Internal Symmetry Group in Categorial Topology
Zoran Majkic
The interdefinability of the universal concepts of category theory has been introduced by Lawvere. The perfect interdefinability between the objects and arrows of some category, defines the class of Perfectly Symmetric Categories (PSC) where each category can be represented equivalently by its arrows or by its objects only. Such symmetry, differently from the global categorial symmetry ( categorial-symmetry group $CS(\mathbb{Z})$ of all comma-propagation transformations), ia a local internal symmetry inside a given PSC category. Given a PSC category (as a "geometric object") $\textbf{C}$ we can consider its properties (the categorial commutative diagrams) preserved under actions of a particular endofunctor $E$ which transforms any commutative diagram into an invariant "up to isomorphism" diagram. We show that this kind of internal categorial invariance is a phenomena of a local categorial symmetry under an Internal Catergorial Symmetry group $ICS(\mathbb{N})$ of all local enfdofunctorial transformations. Then we establish the relationships between this local internal symmetry and global general symmetry between n-dimensional levels (the comma categories obtained from a PSC category $\textbf{C}$) . We show that if a base category $\textbf{C}$ is a PSC, then all its ne-dimensional levels are PSC as well.
Robotic urologic applications of the hinotori™ Surgical Robot System
Shunsuke Miyamoto, Tomoya Hatayama, Hiroyuki Shikuma
et al.
Objective: To assess the safety and effectiveness of urological tumor surgeries using the hinotori™ Surgical Robot System (hinotori) in a real-world clinical setting. Methods: All surgeries including robot-assisted radical prostatectomy (RARP), robot-assisted partial nephrectomy (RAPN), robot-assisted radical nephrectomy (RARN), robot-assisted nephroureterectomy (RANU), robot-assisted adrenalectomy (RAA), and robot-assisted radical cystectomy with intracorporeal urinary diversion (RARC+ICUD) for urological tumors with the hinotori and da Vinci surgical system (da Vinci) from January 2022 to September 2023 were enrolled. We evaluated the safety and effectiveness of surgeries using the hinotori compared with those using the da Vinci. Results: Robotic surgeries using the hinotori were performed in a total of 91 cases, comprising 42 cases of RARP, 18 cases of RAPN, six cases of RARN, 10 cases of RANU, 13 cases of RAA, and two cases of RARC+ICUD; no major intraoperative complications were observed in any of the cases using the hinotori; no major postoperative complications occurred in any of the cases; no case experienced an unrecoverable equipment error during surgery. Meanwhile, robotic surgeries using the da Vinci were performed in a total of 277 cases, comprising 126 cases of RARP, 94 cases of RAPN, 12 cases of RARN, 10 cases of RANU, 20 cases of RAA, and 15 cases of RARC+ICUD; major intraoperative complications occurred in two cases; major postoperative complications occurred in seven cases; seven cases required transfusion; one case underwent conversion to open surgery; during the study period, no case experienced an unrecoverable equipment error. Surgical outcomes for cases with the hinotori were comparable to those with the da Vinci. Conclusion: This study demonstrated that the hinotori is a safe and feasible tool for robotic surgeries in the field of urology.
Diseases of the genitourinary system. Urology
Effects of new assembled titanium mesh cage on the improvement in biomechanical performance of single-level anterior cervical corpectomy and fusion: a finite element analysis
Ke-rui Zhang, Yi Yang, Ya-qin Li
et al.
Abstract Background Anterior cervical corpectomy and fusion (ACCF) with Traditional Titanium Mesh Cages (TTMCs) can lead to complications such as cage subsidence, dysphagia, and implant-related issues. These complications suggest that the biomechanical stability of ACCF with TTMC may be insufficient. This study aims to evaluate whether a New Assembled Titanium Mesh Cage (NTMC) can improve the biomechanical performance after ACCF. Methods ACCF procedures using both TTMC and NTMC models were constructed and compared. The range of motion (ROM) of the surgical segments and stress peaks in various regions including the endplate, bone-screw interface, facet joints, and adjacent intervertebral discs were analyzed. Results The use of NTMC significantly reduced the postoperative ROM of the surgical segments by 80.7%-82.0% compared to ACCF with TTMC. Additionally, stress peaks at the endplate, bone-screw interface, and facet contact force (FCF) were higher in ACCF with TTMC compared to NTMC. TTMC also induced higher stress peaks in the C3/4 and C6/7 intervertebral discs (ranging from 0.2009–6.961 MPa and 0.2477–4.735 MPa, respectively), followed by the NTMC (ranging from 0.1322–3.820 MPa and 0.2227–4.104 MPa, respectively). Conclusions The utilization of NTMC, which includes enlarged spacers and emulates endplate geometries, effectively reduces the risks of cage subsidence and instrument-related complications in ACCF. Furthermore, ACCF with NTMC also decreases the risks of dysphagia, facet joint degeneration, and adjacent disc degeneration during the follow-up period by altering the fixing method while maintaining construct stability.
Diseases of the musculoskeletal system
Synergistic effects of hyperbaric oxygen therapy combined with MPNFS nursing model on neurological recovery and recurrence prevention after chronic subdural hematoma surgery
Ying Xie, Dongmei Yang, Ting Jiang
et al.
BackgroundChronic subdural hematoma (CSDH) has high postoperative recurrence rates. This study investigates the effects of hyperbaric oxygen therapy (HBOT) combined with Medical-Psychosocial-Nursing Functional Support (MPNFS) on functional recovery and recurrence prevention in CSDH patients, and establishes a recurrence prediction model.MethodsA total of 184 CSDH patients undergoing burr hole drainage were randomized into a control group and an observation group (HBOT + MPNFS). Neurological (NIHSS), motor (Fugl-Meyer Assessment), and quality-of-life (SF-36) outcomes were assessed preoperatively and at 1-month postoperatively. Complications and 6-month recurrence rates were recorded. Univariate/multivariate logistic regression identified recurrence risk factors, with ROC analysis evaluating predictive accuracy.ResultsThe observation group showed superior 1-month outcomes: lower NIHSS scores (t = 4.94, p < 0.001), higher FMA and SF-36 scores (p < 0.01). Complication and recurrence rates were significantly reduced (p < 0.05). Independent recurrence predictors included brain atrophy (OR = 2.877), poor brain reexpansion (OR = 3.165), preoperative hematoma width ≥ 20 mm (OR = 2.782), and absence of combined intervention (OR = 2.842). The multifactorial model achieved an AUC of 0.7862, indicating robust predictive efficacy.ConclusionHyperbaric oxygen therapy combined with MPNFS enhances neurological/motor recovery, improves quality of life, and reduces complications/recurrence in postoperative CSDH patients.
Neurology. Diseases of the nervous system
PICOs-RAG: PICO-supported Query Rewriting for Retrieval-Augmented Generation in Evidence-Based Medicine
Mengzhou Sun, Sendong Zhao, Jianyu Chen
et al.
Evidence-based medicine (EBM) research has always been of paramount importance. It is important to find appropriate medical theoretical support for the needs from physicians or patients to reduce the occurrence of medical accidents. This process is often carried out by human querying relevant literature databases, which lacks objectivity and efficiency. Therefore, researchers utilize retrieval-augmented generation (RAG) to search for evidence and generate responses automatically. However, current RAG methods struggle to handle complex queries in real-world clinical scenarios. For example, when queries lack certain information or use imprecise language, the model may retrieve irrelevant evidence and generate unhelpful answers. To address this issue, we present the PICOs-RAG to expand the user queries into a better format. Our method can expand and normalize the queries into professional ones and use the PICO format, a search strategy tool present in EBM, to extract the most important information used for retrieval. This approach significantly enhances retrieval efficiency and relevance, resulting in up to an 8.8\% improvement compared to the baseline evaluated by our method. Thereby the PICOs-RAG improves the performance of the large language models into a helpful and reliable medical assistant in EBM.
CD11b maintains West Nile virus replication through modulation of immune response in human neuroblastoma cells
Yan-Gang Liu, Hao-Ran Peng, Rui-Wen Ren
et al.
Abstract Background West Nile virus (WNV) is a rapidly spreading mosquito-borne virus accounted for neuroinvasive diseases. An insight into WNV-host factors interaction is necessary for development of therapeutic approaches against WNV infection. CD11b has key biological functions and been identified as a therapeutic target for several human diseases. The purpose of this study was to determine whether CD11b was implicated in WNV infection. Methods SH-SY5Y cells with and without MEK1/2 inhibitor U0126 or AKT inhibitor MK-2206 treatment were infected with WNV. CD11b mRNA levels were assessed by real-time PCR. WNV replication and expression of stress (ATF6 and CHOP), pro-inflammatory (TNF-α), and antiviral (IFN-α, IFN-β, and IFN-γ) factors were evaluated in WNV-infected SH-SY5Y cells with CD11b siRNA transfection. Cell viability was determined by MTS assay. Results CD11b mRNA expression was remarkably up-regulated by WNV in a time-dependent manner. U0126 but not MK-2206 treatment reduced the CD11b induction by WNV. CD11b knockdown significantly decreased WNV replication and protected the infected cells. CD11b knockdown markedly increased TNF-α, IFN-α, IFN-β, and IFN-γ mRNA expression induced by WNV. ATF6 mRNA expression was reduced upon CD11b knockdown following WNV infection. Conclusion These results demonstrate that CD11b is involved in maintaining WNV replication and modulating inflammatory as well as antiviral immune response, highlighting the potential of CD11b as a target for therapeutics for WNV infection.
Infectious and parasitic diseases
B cells: roles in physiology and pathology of pregnancy
Jin-Chuan Liu, Jin-Chuan Liu, Qunxiong Zeng
et al.
B cells constitute a diverse and adaptable immune cell population with functions that can vary according to the environment and circumstances. The involvement of B cells in pregnancy, as well as the associated molecular pathways, has yet to be investigated. This review consolidates current knowledge on B cell activities and regulation during pregnancy, with a particular focus on the roles of various B cell subsets and the effects of B cell-derived factors on pregnancy outcomes. Moreover, the review examines the significance of B cell-associated autoantibodies, cytokines, and signaling pathways in relation to pregnancy complications such as pregnancy loss, preeclampsia, and preterm birth.
Immunologic diseases. Allergy
Prevalence of bla OXA-48 and other carbapenemase encoding genes among carbapenem-resistant Pseudomonas aeruginosa clinical isolates in Egypt
Wedad M. Abdelraheem, Doaa Elzaeem Ismail, Safaa S. Hammad
Abstract Background Resistance to carbapenem, the last line of treatment for gram-negative bacterial infections has been increasing globally and becoming a public health threat. Since integrons may aid in the transmission of resistance genes, the purpose of this study was to detect the frequency of class 1, 2, and 3 integrons as well as carbapenem-resistant genes in clinical isolates of P. aeruginosa that are resistant to carbapenem. Methods This study was carried out on 97 clinical isolates of P. aeruginosa isolated from wound and urine samples. The antimicrobial susceptibility for all isolates was tested by the disc diffusion method. The presence of integrons and carbapenem-resistant genes among carbapenem-resistant P. aeruginosa isolates was evaluated by conventional PCR. Results The antimicrobial resistance rate among P. aeruginosa clinical isolates was high, with imipenem resistance in 58.8% of the studied isolates. In this study, 86% of the carbapenem-resistant P. aeruginosa isolates carry carbapenemase genes, with bla VIM being the most common gene followed by the bla OXA−48 gene. Class 1 and class 2 integrons were reported in 37 (64.9%) and 10 (17.5%) of the tested carbapenem-resistant P. aeruginosa isolates, respectively. Conclusion Our data reported a high prevalence of class 1 integrons in carbapenem-resistant P. aeruginosa clinical isolates, suggesting the important role of integrons in carbapenem-resistant gene transfer among such isolates.
Infectious and parasitic diseases
Improving the Sexual Wellbeing of Patients with Psychotic Illness
N. Stanton, E. Angova, K. Diamantopoulos
Introduction
Sexual dysfunction (SD) is common in psychotic illness including schizophrenia, occurring in 30-82% of patients. It negatively impacts wellbeing and antipsychotic compliance, resulting in higher risk of relapse and hospitalisation. Due to over-reliance on spontaneous reports from patients, SD is typically under-identified which prevents investigation and treatment.
Objectives
To establish whether SD is under-identified in patients with psychosis in a general adult community mental health team; to elicit whether the Arizona Sexual Experience Scale (ASEX) improves identification; to investigate and manage identified cases of SD; to make recommendations about identification and monitoring of SD in this patient population.
Methods
A 12-month retrospective audit of patients with psychosis prescribed a long-acting injectable (LAI) antipsychotic (n=36) to identify sexual symptoms was completed. The ASEX was subsequently issued to screen for SD.
Results
Audit: 3/36 (8%) patients had documented sexual symptoms. Of the 18/36 patients that completed the ASEX: 10 (56%) exhibited SD. 4 consented to further investigation. 5 patients experienced significant difficulties with the language used in the ASEX. At the end of the project we revised the ASEX with simpler, colloquial language.
Conclusions
Implementation of the ASEX results in clear improvements in identification and monitoring of SD. Maudsley Practice Guidelines can inform investigation and management of SD. We suggest a review of NICE guidance to incorporate the above into clinical practice. Further work is needed to establish whether the revised ASEX can be developed and validated.
Disclosure of Interest
None Declared
Heterogeneous Entity Representation for Medicinal Synergy Prediction
Jiawei Wu, Jun Wen, Mingyuan Yan
et al.
Medicinal synergy prediction is a powerful tool in drug discovery and development that harnesses the principles of combination therapy to enhance therapeutic outcomes by improving efficacy, reducing toxicity, and preventing drug resistance. While a myriad of computational methods has emerged for predicting synergistic drug combinations, a large portion of them may overlook the intricate, yet critical relationships between various entities in drug interaction networks, such as drugs, cell lines, and diseases. These relationships are complex and multidimensional, requiring sophisticated modeling to capture nuanced interplay that can significantly influence therapeutic efficacy. We introduce a salient deep hypergraph learning method, namely, Heterogeneous Entity Representation for MEdicinal Synergy prediction (HERMES), to predict anti-cancer drug synergy. HERMES integrates heterogeneous data sources, encompassing drug, cell line, and disease information, to provide a comprehensive understanding of the interactions involved. By leveraging advanced hypergraph neural networks with gated residual mechanisms, HERMES can effectively learn complex relationships/interactions within the data. Our results show HERMES demonstrates state-of-the-art performance, particularly in forecasting new drug combinations, significantly surpassing previous methods. This advancement underscores the potential of HERMES to facilitate more effective and precise drug combination predictions, thereby enhancing the development of novel therapeutic strategies.
Insect chaperones Hsp70 and Hsp90 cooperatively enhance toxicity of Bacillus thuringiensis Cry1A toxins and counteract insect resistance
Blanca Ines García-Gomez, Tamara Alejandrina Sánchez, Sayra Natalia Cano
et al.
Bacillus thuringiensis (Bt) produces different insecticidal proteins effective for pest control. Among them, Cry insecticidal proteins have been used in transgenic plants for the control of insect pests. However, evolution of resistance by insects endangers this technology. Previous work showed that the lepidopteran insect Plutella xylostella PxHsp90 chaperone enhanced the toxicity of Bt Cry1A protoxins by protecting them from degradation by the larval gut proteases and by enhancing binding of the protoxin to its receptors present in larval midgut cells. In this work, we show that PxHsp70 chaperone also protects Cry1Ab protoxin from gut proteases degradation, enhancing Cry1Ab toxicity. We also show that both PxHsp70 and PxHsp90 chaperones act cooperatively, increasing toxicity and the binding of Cry1Ab439D mutant, affected in binding to midgut receptors, to cadherin receptor. Also, insect chaperones recovered toxicity of Cry1Ac protein to a Cry1Ac-highly resistant P. xylostella population, NO-QAGE, that has a disruptive mutation in an ABCC2 transporter linked to Cry1Ac resistance. These data show that Bt hijacked an important cellular function for enhancing its infection capability, making use of insect cellular chaperones for enhancing Cry toxicity and for lowering the evolution of insect resistance to these toxins.
Immunologic diseases. Allergy
Frontier AI developers need an internal audit function
Jonas Schuett
This article argues that frontier artificial intelligence (AI) developers need an internal audit function. First, it describes the role of internal audit in corporate governance: internal audit evaluates the adequacy and effectiveness of a company's risk management, control, and governance processes. It is organizationally independent from senior management and reports directly to the board of directors, typically its audit committee. In the IIA's Three Lines Model, internal audit serves as the third line and is responsible for providing assurance to the board, while the Combined Assurance Framework highlights the need to coordinate the activities of internal and external assurance providers. Next, the article provides an overview of key governance challenges in frontier AI development: dangerous capabilities can arise unpredictably and undetected; it is difficult to prevent a deployed model from causing harm; frontier models can proliferate rapidly; it is inherently difficult to assess frontier AI risks; and frontier AI developers do not seem to follow best practices in risk governance. Finally, the article discusses how an internal audit function could address some of these challenges: internal audit could identify ineffective risk management practices; it could ensure that the board of directors has a more accurate understanding of the current level of risk and the adequacy of the developer's risk management practices; and it could serve as a contact point for whistleblowers. In light of rapid progress in AI research and development, frontier AI developers need to strengthen their risk governance. Instead of reinventing the wheel, they should follow existing best practices. While this might not be sufficient, they should not skip this obvious first step.
Baseline Characteristics, Risk Factors and Etiology of Heart Failure Among Patients Hospitalized at a Teaching Hospital in Somalia: Cross-Sectional Study
Farah Yusuf Mohamud M, Jeele MOO, Cetinkaya O
et al.
Mohamed Farah Yusuf Mohamud,1 Mohamed Osman Omar Jeele,1 Osman Cetinkaya,1 Senai Goitom Sereke,2 Felix Bongomin,3 Mohamed AM Ahmed4– 6 1Mogadishu Somali Turkish Training and Research Hospital, Mogadishu, Somalia; 2School of Medicine, College of Health Sciences, Makerere University, Kampala, Uganda; 3Department of Medical Microbiology and Immunology, Faculty of Medicine, Gulu University, Gulu, Uganda; 4Department of Paediatrics, Faculty of Medicine and Surgery, Mogadishu University, Mogadishu, Somalia; 5Department of Paediatric Cardiology, Uganda Heart Institution, Kampala, Uganda; 6Basaksehir Cam ve Sakura Sehir Hospital, University of Health Sciences, Istanbul, TurkeyCorrespondence: Mohamed Farah Yusuf Mohamud, Mogadishu Somali Turkey Education and Research Hospital, Thirty Street, Alikamin, Wartanabada District, Mogadishu, Somalia, Tel +252615591689, Email m.qadar59@gmail.comIntroduction: Heart failure (HF) is a heterogeneous syndrome and growing global epidemic estimated to affect over 26-million people worldwide. The aim of this study is to investigate baseline characteristics, risk factors, and etiology of HF among patients admitted to a tertiary hospital in Somalia.Methods: Between May and October 2021, data on epidemiological characteristics, risk factors, and etiology of HF among patients admitted to an emergency unit of a teaching hospital in Mogadishu, Somalia were retrospectively collected and analyzed.Results: A total of 155 patients were disgnosed with HF, their mean age was 65.9 ± 14 years, 46.5% (n = 72) were aged 65 years or older, and 58.7% (n=91) were female. The prevalence of HF was 3.4% (n = 155); 47.7% (n = 74) had HF with preserved ejection fraction (HFpEF), 34.9% HF with reduced ejection fraction (HFrEF), and 17.4% HF with mildly reduced ejection fraction (HFmrEF). More females than males had HFrEF and HFmrEF (77.8% vs 59.3%, p < 0.01). In contrast, HFpEF was more frequent in males (55.4% vs 44.6%, p < 0.01). Regarding cardiovascular disease risk factors, patients with HFpEF had advanced age (≥ 65), were male, and had co-morbid hypertensive heart disease (HHD) and thyroid disease. On the other hand, patients with HFrEF were more in older age (50– 64 years), were women, and frequently had ischemic heart disease and diabetes mellitus compared to patients with HFpEF and HFmrEF. Among participants with HFpEF, HHD (58.1%) was the most common etiologies of HF, whereas in HFrEF, ischemic heart disease (38.9%) was prominent.Conclusion: HF in Somalia, different risk factors and etiologies were found in three groups of HF patients. Hypertension plays a predominant role both in its risk factors and the underlying cause of HF. We recommend implementation of specialized cardiac centers for the adult patients with cardiovascular diseases and promotion of the awareness of cardiovascular risk factors.Keywords: heart failure, ejection fraction, hypertension, diabetes, emergency unit, Somalia
Diseases of the circulatory (Cardiovascular) system
Development of a remote learning educational model for international Emergency Medicine trainees in the era of COVID-19
Joseph D. Ciano, John Acerra, Aimee Tang
Abstract Background The COVID-19 pandemic has pressured post-graduate medical education programs to shift from traditional in-person teaching to remote teaching and learning. Remote learning in medical education has been described in the literature mostly in the context of local in-country teaching. International remote medical education poses unique challenges for educators, especially in low-middle income countries (LMICs) who need continued Emergency Medicine (EM) specialty development. Our objective is to describe the development and implementation of our remote educational curriculum for EM trainees in West Bengal, India, and to assess trainee satisfaction with our remote learning curriculum. Methods Our curriculum was developed by adapting remote learning techniques used in Western post-graduate medical education, conducting literature searches on remote learning modalities, and through collaboration with local faculty in India. We assessed resident satisfaction in our curriculum with feedback surveys and group discussions. Results The remote educational curriculum had overall high trainee satisfaction ratings for weekly livestream video lectures and throughout our monthly educational modules (median ratings 9-10 out of a 10-point Likert scale). Qualitative feedback regarding specific lecture topics and educational modules were also received. Conclusions International remote education in LMICs poses a unique set of challenges to medical educators. Residents in our study reported high satisfaction with the curriculum, but there is a lack of clarity regarding how a remote curriculum may impact academic and clinical performance. Future studies are needed to further evaluate the efficacy and academic and clinical implications of remote medical education in LMICs.
Medical emergencies. Critical care. Intensive care. First aid
Learning to Discover Medicines
Tri Minh Nguyen, Thin Nguyen, Truyen Tran
Discovering new medicines is the hallmark of human endeavor to live a better and longer life. Yet the pace of discovery has slowed down as we need to venture into more wildly unexplored biomedical space to find one that matches today's high standard. Modern AI-enabled by powerful computing, large biomedical databases, and breakthroughs in deep learning-offers a new hope to break this loop as AI is rapidly maturing, ready to make a huge impact in the area. In this paper we review recent advances in AI methodologies that aim to crack this challenge. We organize the vast and rapidly growing literature of AI for drug discovery into three relatively stable sub-areas: (a) representation learning over molecular sequences and geometric graphs; (b) data-driven reasoning where we predict molecular properties and their binding, optimize existing compounds, generate de novo molecules, and plan the synthesis of target molecules; and (c) knowledge-based reasoning where we discuss the construction and reasoning over biomedical knowledge graphs. We will also identify open challenges and chart possible research directions for the years to come.
On the Boundedness solutions of the difference equation $x_{n+1}=a x^α_{n}+bx^α_{n-1},0<α\leq2$ and its application in medicine
Zeraoulia Rafik, Alvaro humberto Salas, Lorenzo Martinez
Recently, mathematicians have been interested in studying the theory of discrete dynamical system, specifically difference equation, such that considerable works about discussing the behavior properties of its solutions (boundedness and unboundedness) are discussed and published in many areas of mathematics which involves several interesting results and applications in applied mathematics and physics ,One of the most important discrete dynamics which is become of interest for researchers in the field is the rational dynamical system .In this paper we may discuss qualitative behavior and properties of the difference equation $x_{n+1}=ax^2_{n}+bx^2_{n-1}$ with $a$ and $b$ are two parameters and we shall show its application to medicine.
Total Lymphocyte Count, Neutrophil-Lymphocyte Ratio, and Platelet-Lymphocyte Ratio as Prognostic Factors in Advanced Non-Small Cell Lung Cancer with Chemoradiotherapy [Corrigenudm]
Song X, Chen D, Yuan M
et al.
Song X, Chen D, Yuan M, Wang H, Wang Z. Cancer Manag. 2018;10:6677– 6683On page 6677, Abstract, Results subheading, the median baseline PLR should be 136.1.On page 6680, Results section, 2nd paragraph, the median baseline PLR should be 136.1.On page 6680, the red curve should be PLR ≥ 136.1 and the blue cure should be PLR < 136.1. The COX analysis was not correct in the previous publication and it has been revised and shown below in the new Tables 1 and table 2.The correct Figure 3 is shown belowOn page 6680, Table 2, the COX analysis was not correct in the previous publication and it has been revised. The correct Table 2 is shown below.
On page 6681, Table 3, the COX analysis was not correct in the previous publication and it has been revised. The correct Table 3 is shown below.The authors have advised errors were caused by carelessness and mis-operation in statistics.
The authors apologize for this error and advise it does not affect the results of the paper.
Read the original article
Neoplasms. Tumors. Oncology. Including cancer and carcinogens
Erratum: Tetralogy of Fallot with coronary crossing the right ventricular outflow tract: A tale of a bridge and the artery
Using the internal language of toposes in algebraic geometry
Ingo Blechschmidt
Any scheme has its associated little and big Zariski toposes. These toposes support an internal mathematical language which closely resembles the usual formal language of mathematics, but is "local on the base scheme": For example, from the internal perspective, the structure sheaf looks like an ordinary local ring (instead of a sheaf of rings with local stalks) and vector bundles look like ordinary free modules (instead of sheaves of modules satisfying a local triviality condition). The translation of internal statements and proofs is facilitated by an easy mechanical procedure. We investigate how the internal language of the little Zariski topos can be exploited to give simpler definitions and more conceptual proofs of the basic notions and observations in algebraic geometry. To this end, we build a dictionary relating internal and external notions and demonstrate its utility by giving a simple proof of Grothendieck's generic freeness lemma in full generality. We also employ this framework to state a general transfer principle which relates modules with their induced quasicoherent sheaves, to study the phenomenon that some properties spread from points to open neighborhoods, and to compare general notions of spectra. We employ the big Zariski topos to set up the foundations of a synthetic account of scheme theory. This account is similar to the synthetic account of differential geometry, but has a distinct algebraic flavor. Central to the theory is the notion of synthetic quasicoherence, which has no analogue in synthetic differential geometry. We also discuss how various common subtoposes of the big Zariski topos can be described from the internal point of view and derive explicit descriptions of the geometric theories which are classified by the fppf and by the surjective topology.
How important are fluctuations in the treatment of internal friction in polymers?
R. Kailasham, Rajarshi Chakrabarti, J. Ravi Prakash
The Rouse model with internal friction (RIF), a widely used theoretical framework to interpret the effects of internal friction on conformational transitions in biomolecules, is shown to be an approximate treatment that is based on preaveraging internal friction. By comparison with Brownian dynamics simulations of an exact coarse-grained model that incorporates fluctuations in internal friction, the accuracy of the preaveraged model predictions is examined both at and away from equilibrium. While the two models predict intrachain autocorrelations that approach each other for long enough chain segments, they differ in their predictions for shorter segments. Furthermore, the two models differ qualitatively in their predictions for the chain extension and viscosity in shear flow, which is taken to represent a prototypical out-of-equilibrium condition.