported to bind to other unique ligands, the bacterially degraded Igs (N-truncated Igs), for the activation of immune cells. Therefore, LILRA2 is currently attracting significant attention as a novel innate immune receptor. However, the detailed recognition mechanisms required for this interaction remain unclear. In this study, using several biophysical techniques, we uncovered the molecular mechanism of N-truncated Ig recognition by LILRA2. Surface plasmon resonance analysis disclosed that LILRA2 specifically binds to N-truncated Ig with weak affinity (Kd = 4.8 mM) and fast kinetics. However, immobilized LILRA2 exhibited a significantly enhanced interaction with N-truncated Ig due to avidity effects. This suggests that cell surface-bound LILRA2 rapidly monitors and identifies bi- or multivalent abnormal N-truncated Igs through specific cross-linking to induce immune activation. Van\u27t Hoff analysis revealed that this interaction is enthalpy-driven, with a small entropy loss, and results from differential scanning calorimetry indicated the instability of the putative LILRA2-binding site, the Fab region of the N-truncated Ig. Atomic force microscopy revealed that N truncation does not cause significant structural changes in Ig. Furthermore, mutagenesis analysis identified the hydrophobic region of LILRA2 domain 2 as the N-truncated Ig-binding site, representing a novel ligand-binding site for the LILR family. These results provide detailed insights into the molecular regulation of LILR-mediated immune responses targeting ligands that have been modified by bacteria. © 2020 Yamazaki et al. Published under exclusive license by The American Society for Biochemistry and Molecular Biology, Inc

Evaluation of the reactivity and receptor competition of HLA-G isoforms toward available antibodies: Implications of structural characteristics of HLA-G isoforms

金沢大学医薬保健研究域薬学系The human leucocyte antigen (HLA)-G, which consists of seven splice variants, is a tolerogenic immune checkpoint molecule. It plays an important role in the protection of the fetus from the maternal immune response by binding to inhibitory receptors, including leukocyte Ig-like receptors (LILRs). Recent studies have also revealed that HLA-G is involved in the progression of cancer cells and the protection from autoimmune diseases. In contrast to its well characterized isoform, HLA-G1, the binding activities of other major HLA-G isoforms, such as HLA-G2, toward available anti-HLA-G antibodies are only partially understood. Here, we investigate the binding specificities of anti-HLA-G antibodies by using surface plasmon resonance. MEM-G9 and G233 showed strong affinities to HLA-G1, with a nM range for their dissociation constants, but did not show affinities to HLA-G2. The disulfide-linker HLA-G1 dimer further exhibited significant avidity effects. On the other hand, 4H84 and MEM-G1, which can be used for the Western blotting of HLA-G isoforms, can bind to native HLA-G2, while MEM-G9 and G233 cannot. These results reveal that HLA-G2 has a partially intrinsically disordered structure. Furthermore, MEM-G1, but not 4H84, competes with the LILRB2 binding of HLA-G2. These results provide novel insight into the functional characterization of HLA-G isoforms and their detection systems. © 2019 by the authors. Licensee MDPI, Basel, Switzerland

Volumetric Reconstruction and Interactive Rendering of Trees from Photographs

International audienceReconstructing and rendering trees is a challenging problem due to the geometric complexity involved, and the inherent difficulties of capture. In this paper we propose a volumetric approach to capture and render trees with relatively sparse foliage. Photographs of such trees typically have single pixels containing the blended projection of numerous leaves/branches and background. We show how we estimate opacity values on a recursive grid, based on alphamattes extracted from a small number of calibrated photographs of a tree. This data structure is then used to render billboards attached to the centers of the grid cells. Each billboard is assigned a set of view-dependent textures corresponding to each input view. These textures are generated by approximating coverage masks based on opacity and depth from the camera. Rendering is performed using a view-dependent texturing algorithm. The resulting volumetric tree structure has low polygon count, permitting interactive rendering of realistic 3D trees. We illustrate the implementation of our system on several different real trees, and show that we can insert the resulting model in virtual scenes