Optimal and typical L 2 discrepancy of 2-dimensional lattices.

We undertake a detailed study of the L 2 discrepancy of 2-dimensional Korobov lattices and their irrational analogues, either with or without symmetrization. We give a full characterization of such lattices with optimal L 2 discrepancy in terms of the continued fraction partial quotients, and compute the precise asymptotics whenever the continued fraction expansion is explicitly known, such as for quadratic irrationals or Euler's number e. In the metric theory, we find the asymptotics of the L 2 discrepancy for almost every irrational, and the limit distribution for randomly chosen rational and irrational lattices.

One-stop autologous breast reconstruction: A safe and effective cost-saving pathway.

INTRODUCTION: Patients undergoing autologous breast reconstruction usually require further operations as part of their reconstructive journey. This involves contralateral breast symmetrization and nipple-areola complex (NAC) reconstruction. Restrained access to elective operating space led us to implement a one-stop breast reconstruction pathway. METHODS: Patients undergoing contemporaneous contralateral breast symmetrization and immediate NAC reconstruction with free nipple grafts between July 2020 and June 2021 were identified. A retrospective review of our prospectively maintained database was conducted, to retrieve surgical notes, postoperative complications, and length of inpatient stay. A cost analysis was performed considering savings from contralateral symmetrization. RESULTS: A total of 50 eligible cases were identified, which had unilateral one-stop breast reconstructions. Complication rates and length of stay were not affected by this approach, with only one free flap being lost for this cohort. This approach resulted in £181,000 being saved for our service over a calendar year. DISCUSSION: A one-stop breast reconstruction pathway has proven to be safe and effective in our unit. During these uncertain times, it has streamlined the management of eligible patients, while releasing capacity for other elective operations. Patients avoid having to wait for secondary procedures, finishing their reconstructive pathway earlier. We plan to continue providing this service which has shown to be beneficial clinically and financially.

Optimal strategies for addressing developmental breast asymmetry and the significance of symmetrical treatment: A systematic review.

BACKGROUND: Approximately one quarter of women are affected by asymmetry as a result of abnormal breast development, which can lead to significant emotional distress. Despite this, there is currently no widely accepted approach for managing this prevalent condition. This systematic review aimed to review the available literature on the management of developmental breast asymmetry. METHODS: A comprehensive search in MEDLINE, EMBASE, and CENTRAL databases was conducted for primary clinical studies reporting on the management of developmental breast asymmetry from 1962 to November 2022. The primary outcome measures were long-term aesthetic outcomes and patient-reported outcomes. RESULTS: Eleven case series and 2 cohort studies were included, comprising a total of 1237 patients with a mean age of 26.5 years (range 14-65 years). Twelve studies (92%) addressed asymmetry through surgical means, using various augmentation and reduction procedures, whereas one study (8%) utilized external prostheses. Meta-analysis of the data was not deemed to be possible because of heterogeneity of data; a narrative synthesis of the literature was provided. CONCLUSIONS: There is no consensus on how to manage developmental breast asymmetry. Furthermore, there is a lack of consistency in the classification of patients with developmental breast asymmetry and in the reporting of outcomes, highlighting the need for a consensus. Further research outlining long-term aesthetic and patient-reported outcomes is needed to understand which procedures provide optimal outcomes. In addition, external breast prosthesis is a promising nonsurgical alternative, and further studies into its efficacy are needed.

Quantum Haecceity.

There is an extensive philosophical literature on the interrelated issues of identity, individuality and distinguishability in quantum systems. A key consideration is whether quantum systems are subject to a strong form of individuality termed 'haecceity' (from the Latin for 'this-ness'). I argue that the traditional, strong form of haecceity does not apply at the quantum level, but that in order to properly account for the need for symmetrization in quantum systems, a weaker kind of haecceity must be involved, which I call quantum haecceity. In the process, I also question some generally accepted tenets of the current debate, such as the idea that symmetrization of states for identical quanta must be postulated and reflects permutation invariance. Instead, I note that a perturbative Hamiltonian is required for exchange effects, which suggests that the need for symmetrization arises from specific physical conditions. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Entanglement and discernibility of identical particles.

This article follows an unorthodox approach to the individuation of quantum particles of the same type. According to this approach, individuation of the components of a composite system of identical particles is done not with the help of unphysical labels (indices) but physically meaningful projection operators. This unorthodox conception requires a modification of the standard notion of entanglement, in order to exclude states whose non-factorizability arises merely from the (anti)symmetrization of a product state. I will report several facts regarding the connections of the modified concept of entanglement with the issue of discernibility. I will also discuss recent experiments involving measurement-induced entanglement, and I will point out that they do not threaten the cogency of the new concept of entanglement. The statistical correlations observed in these experiments are explainable not by the entanglement of the initial state but by the creation of a new, genuinely entangled state by means of a pre-measurement selection. Finally, I will identify and discuss a genuine difference between non-entangled but non-factorizable states of identical particles and ordinary product states, which is that the former but not the latter admits an infinity of alternative and incompatible individuations by single-particle properties. This phenomenon can be accounted for using the concept of emergent particles proposed by Dennis Dieks. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Breast reconstruction using DIEP flap: The free flap alone be enough? Quality of life and satisfaction analysis after complementary surgeries.

INTRODUCTION: Breast reconstruction using Deep Inferior Epigastric Perforator (DIEP) flap involves complementary surgeries such as lipofilling, symmetrization, and nipple-areolar complex (NAC) reconstruction. Their role and impact have not been explored yet after the DIEP flap use. MATERIAL AND METHODS: A retrospective study was performed to evaluate the impact of complementary surgeries on the quality of life of 75 patients after DIEP flap breast reconstruction between 2012 and 2021, comparing the BREAST-Q© score of two groups, patients with DIEP flap only reconstruction and patients with DIEP flap and additional surgeries. Satisfaction for each surgery was assessed using a numeric visual scale on five dimensions (esthetic, self-image, confidence in society, pain, and intimate relationship). Complications and healthcare pathways were also recorded. RESULTS: Psychosocial well-being (Q1 BREAST-Q©), satisfaction with medical team (Q9) and with surgeon (Q11) was superior in group 2 (p = 0041, p = 0.001 and p = 0.001 respectively). NAC reconstruction improved BREAST-Q© (p = 0029) by regression analysis and was deemed indispensable by 64% of the patients. An important satisfaction is observed after each surgery (DIEP flap, symmetrization, lipofilling and NAC reconstruction). Complications were uncommon (0-4%) for lipofilling and NAC reconstruction and notable but harmless for symmetrization (wound dressings more than a month in 17%). CONCLUSION: Complementary surgeries, especially NAC reconstruction, improved BREAST-Q© score, and have a major impact on satisfaction with minor complications. These surgeries should always be proposed to the patients to assess a satisfactory breast reconstruction using DIEP flap.

Therapeutic Reduction Mammoplasty: Experience of a Single Institute.

INTRODUCTION: Breast cancer is the most common malignancy in women worldwide as reported by the World Health Organization. The concept of oncoplastic breast surgery appeared as an extension of breast-conserving surgery, applying breast reduction techniques with more acceptable aesthetic and functional outcomes. The purpose of the present study was to describe the breast cancer population of a single institute submitted to lumpectomy and bilateral immediate breast reduction or mastopexy and its complications. MATERIAL AND METHODS: This is a retrospective observational study including patients submitted to lumpectomy and immediate bilateral breast reduction or mastopexy. Patients and tumour characteristics, surgical technique, complications, follow-up period, and recurrence data were obtained and analyzed. RESULTS: A total of 49 patients were submitted to lumpectomy and bilateral breast therapeutic reduction/mastopexy, with a mean age of 56.47 ±8.58 years and a mean body mass index of 28.68kg/m2 ±3.94 kg/m² between January 2019 and December 2021. Invasive tumours of no specific type, associated or not, with carcinoma intraductal in situ were the most common histological type corresponding to almost 80% of the cases with T1 stage corresponding to more than half of the cases. Sixteen percent of the patients had early minor complications with wound dehiscence associated with wound delayed healing, corresponding to 75% of the cases. Body mass index had a statistical difference between groups (p=0,006, t-test). CONCLUSIONS: The low rates of minor and major complications show that immediate therapeutic breast reduction can be a suitable approach in selected cases.

Displacement Estimation Based on Optical and Inertial Sensor Fusion.

This article aims to develop a system capable of estimating the displacement of a moving object with the usage of a relatively cheap and easy to apply sensors. There is a growing need for such systems, not only for robots, but also, for instance, pedestrian navigation. In this paper, the theory for this idea, including data postprocessing algorithms for a MEMS accelerometer and an optical flow sensor (OFS), as well as the developed complementary filter applied for sensor fusion, are presented. In addition, a vital part of the accelerometer's algorithm, the zero velocity states detection, is implemented. It is based on analysis of the acceleration's signal and further application of acceleration symmetrization, greatly improving the obtained displacement. A test stand with a linear guide and motor enabling imposing a specified linear motion is built. The results of both sensors' testing suggest that the displacement estimated by each of them is highly correct. Fusion of the sensors' data gives even better outcomes, especially in cases with external disturbance of OFS. The comparative evaluation of estimated linear displacements, in each case related to encoder data, confirms the algorithms' operation correctness and proves the chosen sensors' usefulness in the development of a linear displacement measuring system.

Long-Term Dynamic Changes in Cosmetic Outcomes and Patient Satisfaction after Implant-Based Postmastectomy Breast Reconstruction and Contralateral Mastopexy with or without an Ultrapro Mesh Sling Used for the Inner Bra Technique. A Retrospective Correlational Study.

Immediate implant-based postmastectomy breast reconstruction (IPMBR) with contralateral symmetrization has mostly short-term limited evidence of cosmetic outcomes. Because 84% of early-stage breast cancer patients have overall survival of more than 10 years, reconstructed breast symmetry should provide long-lasting results and acceptable patient satisfaction. Ageing, changes in body weight, and biomechanical changes after IPMBR and symmetrization may contribute to symmetry worsening. This non-interventional single-centre retrospective correlational study presents the clinical and aesthetic results of synthetic ULTRAPRO® mesh inner bra sling.

The role of water in Earth's mantle.

Geophysical observations suggest that the transition zone is wet locally. Continental and oceanic sediment components together with the basaltic and peridotitic components might be transported and accumulated in the transition zone. Low-velocity anomalies at the upper mantle-transition zone boundary might be caused by the existence of dense hydrous magmas. Water can be carried farther into the lower mantle by the slabs. The anomalous Q and shear wave regions locating at the uppermost part of the lower mantle could be caused by the existence of fluid or wet magmas in this region because of the water-solubility contrast between the minerals in the transition zone and those in the lower mantle. δ-H solid solution AlO2H-MgSiO4H2 carries water into the lower mantle. Hydrogen-bond symmetrization exists in high-pressure hydrous phases and thus they are stable at the high pressures of the lower mantle. Thus, the δ-H solid solution in subducting slabs carries water farther into the bottom of the lower mantle. Pyrite FeO2H x is formed due to a reaction between the core and hydrated slabs. This phase could be a candidate for the anomalous regions at the core-mantle boundary.

A hierarchically trained generative network for robust facial symmetrization.

Face symmetrization has extensive applications in both medical and academic fields, such as facial disorder diagnosis. Human face possesses an important characteristic, which is as known as symmetry. However, in many scenarios, the perfect symmetry doesn't exist in human faces, which yields a large number of studies around this topic. For example, facial palsy evaluation, facial beauty evaluation based on facial symmetry analysis, and many among others. Currently, there are still very limited researches dedicated for automatic facial symmetrization. Most of the existing studies only utilized their own implantations for facial symmetrization to assist their interdisciplinary academic researches. Limitations thus can be noticed in their methods, such as the requirements for manual interventions. Furthermore, most existing methods utilize facial landmark detection algorithms for automatic facial symmetrization. Though accuracies of the landmark detection algorithms are promising, the uncontrolled conditions in the facial images can still negatively impact the performance of the symmetrical face production. To this end, this paper presents a joint-loss enhanced deep generative network model for automatic facial symmetrization, which is achieved by a full facial image analysis. The joint-loss consists of a pair of adversarial losses and an identity loss. The adversarial losses try to make the generated symmetrical face as realistic as possible, while the identity loss helps to constrain the output to have the same identity of the person in the original input as much as possible. Rather than an end-to-end learning strategy, the proposed model is constructed by a multi-stage training process, which avoids the demand for a large size of the symmetrical face as training data. Experiments are conducted with comparisons with several existing methods based on some of the most popular facial landmark detection algorithms. Competitive results of the proposed method are demonstrated.

Symmetry-guided nonrigid registration: The case for distortion correction in multidimensional photoemission spectroscopy.

Image symmetrization is an effective strategy to correct symmetry distortion in experimental data for which symmetry is essential in the subsequent analysis. In the process, a coordinate transform, the symmetrization transform, is required to undo the distortion. The transform may be determined by image registration (i.e. alignment) with symmetry constraints imposed in the registration target and in the iterative parameter tuning, which we call symmetry-guided registration. An example use case of image symmetrization is found in electronic band structure mapping by multidimensional photoemission spectroscopy, which employs a 3D time-of-flight detector to measure electrons sorted into the momentum (kx, ky) and energy (E) coordinates. In reality, imperfect instrument design, sample geometry and experimental settings cause distortion of the photoelectron trajectories and, therefore, the symmetry in the measured band structure, which hinders the full understanding and use of the volumetric band mapping datasets. We demonstrate that symmetry-guided registration can correct the symmetry distortion in the momentum-resolved photoemission patterns. Using proposed symmetry metrics, we show quantitatively that the iterative approach to symmetrization outperforms its non-iterative counterpart in the restored symmetry of the outcome while preserving the average shape of the photoemission pattern. Our approach is generalizable to distortion corrections in different types of symmetries and should also find applications in other experimental methods that produce images with similar features.

Enhanced Photovoltaic Performance and Thermal Stability of CH3NH3PbI3 Perovskite through Lattice Symmetrization.

The organic-inorganic lead halide perovskites are attractive materials for photovoltaic application. The most widely studied perovskites based on methyl ammonium organic cation are less likely to form an ideal high-symmetry configuration at room temperature, leading to the appearance of local lattice strain. Herein, this study reports a strategy for the construction of thermally stable cubic perovskites at room temperature through the incorporation of the larger organic cation dimethyl ammonium. Detailed characterization on the single crystals and thin films reveals the formation of cubic phase with the addition of a certain amount of dimethyl ammonium at room temperature. With the presence of dimethyl ammonium, the nonradiative recombination in perovskite is suppressed, showing a longer PL lifetime and hole diffusion length. The more efficient charge extraction leads to an improvement in the photocurrent density, and then the device efficiency from 17.1% to 18.6%, together with an enhanced thermal stability at 85 °C. The influence of incorporating a larger organic cation on the structural configuration, optical properties, charge extraction, as well as the photovoltaic performance is systematically investigated, which offers an alternative way to improve the intrinsic stability of hybrid perovskites.

Mirror-Image Equivalence and Interhemispheric Mirror-Image Reversal.

Mirror-image confusions are common, especially in children and in some cases of neurological impairment. They can be a special impediment in activities such as reading and writing directional scripts, where mirror-image patterns (such as b and d) must be distinguished. Treating mirror images as equivalent, though, can also be adaptive in the natural world, which carries no systematic left-right bias and where the same object or event can appear in opposite viewpoints. Mirror-image equivalence and confusion are natural consequences of a bilaterally symmetrical brain. In the course of learning, mirror-image equivalence may be established through a process of symmetrization, achieved through homotopic interhemispheric exchange in the formation of memory circuits. Such circuits would not distinguish between mirror images. Learning to discriminate mirror-image discriminations may depend either on existing brain asymmetries, or on extensive learning overriding the symmetrization process. The balance between mirror-image equivalence and mirror-image discrimination may nevertheless be precarious, with spontaneous confusions or reversals, such as mirror writing, sometimes appearing naturally or as a manifestation of conditions like dyslexia.

Comparison of objective and subjective evaluation of breast symmetrization results in patients with Poland syndrome.

INTRODUCTION: There are many methods of analyzing the appearance of the breasts, but most of them are based on the patient's subjective assessment or on the opinion of a specialist panel. Anthropometric measurements enable objective breast evaluation. The aim of the study was to compare the objective and subjective evaluation of aesthetic results of breast symmetrization in patients with Poland syndrome. MATERIAL AND METHODS: The analysis of the results of the treatment was performed in 7 patients treated surgically due to unilateral breast underdevelopment in Poland syndrome. In the postoperative assessment, the following features were considered: 1 - breast volume, symmetry of: 2 - nipple areola-complexes (NAC), 3 - inframammary folds (IMF), 4 - upper poles (UP). The subjective assessment performed by the patient included each of the listed features and the overall satisfaction with the results of symmetrization on the 10-point Likert scale. Then, objective metric breast analysis was performed. RESULTS: Overall assessment of postoperative breast asymmetry (mean 8.1) indicates a high level of patients' satisfaction with breasts symmetrization. An objective analysis showed that the average breasts' difference in volume was about 36 cc and the difference in NAC location was about 1.2 cm. CONCLUSION: 3D imaging is helpful in planning breast symmetrization procedures, especially in breast prostheses' selection. Combination of this method with clinical experience results in good postoperative effects.

[PRIMARY STUDY ON CONTRALATERAL BREAST SYMMETRIZATION MAMMAPLASTY IN BREAST RECONSTRUCTION].

OBJECTIVE: To explore the techniques and short-term effectivness of contralateral breast symmetrization mammaplasty in breast reconstruction. METHODS: Between February 2014 and December 2015, 11 patients received immediate or delayed breast reconstruction after nipple-sparing mastectomy (6 and 5 cases respectively) for contralateral breast symmetrization mammaplasty. The age ranged 36-55 years (mean, 45 years). The disease duration was from 7 days to 6 months (mean, 2.5 months) in 6 patients undergoing immediate breast reconstruction. According to tumor TNM staging, 2 cases were rated as TisN0M0, 3 cases as T1N0M0, and 1 case as T2N0M0. The duration was from 2 to 25 years (mean, 8 years) in 5 patients undergoing delayed breast reconstruction. The implant (7 cases) and latissimus dorsi (4 cases) were used for breast reconstruction; and breast augmentation (6 cases) and breast reduction (5 cases) were performed for contralateral breast symmetrization. RESULTS: One patient had local poor wound healing postoperatively and was cured; primary healing was obtained in the other patients, and no other postoperative complication of infection, implant exposure or capsular contracture was found. The patients were followed up 3 to 24 months (mean, 12 months). The reconstructive outcomes were excellent in 9 cases and good in 2 cases, with an excellent and good rate of 100%. There was no recurrence or metastasis. CONCLUSIONS: Simultaneous contralateral symmetrization with augmentation/reduction mammaplasty after breast reconstruction can obtain satisfactory symmetric outcomes.

Symmetrization in jellyfish: reorganization to regain function, and not lost parts.

We recently reported a previously unidentified strategy of self-repair in the moon jellyfish Aurelia aurita. Rather than regenerating lost parts, juvenile Aurelia reorganize remaining parts to regain essential body symmetry. This process that we called symmetrization is rapid and frequent, and is not driven by cell proliferation or cell death. Instead, the swimming machinery generates mechanical forces that drive symmetrization. We found evidence for symmetrization across three other species of jellyfish (Chrysaora pacifica, Mastigias sp., and Cotylorhiza tuberculata). We propose reorganization to regain function without recovery of initial morphology as a potentially broad class of self-repair strategy beyond radially symmetrical animals, and discuss the implications of this finding on the evolution of self-repair strategies in animals.

Effect of salt on the H-bond symmetrization in ice.

The richness of the phase diagram of water reduces drastically at very high pressures where only two molecular phases, proton-disordered ice VII and proton-ordered ice VIII, are known. Both phases transform to the centered hydrogen bond atomic phase ice X above about 60 GPa, i.e., at pressures experienced in the interior of large ice bodies in the universe, such as Saturn and Neptune, where nonmolecular ice is thought to be the most abundant phase of water. In this work, we investigate, by Raman spectroscopy up to megabar pressures and ab initio simulations, how the transformation of ice VII in ice X is affected by the presence of salt inclusions in the ice lattice. Considerable amounts of salt can be included in ice VII structure under pressure via rock-ice interaction at depth and processes occurring during planetary accretion. Our study reveals that the presence of salt hinders proton order and hydrogen bond symmetrization, and pushes ice VII to ice X transformation to higher and higher pressures as the concentration of salt is increased.

Impact of contra-lateral breast reshaping on mammographic surveillance in women undergoing breast reconstruction following mastectomy for breast cancer.

BACKGROUND: The ultimate goal of breast reconstruction is to achieve symmetry with the contra-lateral breast. Contra-lateral procedures with wide parenchymal rearrangements are suspected to impair mammographic surveillance. This study aims to evaluate the impact on mammographic detection of mastopexies and breast reductions for contralateral adjustment in breast reconstruction. PATIENTS AND METHODS: We retrospectively evaluated 105 women affected by uni-lateral breast cancer who underwent mastectomy and immediate two-stage reconstruction between 2002 and 2007. We considered three groups according to the contra-lateral reshaping technique: mastopexy or breast reduction with inferior dermoglandular flap (group 1); mastopexy or breast reduction without inferior dermoglandular flap (group 2); no contra-lateral reshaping (group 3). We assessed qualitative mammographic variations and breast density in the three groups. RESULTS: Statistically significant differences have been found when comparing reshaped groups with non reshaped groups regarding parenchymal distortions, skin thickening and stromal edema, but these differences did not affect cancer surveillance. The surveillance mammography diagnostic accuracy in contra-lateral cancer detection was not significantly different between the three groups (p = 0.56), such as the need for MRI for equivocal findings at mammographic contra-lateral breast (p = 0.77) and the need for core-biopsies to confirm mammographic suspect of contra-lateral breast cancer (p = 0.90). CONCLUSIONS: This study confirms previous reports regarding the safety of mastopexies and breast reductions when performed in the setting of contra-lateral breast reshaping after breast reconstruction. Mammographic accuracy, sensitivity and specificity are not affected by the glandular re-arrangement. These results provide a further validation of the safety of current reconstructive paradigms.

Split green fluorescent protein as a modular binding partner for protein crystallization.

A modular strategy for protein crystallization using split green fluorescent protein (GFP) as a crystallization partner is demonstrated. Insertion of a hairpin containing GFP ß-strands 10 and 11 into a surface loop of a target protein provides two chain crossings between the target and the reconstituted GFP compared with the single connection afforded by terminal GFP fusions. This strategy was tested by inserting this hairpin into a loop of another fluorescent protein, sfCherry. The crystal structure of the sfCherry-GFP(10-11) hairpin in complex with GFP(1-9) was determined at a resolution of 2.6 Å. Analysis of the complex shows that the reconstituted GFP is attached to the target protein (sfCherry) in a structurally ordered way. This work opens the way to rapidly creating crystallization variants by reconstituting a target protein bearing the GFP(10-11) hairpin with a variety of GFP(1-9) mutants engineered for favorable crystallization.