General Setting Research Articles

Personalized Pricing and Assortment Optimization Under Consumer Choice Models with Local Network Effects

We introduce a consumer choice model where each consumer’s utility is affected by their neighbors’ purchase probabilities in a network. We first characterize the choice probabilities and then consider the associated personalized assortment optimization problem. Although this problem is NP-hard, we show that for star networks, the optimal assortment to the central consumer cannot be strictly larger than that without network effects; and the optimal assortment to each peripheral consumer must be a revenue-ordered assortment. Then, we propose a novel idea in which the sellers are allowed to offer “randomized assortments” to each node in the network by viewing each node as a consumer group. We show that randomized assortments may further increase the revenue, and for general network setting, under certain conditions, the optimal assortment must be a combination of two adjacent revenue-ordered assortments. Finally, we study the associated optimal pricing problem and develop structural properties and efficient algorithms.

Fast convergence of the primal-dual dynamical system and corresponding algorithms for a nonsmooth bilinearly coupled saddle point problem

AbstractThis paper studies the convergence rate of a second-order dynamical system associated with a nonsmooth bilinearly coupled convex-concave saddle point problem, as well as the convergence rate of its corresponding discretizations. We derive the convergence rate of the primal-dual gap for the second-order dynamical system with asymptotically vanishing damping term. Based on an implicit discretization scheme, we propose a primal-dual algorithm and provide a non-ergodic convergence rate under a general setting for the inertial parameters when one objective function is continuously differentiable and convex and the other is a proper, convex and lower semicontinuous function. For this algorithm we derive a $$O\left( 1/k^2 \right) $$ O 1 / k 2 convergence rate under three classical rules proposed by Nesterov, Chambolle-Dossal and Attouch-Cabot without assuming strong convexity, which is compatible with the results of the continuous-time dynamic system. For the case when both objective functions are continuously differentiable and convex, we further present a primal-dual algorithm based on an explicit discretization. We provide a corresponding non-ergodic convergence rate for this algorithm and show that the sequence of iterates generated weakly converges to a primal-dual optimal solution. Finally, we present numerical experiments that indicate the superior numerical performance of both algorithms.

Dirichlet problem for semilinear partial integro-differential equations: the method of orthogonal projection

AbstractWe study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the classical method of orthogonal projection. We treat in a unified form equations with operators belonging to the broad class of integro-differential operators associated with symmetric regular Dirichlet forms.

Pairs in discrete lattice orbits with applications to Veech surfaces (with an appendix by Jon Chaika)

Let \Lambda_{1} , \Lambda_{2} be two discrete orbits under the linear action of a lattice \Gamma<\mathrm{SL}_{2}(\mathbf{R}) on the Euclidean plane. We prove a Siegel–Veech-type integral formula for the averages \sum_{{\bf x}\in\Lambda_1}\sum_{{\bf y}\in\Lambda_2}f({\bf x},{\bf y}), from which we derive new results for the set S_{M} of holonomy vectors of saddle connections of a Veech surface M . This includes an effective count for generic Borel sets with respect to linear transformations, and upper bounds on the number of pairs in S_{M} with bounded determinant and on the number of pairs in S_{M} with bounded distance. This last estimate is used in the appendix to prove that for almost every (\theta,\psi)\in S^{1}\times S^{1} the translation flows F_{\theta}^{t} and F_{\psi}^{t} on any Veech surface M are disjoint.

Advances in methods and concepts provide new insight into antibiotic fluxes across the bacterial membrane.

The sophisticated envelope of Gram-negative bacteria modulates the uptake of small molecules in a side-chain-sensitive manner. Despite intensive theoretical and experimental investigations, a general set of pathways underpinning antibiotic uptake has not been identified. This manuscript discusses the passive influx versus active efflux of antibiotics, considering the responsible membrane proteins and the transported molecules. Recent methods have analyzed drug transport across the bacterial membrane in order to understand their activity. The combination of in vitro, in cellulo and in silico methods shed light on the key, mainly electrostatic, interactions between the molecule surface, porins and transporters during permeation. A key factor is the relationship between the dose of an active compound near its target and its antibacterial activity during the critical early window. Today, methodology breakthroughs provide fruitful tools to precisely dissect drug transport, identify key steps in drug resistance associated with membrane impermeability and efflux, and highlight key parameters to generate more effective drugs.

HPB SO53 - Implementation of High Volume-Low Complexity 'GIRFT' lists for laparoscopic cholecystectomy

Abstract Background Waiting times for elective surgery have risen steadily since 2010, with particularly sharp increases after the Covid pandemic. There have been several initiatives to improve theatre productivity and increase operative numbers and these are broadly encompassed within GIRFT standards and the development of the concept of a High Volume-Low Complexity list. Current GIRFT standards recommend six laparoscopic cholecystectomies on an all-day operating list. This study aimed to describe the development and implementation of these lists within out district general hospital setting and outline the key barriers and solutions for other units to learn from. Method All patients on the waiting list for laparoscopic cholecystectomy were assessed and screened by a panel of consultant surgeons to assess suitability for a HVLC list. Theatre staff, anaesthetists and surgeons were widely consulted within local focus groups and a novel method of remuneration for additional work was developed: a 'cost-per-case (CPC)' remuneration structure was introduced (in contrast to standard remuneration by session time) to ensure productivity and high quality surgery. Operations were carried out on weekend lists in a dedicated accredited Elective Surgical Hub and staff were able to finish the day when all operations were completed. Results CPC lists took place from August 2023 to May 2024. All lists had six laparoscopic cholecystectomies or eight hernia repairs (or a combination) in line with GIRFT standards. Overall 124 cholecystectomies were performed and 119 were completed on a day case basis. The remaining 5 patients had a single night stay. There were no returns-to-theatre or major morbidity. All lists had started by 830AM and the latest finish time throughout the study period was 1525PM. The utilisation of CPC lists contributed to waiting times falling dramatically from over 52 weeks to 28 weeks by the end of the study period. Conclusion By utilising a novel form of remuneration, based on volume of work completed rather than time, we were able to maximise productivity without compromising safety whilst developing employment conditions that encouraged colleagues to perform additional work. Key facets to successful implementation include appropriate screening of cases, allowing staff to leave when the work is completed (rather than have to wait till the end of the day) and standardising equipment and kit to reduce wastage and turnaround time between cases. These lessons can be implemented in any surgical unit to improve productivity and increase volume of cases performed.

The linearization of the boundary rigidity problem for MP-systems and generic local boundary rigidity

Abstract We consider an MP -system, that is, a compact Riemannian manifold with boundary, endowed with a magnetic field and a potential. On simple MP -systems, we study the MP -ray transform in order to obtain new boundary rigidity results for MP -systems. We show that there is an explicit relation between the MP -ray transform and the magnetic one, which allows us to apply results from Dairbekov et al (2007 Adv. Math. 216 535–609) to our case. Regarding rigidity, we show that there exists a generic set G m of simple MP -systems, which is open and dense, such that any two MP -systems close to an element in it and having the same boundary action function, must be k-gauge equivalent.

Multidisciplinary Approaches in General Medical Practice: Enhancing Collaboration for Better Patient Care

Multidisciplinary approaches in general medical practice have become integral to providing comprehensive, patient-centered care, as the complexity of modern health issues often requires a diverse range of expertise. This review explores the role and benefits of multidisciplinary teams in enhancing patient outcomes, improving resource efficiency, and increasing patient satisfaction in general medical settings. By examining the contributions of various healthcare professionals—including primary care physicians, specialists, allied health professionals, and behavioral health specialists—this review emphasizes how collaborative efforts address complex health needs more effectively than traditional, siloed approaches. Key case studies illustrate successful multidisciplinary practices in managing chronic diseases and complex conditions, highlighting the advantages of coordinated care models. The review also addresses challenges, such as communication barriers, hierarchical dynamics, and logistical constraints, that can hinder effective collaboration. Furthermore, it discusses technological supports, such as electronic health records (EHR) and telemedicine, which facilitate real-time communication and care coordination. The article concludes with recommendations for expanding multidisciplinary teams in primary care, promoting educational initiatives for team-based care skills, and advocating for policy support to institutionalize multidisciplinary approaches in general medicine. These findings suggest that well-coordinated multidisciplinary teams can transform patient care, making it more holistic, efficient, and responsive to individual needs.

Patient Safety and Medical Error Prevention in General Practice: A Comprehensive Systematic Review

Patient safety and medical error prevention remain critical issues in general practice, where medical errors can lead to adverse patient outcomes and increased healthcare costs. This systematic review synthesizes recent evidence on prevalent types of medical errors, effective prevention strategies, and outcomes of patient safety interventions within general practice settings. Following a comprehensive search across multiple databases, 52 studies published from 2014 to 2024 were included. Findings highlight medication errors, diagnostic inaccuracies, and communication lapses as the most common types of errors. Effective prevention strategies include the adoption of electronic health records (EHR), structured team communication protocols, checklist systems, and staff training programs on safety practices. These interventions have shown significant reductions in error rates and improvements in patient outcomes, though implementation is often hindered by barriers such as limited resources, resistance to change, and lack of training. This review underscores the importance of a multifaceted approach that combines technological, organizational, and educational interventions to enhance patient safety in general practice. Future research should explore long-term impacts of these interventions and address context-specific challenges to foster a culture of safety in healthcare settings.

Sociological research methods with a differentiated approachin regional nursing

Background.In the professional audit of the quality of nursing care, sociological research methods are of particular importance in the context of the formation of skills and abilities, with the help of which a set of expert criteria is formed from the general set of practical activities. Taking into account that the selection of qualified elements requires information about the scientific approach, in proportion to the originality of the expert function, it is relevant to identify them more clearly in the examination, which allows correcting the process of training and retraining of personnel. Objective.Toevaluate the sociological research methods of regional nursing on the example of the Orenburg region. Materials and methods.The main criteria for evaluating the activities of medical workers using the Delphi method are presented. The examination performed by the method of sociological and expert survey of average medical workers (n=535), doctors (n=80), heads of medical institutions (n=10) and patients (n=500) allowed us to formulate formalized indicators for evaluating measures to create innovative training and retraining programs for nursing staff. Mathematical "sketches" of the programs are based on factorial/cluster/discriminant analyses. Results. Sociological research methods in regional nursing have sanctioned a set of parameters of the qualities of a specialist in his professional activity in the context of training and retraining of nursing staff. Conclusion. Mathematical prototypes of programmatic training of medical staff created on the basis of sociological research methods in regional nursing contribute to the algorithmization of improvements in the format of the content and quality of training in order to provide competent and competitive specialists for the industry.

On Optimality of Mallows Model Averaging

In the past decades, model averaging (MA) has attracted much attention as it has emerged as an alternative tool to the model selection (MS) statistical approach. Hansen introduced a Mallows model averaging (MMA) method with model weights selected by minimizing a Mallows’ C p criterion. The main theoretical justification for MMA is an asymptotic optimality (AOP), which states that the risk/loss of the resulting MA estimator is asymptotically equivalent to that of the best but infeasible averaged model. MMA’s AOP is proved in the literature by either constraining weights in a special discrete weight set or limiting the number of candidate models. In this work, it is first shown that under these restrictions, however, the optimal risk of MA becomes an unreachable target, and MMA may converge more slowly than MS. In this background, a foundational issue that has not been addressed is: When a suitably large set of candidate models is considered, and the model weights are not harmfully constrained, can the MMA estimator perform asymptotically as well as the optimal convex combination of the candidate models? We answer this question in both nested and non-nested settings. In the nested setting, we provide finite sample inequalities for the risk of MMA and show that without unnatural restrictions on the candidate models, MMA’s AOP holds in a general continuous weight set under certain mild conditions. In the non-nested setting, a sufficient condition and a negative result are established for the achievability of the optimal MA risk. Implications on minimax adaptivity are given as well. The results from simulations and real data analysis back up our theoretical findings. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Extreme value statistics for analysing simulated environmental extremes

AbstractWe present the methods employed by team ‘Uniofbathtopia’ as part of a competition organised for the 13th International Conference on Extreme Value Analysis (EVA2023), including our winning entry for the third sub-challenge. Our approaches unite ideas from extreme value theory, which provides a statistical framework for the estimation of probabilities/return levels associated with rare events, with techniques from unsupervised statistical learning, such as clustering and support identification. The methods are demonstrated on the data provided for the EVA (2023) Conference Data Challenge – environmental data sampled from the fantasy country of ‘Utopia’ – but the underlying assumptions and frameworks should apply in more general settings and applications.

Streamlining the Non-operative Management of Adhesive Small Bowel Obstruction: A Closed-Loop Audit Evaluating the Introduction of a Standardised Gastrografin Protocol in a District General Hospital.

Introduction Adhesive small bowel obstruction (ASBO) is a common cause of admissions to general surgery services. Water-soluble contrast (WSC), such as Gastrografin® (GGF), can be utilised in the conservative management of patients with ASBO, with predictive and possible therapeutic value. We audited the non-operative management of ASBO in the general surgery department of East and North Hertfordshire NHS Trust, a district general hospital. Following the introduction of a hospital-wide protocol standardising the use of GGF in patients with ASBO, a re-audit was conducted to assess its impact. Methods A retrospective audit of ASBO patients who received GGF was conducted in two cycles: before and after the implementation of the protocol. Data were collected between February and June 2022 for group 1 (pre-protocol) and between August and November 2023 for group 2 (post-protocol). Results Forty-eight patients were included in the analysis across both groups: 31 in group 1 (pre-protocol) and 17 in group 2 (post-protocol). The success rate of this non-operative trial with GGF increased from 77%(24/31) in group 1 to 88% (15/17) in group 2. The median duration of conservative management was two days in both groups. The median time from CT scan to GGF administration decreased from 24 hours in group 1 to 19 hours 22 minutes in group 2, and the interval between GGF administration and first abdominal radiograph decreased from 9 hours in group 1 to 6 hours 25 minutes in group 2. Conclusion Our closed-loop audit suggests that by streamlining the non-operative management pathway of adhesive small bowel obstruction, our standardised protocol is safe and possibly improves efficiency within a district general hospital setting.

A unified framework for the analysis of accuracy and stability of a class of approximate Gaussian filters for the Navier–Stokes equations

Abstract Bayesian state estimation of a dynamical system utilising a stream of noisy measurements is important in many geophysical and engineering applications. In these cases, nonlinearities, high (or infinite) dimensionality of the state space, and sparse observations pose key challenges for deriving efficient and accurate data assimilation (DA) techniques. A number of DA algorithms used commonly in practice, such as the Ensemble Kalman Filter (EnKF) or Ensemble Square Root Kalman Filter (EnSRKF), suffer from serious drawbacks such as catastrophic filter divergence and filter instability. The analysis of stability and accuracy of these DA schemes has thus far focused either on finite-dimensional dynamics, or on complete observations in case of infinite-dimensional dissipative systems. We develop a unified framework for the analysis of several well-known and empirically efficient DA techniques derived from various Gaussian approximations of the Bayesian filtering schemes for geophysical-type dissipative dynamics with quadratic nonlinearities. We establish rigorous results on (time-asymptotic) accuracy and stability of these algorithms with general covariance and observation operators. The accuracy and stability results for EnKF and EnSRKF for dissipative PDEs are, to the best of our knowledge, completely new in this general setting. It turns out that a hitherto unexploited cancellation property involving the ensemble covariance and observation operators and the concept of covariance localization in conjunction with covariance inflation play a pivotal role in the accuracy and stability for EnKF and EnSRKF. Our approach also elucidates the links, via determining functionals, between the approximate-Bayesian and control-theoretic approaches to DA. We consider the ‘model’ dynamics governed by the two-dimensional incompressible Navier–Stokes equations (NSEs) and observations given by noisy measurements of averaged volume elements or spectral/modal observations of the velocity field. In this setup, several continuous-time DA techniques, namely the so-called 3DVar, EnKF and EnSRKF reduce to a stochastically forced NSEs. For the first time, we derive conditions for accuracy and stability of EnKF and EnSRKF. The derived bounds are given for the limit supremum of the expected value of the L 2 norm and of the H 1 Sobolev norm of the difference between the approximating solution and the actual solution as the time tends to infinity. Moreover, our analysis reveals an interplay between the resolution of the observations (roughly, the ‘richness’ of the observation space) associated with the observation operator underlying the DA algorithms and covariance inflation and localization which are employed in practice for improved filter performance.

Optimal Algorithms for Online b-Matching with Variable Vertex Capacities

AbstractWe study the b-matching problem, which generalizes classical online matching introduced by Karp, Vazirani and Vazirani (STOC 1990). Consider a bipartite graph $$G=(S\dot{\cup }R,E)$$ G = ( S ∪ ˙ R , E ) . Every vertex $$s\in S$$ s ∈ S is a server with a capacity $$b_s$$ b s , indicating the number of possible matching partners. The vertices $$r\in R$$ r ∈ R are requests that arrive online and must be matched immediately to an eligible server. The goal is to maximize the cardinality of the constructed matching. In contrast to earlier work, we study the general setting where servers may have arbitrary, individual capacities. We prove that the most natural and simple online algorithms achieve optimal competitive ratios. As for deterministic algorithms, we give a greedy algorithm RelativeBalance and analyze it by extending the primal-dual framework of Devanur, Jain and Kleinberg (SODA 2013). In the area of randomized algorithms we study the celebrated Ranking algorithm by Karp, Vazirani and Vazirani. We prove that the original Ranking strategy, simply picking a random permutation of the servers, achieves an optimal competitiveness of $$1-1/e$$ 1 - 1 / e , independently of the server capacities. Hence it is not necessary to resort to a reduction, replacing every server s by $$b_s$$ b s vertices of unit capacity and to then run Ranking on this graph with $$\sum _{s\in S} b_s$$ ∑ s ∈ S b s vertices on the left-hand side. Additionally, we extend this result to the vertex-weighted b-matching problem. Technically, we formulate a new configuration LP for the b-matching problem and conduct a primal-dual analysis.

Variety of General Position Problems in Graphs

Let X be a vertex subset of a graph G. Then u,v∈V(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u, v\\in V(G)$$\\end{document} are X-positionable if V(P)∩X⊆{u,v}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(P)\\cap X \\subseteq \\{u,v\\}$$\\end{document} holds for any shortest u, v-path P. If each two vertices from X are X-positionable, then X is a general position set. The general position number of G is the cardinality of a largest general position set of G and has been already well investigated. In this paper a variety of general position problems is introduced based on which natural pairs of vertices are required to be X-positionable. This yields the total (resp. dual, outer) general position number. It is proved that the total general position sets coincide with sets of simplicial vertices, and that the outer general position sets coincide with sets of mutually maximally distant vertices. It is shown that a general position set is a dual general position set if and only if its complement is convex. Several sufficient conditions are presented that guarantee that a given graph has no dual general position set. The total general position number, the outer general position number, and the dual general position number of arbitrary Cartesian products are determined.

Some Fock spaces with depth two action

Abstract The subject of this article is operators represented on a Fock space which act only on the two leading components of the tensor. We unify the constructions from [Ans07, BL09, BL11, LS08] and extend a number of results from these articles to our more general setting. The results include the quadratic relation satisfied by the kernel of the free cumulant generating function, the resolvent form of the generating function for the Wick polynomials, and classification results for the case when the vacuum state on the operator algebra is tracial. We handle the generating functions in infinitely many variables by considering their matrix-valued versions.

The mean number of $2$-torsion elements in the class groups of cubic orders

We determine the mean number of 2-torsion elements in class groups of cubic orders, when such orders are enumerated by discriminant. Specifically, we prove that when isomorphism classes of totally real (resp., complex) cubic orders are enumerated by discriminant, the average 2 -torsion in the class group is 1 + \frac{1}{4}\times \frac{\zeta(2)}{\zeta(4)} (resp., 1 + \frac{1}{2}\times \frac{\zeta(2)}{\zeta(4)} ). In particular, we find that the average 2 -torsion in the class group increases when one ranges over all orders in cubic fields instead of restricting to the subfamily of rings of integers of cubic fields, where the average 2 -torsion in the class group was first determined in work of Bhargava to be \frac{5}{4} (resp., \frac{3}{2} ).By work of Bhargava–Varma, proving this result amounts to obtaining an asymptotic count of the number of “reducible” \operatorname{SL}_{3}(\mathbb{Z}) -orbits on the space \mathbb{Z}^{2} \otimes_{\mathbb{Z}}\operatorname{Sym}^{2} \mathbb{Z}^{3} of 3 \times 3 symmetric integer matrices having bounded invariants and satisfying local conditions. In this paper, we resolve the generalization of this orbit-counting problem where the dimension 3 is replaced by any fixed odd integer N \geq 3 . More precisely, we determine asymptotic formulas for the number of reducible \operatorname{SL}_{N}(\mathbb{Z}) -orbits on \mathbb{Z}^{2} \otimes_{\mathbb{Z}}\operatorname{Sym}^{2} \mathbb{Z}^{N} satisfying general infinite sets of congruence conditions.

Diagnosis, prevention and management of delirium: spot it, stop it, treat it

SUMMARY Delirium frequently occurs among hospital in-patients, with significant attributable healthcare costs. It is associated with long-term adverse outcomes, including an eightfold increased risk of subsequent dementia. The purpose of this article is to inform clinicians of the best practices for spotting, stopping and treating delirium and provide guidance on common challenging clinical dilemmas. For spotting delirium, suggested screening tools are the 4 ‘A's Test (in general medical settings) and the Confusion Assessment Method for the Intensive Care Unit (CAM-ICU). Prevention is best achieved with multicomponent interventions and targeted strategies focusing on: (a) avoiding iatrogenic causes; (b) brain optimisation by ensuring smooth bodily functioning; (c) maintaining social interactions and normality. Non-pharmacological approaches are the first line for treatment; they largely mirror prevention strategies, but the focus of empirical evidence is on prevention. Although sufficient evidence is lacking for most pharmacological approaches, an antipsychotic at low doses for short durations may be of utility for highly distressing or high-risk situations, particularly in hyperactive delirium, but only as a last resort.

Dental team barriers and enablers for the dental management of adults with severe obesity: a qualitative analysis

BackgroundBroad challenges regarding the dental management of people with severe obesity experienced by general dentists have been minimally explored. The perspectives of the dental team regarding these multifaceted issues are currently unknown and they potentially impede the delivery of optimal dental care to this population and contribute to poor oral and general health.AimsOur qualitative study aimed to identify and explore barriers and enablers in the dental management of adults with severe obesity among dental professionals and support staff in Australia.MethodsFocus groups and semi-structured interviews (n = 34 participants) were conducted with dental professionals (n = 23) and support staff (n = 11). Recordings were transcribed verbatim and synthesised using thematic, inductive analysis.ResultsMultiple barriers to adequate provision of dental care for people living with severe obesity in both general and specialist dental settings were identified. Key themes emerged related to the clinical challenges reported by participants in providing dental management for people living with severe obesity, appropriateness of existing bariatric dental service provision and safety of care. Enablers to access were identified, including increased availability of bariatric dental chairs, environmental modifications, education of both patients and the entire dental team and for guideline development.ConclusionThe current study explored multiple barriers to optimal dental management of people living with severe obesity in both general and specialist dental settings. Enablers should be used to inform future practice. The optimisation of existing bariatric dental service provision requires urgent review with solutions guided by systemic change. Study findings suggest a review of current health systems, economics, access barriers, policies and procedures and education and training beyond the individual level are needed. Future directions to improve the dental management of people living with severe obesity are proposed.